Adding upstream version 4:24.2.0.upstream/4%24.2.0

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

56 files changed, 28438 insertions, 0 deletions

diff --git a/basegfx/source/color/bcolormodifier.cxx b/basegfx/source/color/bcolormodifier.cxx
new file mode 100644
index 0000000000..75c06f5cb8
--- /dev/null
+++ b/basegfx/source/color/bcolormodifier.cxx
@@ -0,0 +1,539 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <sal/config.h>
+#include <algorithm>
+#include <float.h>
+#include <basegfx/color/bcolormodifier.hxx>
+#include <comphelper/random.hxx>
+
+namespace basegfx
+{
+    BColorModifier::~BColorModifier()
+    {
+    }
+
+    BColorModifier_gray::~BColorModifier_gray()
+    {
+    }
+
+    bool BColorModifier_gray::operator==(const BColorModifier& rCompare) const
+    {
+        return dynamic_cast< const BColorModifier_gray* >(&rCompare) != nullptr;
+    }
+
+    ::basegfx::BColor BColorModifier_gray::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        const double fLuminance(aSourceColor.luminance());
+
+        return ::basegfx::BColor(fLuminance, fLuminance, fLuminance);
+    }
+
+    OUString BColorModifier_gray::getModifierName() const
+    {
+        return "gray";
+    }
+
+    BColorModifier_invert::~BColorModifier_invert()
+    {
+    }
+
+    bool BColorModifier_invert::operator==(const BColorModifier& rCompare) const
+    {
+        return dynamic_cast< const BColorModifier_invert* >(&rCompare) != nullptr;
+    }
+
+    ::basegfx::BColor BColorModifier_invert::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        return ::basegfx::BColor(1.0 - aSourceColor.getRed(), 1.0 - aSourceColor.getGreen(), 1.0 - aSourceColor.getBlue());
+    }
+
+    OUString BColorModifier_invert::getModifierName() const
+    {
+        return "invert";
+    }
+
+    BColorModifier_luminance_to_alpha::~BColorModifier_luminance_to_alpha()
+    {
+    }
+
+    bool BColorModifier_luminance_to_alpha::operator==(const BColorModifier& rCompare) const
+    {
+        return dynamic_cast< const BColorModifier_luminance_to_alpha* >(&rCompare) != nullptr;
+    }
+
+    ::basegfx::BColor BColorModifier_luminance_to_alpha::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        const double fAlpha(1.0 - ((aSourceColor.getRed() * 0.2125) + (aSourceColor.getGreen() * 0.7154) + (aSourceColor.getBlue() * 0.0721)));
+
+        return ::basegfx::BColor(fAlpha, fAlpha, fAlpha);
+    }
+
+    OUString BColorModifier_luminance_to_alpha::getModifierName() const
+    {
+        return "luminance_to_alpha";
+    }
+
+    BColorModifier_replace::~BColorModifier_replace()
+    {
+    }
+
+    bool BColorModifier_replace::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_replace* pCompare = dynamic_cast< const BColorModifier_replace* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return getBColor() == pCompare->getBColor();
+    }
+
+    ::basegfx::BColor BColorModifier_replace::getModifiedColor(const ::basegfx::BColor& /*aSourceColor*/) const
+    {
+        return maBColor;
+    }
+
+    OUString BColorModifier_replace::getModifierName() const
+    {
+        return "replace";
+    }
+
+    BColorModifier_interpolate::~BColorModifier_interpolate()
+    {
+    }
+
+    bool BColorModifier_interpolate::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_interpolate* pCompare = dynamic_cast< const BColorModifier_interpolate* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return maBColor == pCompare->maBColor && mfValue == pCompare->mfValue;
+    }
+
+    ::basegfx::BColor BColorModifier_interpolate::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        return interpolate(maBColor, aSourceColor, mfValue);
+    }
+
+    OUString BColorModifier_interpolate::getModifierName() const
+    {
+        return "interpolate";
+    }
+
+    BColorModifier_matrix::~BColorModifier_matrix()
+    {
+    }
+
+    bool BColorModifier_matrix::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_matrix* pCompare = dynamic_cast< const BColorModifier_matrix* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return maVector == pCompare->maVector;
+    }
+
+    ::basegfx::BColor BColorModifier_matrix::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        if (maVector.size() != 20)
+            return aSourceColor;
+
+        const double aRed = maVector[0] * aSourceColor.getRed()
+            + maVector[1] * aSourceColor.getGreen()
+            + maVector[2] * aSourceColor.getBlue()
+            + maVector[3] * 1.0
+            + maVector[4];
+        const double aGreen = maVector[5] * aSourceColor.getRed()
+            + maVector[6] * aSourceColor.getGreen()
+            + maVector[7] * aSourceColor.getBlue()
+            + maVector[8] * 1.0
+            + maVector[9];
+        const double aBlue = maVector[10] * aSourceColor.getRed()
+            + maVector[11] * aSourceColor.getGreen()
+            + maVector[12] * aSourceColor.getBlue()
+            + maVector[13] * 1.0
+            + maVector[14];
+        /*TODO: add support for alpha
+        const double aAlpha = maVector[15] * aSourceColor.getRed()
+            + maVector[16] * aSourceColor.getGreen()
+            + maVector[17] * aSourceColor.getBlue()
+            + maVector[18] * 1.0
+            + maVector[19]);
+        */
+
+        return ::basegfx::BColor(
+                std::clamp(aRed, 0.0, 1.0),
+                std::clamp(aGreen, 0.0, 1.0),
+                std::clamp(aBlue, 0.0, 1.0));
+    }
+
+    OUString BColorModifier_matrix::getModifierName() const
+    {
+        return "matrix";
+    }
+
+    BColorModifier_saturate::BColorModifier_saturate(double fValue)
+    {
+        maSatMatrix.set(0, 0, 0.213 + 0.787 * fValue);
+        maSatMatrix.set(0, 1, 0.715 - 0.715 * fValue);
+        maSatMatrix.set(0, 2, 0.072 - 0.072 * fValue);
+        maSatMatrix.set(1, 0, 0.213 - 0.213 * fValue);
+        maSatMatrix.set(1, 1, 0.715 + 0.285 * fValue);
+        maSatMatrix.set(1, 2, 0.072 - 0.072 * fValue);
+        maSatMatrix.set(2, 0, 0.213 - 0.213 * fValue);
+        maSatMatrix.set(2, 1, 0.715 - 0.715 * fValue);
+        maSatMatrix.set(2, 2, 0.072 + 0.928 * fValue);
+    }
+
+    BColorModifier_saturate::~BColorModifier_saturate()
+    {
+    }
+
+    bool BColorModifier_saturate::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_saturate* pCompare = dynamic_cast< const BColorModifier_saturate* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return maSatMatrix == pCompare->maSatMatrix;
+    }
+
+    ::basegfx::BColor BColorModifier_saturate::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        basegfx::B3DHomMatrix aColorMatrix;
+        aColorMatrix.set(0, 0, aSourceColor.getRed());
+        aColorMatrix.set(1, 0, aSourceColor.getGreen());
+        aColorMatrix.set(2, 0, aSourceColor.getBlue());
+
+        aColorMatrix = maSatMatrix * aColorMatrix;
+        return ::basegfx::BColor(aColorMatrix.get(0, 0), aColorMatrix.get(1, 0), aColorMatrix.get(2, 0));
+    }
+
+    OUString BColorModifier_saturate::getModifierName() const
+    {
+        return "saturate";
+    }
+
+    BColorModifier_hueRotate::BColorModifier_hueRotate(double fRad)
+    {
+        const double fCos = cos(fRad);
+        const double fSin = sin(fRad);
+
+        maHueMatrix.set(0, 0, 0.213 + fCos * 0.787 - fSin * 0.213);
+        maHueMatrix.set(0, 1, 0.715 - fCos * 0.715 - fSin * 0.715);
+        maHueMatrix.set(0, 2, 0.072 - fCos * 0.072 + fSin * 0.928);
+        maHueMatrix.set(1, 0, 0.213 - fCos * 0.213 + fSin * 0.143);
+        maHueMatrix.set(1, 1, 0.715 + fCos * 0.285 + fSin * 0.140);
+        maHueMatrix.set(1, 2, 0.072 - fCos * 0.072 - fSin * 0.283);
+        maHueMatrix.set(2, 0, 0.213 - fCos * 0.213 - fSin * 0.787);
+        maHueMatrix.set(2, 1, 0.715 - fCos * 0.715 + fSin * 0.715);
+        maHueMatrix.set(2, 2, 0.072 + fCos * 0.928 + fSin * 0.072);
+    }
+
+    BColorModifier_hueRotate::~BColorModifier_hueRotate()
+    {
+    }
+
+    bool BColorModifier_hueRotate::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_hueRotate* pCompare = dynamic_cast< const BColorModifier_hueRotate* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return maHueMatrix == pCompare->maHueMatrix;
+    }
+
+    ::basegfx::BColor BColorModifier_hueRotate::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        basegfx::B3DHomMatrix aColorMatrix;
+        aColorMatrix.set(0, 0, aSourceColor.getRed());
+        aColorMatrix.set(1, 0, aSourceColor.getGreen());
+        aColorMatrix.set(2, 0, aSourceColor.getBlue());
+
+        aColorMatrix = maHueMatrix * aColorMatrix;
+        return ::basegfx::BColor(
+                std::clamp(aColorMatrix.get(0, 0), 0.0, 1.0),
+                std::clamp(aColorMatrix.get(1, 0), 0.0, 1.0),
+                std::clamp(aColorMatrix.get(2, 0), 0.0, 1.0));
+    }
+
+    OUString BColorModifier_hueRotate::getModifierName() const
+    {
+        return "hueRotate";
+    }
+
+    BColorModifier_black_and_white::~BColorModifier_black_and_white()
+    {
+    }
+
+    bool BColorModifier_black_and_white::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_black_and_white* pCompare = dynamic_cast< const BColorModifier_black_and_white* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return mfValue == pCompare->mfValue;
+    }
+
+    ::basegfx::BColor BColorModifier_black_and_white::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        const double fLuminance(aSourceColor.luminance());
+
+        if(fLuminance < mfValue)
+        {
+            return ::basegfx::BColor::getEmptyBColor();
+        }
+        else
+        {
+            return ::basegfx::BColor(1.0, 1.0, 1.0);
+        }
+    }
+
+    OUString BColorModifier_black_and_white::getModifierName() const
+    {
+        return "black_and_white";
+    }
+
+    BColorModifier_gamma::BColorModifier_gamma(double fValue)
+    :   mfValue(fValue),
+        mfInvValue(fValue),
+        mbUseIt(!basegfx::fTools::equal(fValue, 1.0) && basegfx::fTools::more(fValue, 0.0) && basegfx::fTools::lessOrEqual(fValue, 10.0))
+    {
+        if(mbUseIt)
+        {
+            mfInvValue = 1.0 / mfValue;
+        }
+    }
+
+    BColorModifier_gamma::~BColorModifier_gamma()
+    {
+    }
+
+    bool BColorModifier_gamma::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_gamma* pCompare = dynamic_cast< const BColorModifier_gamma* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        // getValue is sufficient, mfInvValue and mbUseIt are only helper values
+        return mfValue == pCompare->mfValue;
+    }
+
+    ::basegfx::BColor BColorModifier_gamma::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        if(mbUseIt)
+        {
+            ::basegfx::BColor aRetval(
+                pow(aSourceColor.getRed(), mfInvValue),
+                pow(aSourceColor.getGreen(), mfInvValue),
+                pow(aSourceColor.getBlue(), mfInvValue));
+
+            aRetval.clamp();
+            return aRetval;
+        }
+        else
+        {
+            return aSourceColor;
+        }
+    }
+
+    OUString BColorModifier_gamma::getModifierName() const
+    {
+        return "gamma";
+    }
+
+    BColorModifier_RGBLuminanceContrast::BColorModifier_RGBLuminanceContrast(double fRed, double fGreen, double fBlue, double fLuminance, double fContrast)
+    :   mfRed(std::clamp(fRed, -1.0, 1.0)),
+        mfGreen(std::clamp(fGreen, -1.0, 1.0)),
+        mfBlue(std::clamp(fBlue, -1.0, 1.0)),
+        mfLuminance(std::clamp(fLuminance, -1.0, 1.0)),
+        mfContrast(std::clamp(fContrast, -1.0, 1.0)),
+        mfContrastOff(1.0),
+        mfRedOff(0.0),
+        mfGreenOff(0.0),
+        mfBlueOff(0.0),
+        mbUseIt(false)
+    {
+        if(basegfx::fTools::equalZero(mfRed)
+            && basegfx::fTools::equalZero(mfGreen)
+            && basegfx::fTools::equalZero(mfBlue)
+            && basegfx::fTools::equalZero(mfLuminance)
+            && basegfx::fTools::equalZero(mfContrast))
+            return;
+
+        // calculate slope
+        if(mfContrast >= 0.0)
+        {
+            mfContrastOff = 128.0 / (128.0 - (mfContrast * 127.0));
+        }
+        else
+        {
+            mfContrastOff = ( 128.0 + (mfContrast * 127.0)) / 128.0;
+        }
+
+        // calculate unified contrast offset
+        const double fPreparedContrastOff((128.0 - mfContrastOff * 128.0) / 255.0);
+        const double fCombinedOffset(mfLuminance + fPreparedContrastOff);
+
+        // set full offsets
+        mfRedOff = mfRed + fCombinedOffset;
+        mfGreenOff = mfGreen + fCombinedOffset;
+        mfBlueOff = mfBlue + fCombinedOffset;
+
+        mbUseIt = true;
+    }
+
+    BColorModifier_RGBLuminanceContrast::~BColorModifier_RGBLuminanceContrast()
+    {
+    }
+
+    bool BColorModifier_RGBLuminanceContrast::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_RGBLuminanceContrast* pCompare = dynamic_cast< const BColorModifier_RGBLuminanceContrast* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        // no need to compare other values, these are just helpers
+        return mfRed == pCompare->mfRed
+            && mfGreen == pCompare->mfGreen
+            && mfBlue == pCompare->mfBlue
+            && mfLuminance == pCompare->mfLuminance
+            && mfContrast == pCompare->mfContrast;
+    }
+
+    ::basegfx::BColor BColorModifier_RGBLuminanceContrast::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        if(mbUseIt)
+        {
+            return basegfx::BColor(
+                std::clamp(aSourceColor.getRed() * mfContrastOff + mfRedOff, 0.0, 1.0),
+                std::clamp(aSourceColor.getGreen() * mfContrastOff + mfGreenOff, 0.0, 1.0),
+                std::clamp(aSourceColor.getBlue() * mfContrastOff + mfBlueOff, 0.0, 1.0));
+        }
+        else
+        {
+            return aSourceColor;
+        }
+    }
+
+    OUString BColorModifier_RGBLuminanceContrast::getModifierName() const
+    {
+        return "RGBLuminanceContrast";
+    }
+
+    BColorModifier_randomize::BColorModifier_randomize(double fRandomPart)
+    : mfRandomPart(fRandomPart)
+    {
+    }
+
+    BColorModifier_randomize::~BColorModifier_randomize()
+    {
+    }
+
+    // compare operator
+    bool BColorModifier_randomize::operator==(const BColorModifier& rCompare) const
+    {
+        const BColorModifier_randomize* pCompare = dynamic_cast< const BColorModifier_randomize* >(&rCompare);
+
+        if(!pCompare)
+        {
+            return false;
+        }
+
+        return mfRandomPart == pCompare->mfRandomPart;
+    }
+
+    // compute modified color
+    ::basegfx::BColor BColorModifier_randomize::getModifiedColor(const ::basegfx::BColor& aSourceColor) const
+    {
+        if(0.0 >= mfRandomPart)
+        {
+            // no randomizing, use orig color
+            return aSourceColor;
+        }
+
+        if(1.0 <= mfRandomPart)
+        {
+            // full randomized color
+            return basegfx::BColor(
+                    comphelper::rng::uniform_real_distribution(0.0, nextafter(1.0, DBL_MAX)),
+                    comphelper::rng::uniform_real_distribution(0.0, nextafter(1.0, DBL_MAX)),
+                    comphelper::rng::uniform_real_distribution(0.0, nextafter(1.0, DBL_MAX)));
+        }
+
+        // mixed color
+        const double fMulA(1.0 - mfRandomPart);
+        return basegfx::BColor(
+            aSourceColor.getRed() * fMulA +
+                comphelper::rng::uniform_real_distribution(0.0, nextafter(mfRandomPart, DBL_MAX)),
+            aSourceColor.getGreen() * fMulA +
+                comphelper::rng::uniform_real_distribution(0.0, nextafter(mfRandomPart, DBL_MAX)),
+            aSourceColor.getBlue() * fMulA +
+                comphelper::rng::uniform_real_distribution(0.0, nextafter(mfRandomPart, DBL_MAX)));
+    }
+
+    OUString BColorModifier_randomize::getModifierName() const
+    {
+        return "randomize";
+    }
+
+    ::basegfx::BColor BColorModifierStack::getModifiedColor(const ::basegfx::BColor& rSource) const
+    {
+        if(maBColorModifiers.empty())
+        {
+            return rSource;
+        }
+
+        ::basegfx::BColor aRetval(rSource);
+
+        for(sal_uInt32 a(maBColorModifiers.size()); a;)
+        {
+            a--;
+            aRetval = maBColorModifiers[a]->getModifiedColor(aRetval);
+        }
+
+        return aRetval;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/color/bcolortools.cxx b/basegfx/source/color/bcolortools.cxx
new file mode 100644
index 0000000000..160b483289
--- /dev/null
+++ b/basegfx/source/color/bcolortools.cxx
@@ -0,0 +1,195 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/color/bcolor.hxx>
+#include <basegfx/color/bcolortools.hxx>
+#include <rtl/math.hxx>
+
+namespace basegfx::utils
+{
+    BColor rgb2hsl(const BColor& rRGBColor)
+    {
+        const double r=rRGBColor.getRed(), g=rRGBColor.getGreen(), b=rRGBColor.getBlue();
+        const double minVal = std::min( std::min( r, g ), b );
+        const double maxVal = std::max( std::max( r, g ), b );
+        const double d = maxVal - minVal;
+
+        double h=0, s=0, l=0;
+
+        l = (maxVal + minVal) / 2.0;
+
+        if( ::basegfx::fTools::equalZero(d) )
+        {
+            s = h = 0; // hue undefined (achromatic case)
+        }
+        else
+        {
+            s = l > 0.5 ? d/(2.0-maxVal-minVal) :
+                d/(maxVal + minVal);
+
+            if( rtl::math::approxEqual(r, maxVal) )
+                h = (g - b)/d;
+            else if( rtl::math::approxEqual(g, maxVal) )
+                h = 2.0 + (b - r)/d;
+            else
+                h = 4.0 + (r - g)/d;
+
+            h *= 60.0;
+
+            if( h < 0.0 )
+                h += 360.0;
+        }
+
+        return BColor(h,s,l);
+    }
+
+    static double hsl2rgbHelper( double nValue1, double nValue2, double nHue )
+    {
+        // clamp hue to [0,360]
+        nHue = fmod( nHue, 360.0 );
+
+        // cope with wrap-arounds
+        if( nHue < 0.0 )
+            nHue += 360.0;
+
+        if( nHue < 60.0 )
+            return nValue1 + (nValue2 - nValue1)*nHue/60.0;
+        else if( nHue < 180.0 )
+            return nValue2;
+        else if( nHue < 240.0 )
+            return nValue1 + (nValue2 - nValue1)*(240.0 - nHue)/60.0;
+        else
+            return nValue1;
+    }
+
+    BColor hsl2rgb(const BColor& rHSLColor)
+    {
+        const double h=rHSLColor.getRed(), s=rHSLColor.getGreen(), l=rHSLColor.getBlue();
+
+        if( fTools::equalZero(s) )
+            return BColor(l, l, l ); // achromatic case
+
+        const double nVal1( l <= 0.5 ? l*(1.0 + s) : l + s - l*s );
+        const double nVal2( 2.0*l - nVal1 );
+
+        return BColor(
+            hsl2rgbHelper(nVal2,
+                          nVal1,
+                          h + 120.0),
+            hsl2rgbHelper(nVal2,
+                          nVal1,
+                          h),
+            hsl2rgbHelper(nVal2,
+                          nVal1,
+                          h - 120.0) );
+    }
+
+    BColor rgb2hsv(const BColor& rRGBColor)
+    {
+        const double r=rRGBColor.getRed(), g=rRGBColor.getGreen(), b=rRGBColor.getBlue();
+        const double maxVal = std::max(std::max(r,g),b);
+        const double minVal = std::min(std::min(r,g),b);
+        const double delta = maxVal-minVal;
+
+        double h=0, s=0, v=0;
+
+        v = maxVal;
+        if( fTools::equalZero(v) )
+            s = 0;
+        else
+            s = delta / v;
+
+        if( !fTools::equalZero(s) )
+        {
+            if( rtl::math::approxEqual(maxVal, r) )
+            {
+                h = (g - b) / delta;
+            }
+            else if( rtl::math::approxEqual(maxVal, g) )
+            {
+                h = 2.0 + (b - r) / delta;
+            }
+            else
+            {
+                h = 4.0 + (r - g) / delta;
+            }
+
+            h *= 60.0;
+
+            if( h < 0 )
+                h += 360;
+        }
+
+        return BColor(h,s,v);
+    }
+
+    BColor hsv2rgb(const BColor& rHSVColor)
+    {
+        double h=rHSVColor.getRed();
+        const double s=rHSVColor.getGreen(), v=rHSVColor.getBlue();
+
+        if( fTools::equalZero(s) )
+        {
+            // achromatic case: no hue.
+            return BColor(v,v,v);
+        }
+        else
+        {
+            if( fTools::equal(h, 360.0) )
+                h = 0; // 360 degrees is equivalent to 0 degrees
+
+            h /= 60.0;
+            const sal_Int32 intval = static_cast< sal_Int32 >( h );
+            const double f = h - intval;
+            const double p = v*(1.0-s);
+            const double q = v*(1.0-(s*f));
+            const double t = v*(1.0-(s*(1.0-f)));
+
+            /* which hue area? */
+            switch( intval )
+            {
+                case 0:
+                    return BColor(v,t,p);
+
+                case 1:
+                    return BColor(q,v,p);
+
+                case 2:
+                    return BColor(p,v,t);
+
+                case 3:
+                    return BColor(p,q,v);
+
+                case 4:
+                    return BColor(t,p,v);
+
+                case 5:
+                    return BColor(v,p,q);
+
+                default:
+                    // hue overflow
+                    return BColor();
+            }
+        }
+    }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/curve/b2dbeziertools.cxx b/basegfx/source/curve/b2dbeziertools.cxx
new file mode 100644
index 0000000000..8fd4c4b84c
--- /dev/null
+++ b/basegfx/source/curve/b2dbeziertools.cxx
@@ -0,0 +1,117 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/curve/b2dbeziertools.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <algorithm>
+
+namespace basegfx
+{
+    B2DCubicBezierHelper::B2DCubicBezierHelper(const B2DCubicBezier& rBase, sal_uInt32 nDivisions)
+    :   mnEdgeCount(0)
+    {
+        const bool bIsBezier(rBase.isBezier());
+
+        if(bIsBezier)
+        {
+            // check nDivisions; at least one is needed, but also prevent too big values
+            if(nDivisions < 1)
+            {
+                nDivisions = 1;
+            }
+            else if(nDivisions > 1000)
+            {
+                nDivisions = 1000;
+            }
+
+            // set nEdgeCount
+            mnEdgeCount = nDivisions + 1;
+
+            // fill in maLengthArray
+            maLengthArray.clear();
+            maLengthArray.reserve(mnEdgeCount);
+            B2DPoint aCurrent(rBase.getStartPoint());
+            double fLength(0.0);
+
+            for(sal_uInt32 a(1);;)
+            {
+                const B2DPoint aNext(rBase.interpolatePoint(static_cast<double>(a) / static_cast<double>(mnEdgeCount)));
+                const B2DVector aEdge(aNext - aCurrent);
+
+                fLength += aEdge.getLength();
+                maLengthArray.push_back(fLength);
+
+                if(++a < mnEdgeCount)
+                {
+                    aCurrent = aNext;
+                }
+                else
+                {
+                    const B2DPoint& aLastNext(rBase.getEndPoint());
+                    const B2DVector aLastEdge(aLastNext - aNext);
+
+                    fLength += aLastEdge.getLength();
+                    maLengthArray.push_back(fLength);
+                    break;
+                }
+            }
+        }
+        else
+        {
+            maLengthArray.clear();
+            maLengthArray.push_back(rBase.getEdgeLength());
+            mnEdgeCount = 1;
+        }
+    }
+
+    double B2DCubicBezierHelper::distanceToRelative(double fDistance) const
+    {
+        if(fDistance <= 0.0)
+        {
+            return 0.0;
+        }
+
+        const double fLength(getLength());
+
+        if(fTools::moreOrEqual(fDistance, fLength))
+        {
+            return 1.0;
+        }
+
+        // fDistance is in ]0.0 .. fLength[
+
+        if(mnEdgeCount == 1)
+        {
+            // not a bezier, linear edge
+            return fDistance / fLength;
+        }
+
+        // it is a bezier
+        std::vector< double >::const_iterator aIter = std::lower_bound(maLengthArray.begin(), maLengthArray.end(), fDistance);
+        const sal_uInt32 nIndex(aIter - maLengthArray.begin());
+        const double fHighBound(maLengthArray[nIndex]);
+        const double fLowBound(nIndex ?  maLengthArray[nIndex - 1] : 0.0);
+        const double fLinearInterpolatedLength((fDistance - fLowBound) / (fHighBound - fLowBound));
+
+        return (static_cast< double >(nIndex) + fLinearInterpolatedLength) / static_cast< double >(mnEdgeCount);
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/curve/b2dcubicbezier.cxx b/basegfx/source/curve/b2dcubicbezier.cxx
new file mode 100644
index 0000000000..d33cd82b19
--- /dev/null
+++ b/basegfx/source/curve/b2dcubicbezier.cxx
@@ -0,0 +1,1055 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+#include <osl/diagnose.h>
+
+#include <limits>
+
+// #i37443#
+#define FACTOR_FOR_UNSHARPEN    (1.6)
+#ifdef DBG_UTIL
+const double fMultFactUnsharpen = FACTOR_FOR_UNSHARPEN;
+#endif
+
+namespace basegfx
+{
+    namespace
+    {
+        void ImpSubDivAngle(
+            const B2DPoint& rfPA,           // start point
+            const B2DPoint& rfEA,           // edge on A
+            const B2DPoint& rfEB,           // edge on B
+            const B2DPoint& rfPB,           // end point
+            B2DPolygon& rTarget,            // target polygon
+            double fAngleBound,             // angle bound in [0.0 .. 2PI]
+            bool bAllowUnsharpen,           // #i37443# allow the criteria to get unsharp in recursions
+            sal_uInt16 nMaxRecursionDepth)  // endless loop protection
+        {
+            if(nMaxRecursionDepth)
+            {
+                // do angle test
+                B2DVector aLeft(rfEA - rfPA);
+                B2DVector aRight(rfEB - rfPB);
+
+                // #i72104#
+                if(aLeft.equalZero())
+                {
+                    aLeft = rfEB - rfPA;
+                }
+
+                if(aRight.equalZero())
+                {
+                    aRight = rfEA - rfPB;
+                }
+
+                const double fCurrentAngle(aLeft.angle(aRight));
+
+                if(fabs(fCurrentAngle) > (M_PI - fAngleBound))
+                {
+                    // end recursion
+                    nMaxRecursionDepth = 0;
+                }
+                else
+                {
+                    if(bAllowUnsharpen)
+                    {
+                        // #i37443# unsharpen criteria
+#ifdef DBG_UTIL
+                        fAngleBound *= fMultFactUnsharpen;
+#else
+                        fAngleBound *= FACTOR_FOR_UNSHARPEN;
+#endif
+                    }
+                }
+            }
+
+            if(nMaxRecursionDepth)
+            {
+                // divide at 0.5
+                const B2DPoint aS1L(average(rfPA, rfEA));
+                const B2DPoint aS1C(average(rfEA, rfEB));
+                const B2DPoint aS1R(average(rfEB, rfPB));
+                const B2DPoint aS2L(average(aS1L, aS1C));
+                const B2DPoint aS2R(average(aS1C, aS1R));
+                const B2DPoint aS3C(average(aS2L, aS2R));
+
+                // left recursion
+                ImpSubDivAngle(rfPA, aS1L, aS2L, aS3C, rTarget, fAngleBound, bAllowUnsharpen, nMaxRecursionDepth - 1);
+
+                // right recursion
+                ImpSubDivAngle(aS3C, aS2R, aS1R, rfPB, rTarget, fAngleBound, bAllowUnsharpen, nMaxRecursionDepth - 1);
+            }
+            else
+            {
+                rTarget.append(rfPB);
+            }
+        }
+
+        void ImpSubDivAngleStart(
+            const B2DPoint& rfPA,           // start point
+            const B2DPoint& rfEA,           // edge on A
+            const B2DPoint& rfEB,           // edge on B
+            const B2DPoint& rfPB,           // end point
+            B2DPolygon& rTarget,            // target polygon
+            const double& rfAngleBound)     // angle bound in [0.0 .. 2PI]
+        {
+            sal_uInt16 nMaxRecursionDepth(8);
+            const B2DVector aLeft(rfEA - rfPA);
+            const B2DVector aRight(rfEB - rfPB);
+            bool bLeftEqualZero(aLeft.equalZero());
+            bool bRightEqualZero(aRight.equalZero());
+            bool bAllParallel(false);
+
+            if(bLeftEqualZero && bRightEqualZero)
+            {
+                nMaxRecursionDepth = 0;
+            }
+            else
+            {
+                const B2DVector aBase(rfPB - rfPA);
+                const bool bBaseEqualZero(aBase.equalZero()); // #i72104#
+
+                if(!bBaseEqualZero)
+                {
+                    const bool bLeftParallel(bLeftEqualZero || areParallel(aLeft, aBase));
+                    const bool bRightParallel(bRightEqualZero || areParallel(aRight, aBase));
+
+                    if(bLeftParallel && bRightParallel)
+                    {
+                        bAllParallel = true;
+
+                        if(!bLeftEqualZero)
+                        {
+                            double fFactor;
+
+                            if(fabs(aBase.getX()) > fabs(aBase.getY()))
+                            {
+                                fFactor = aLeft.getX() / aBase.getX();
+                            }
+                            else
+                            {
+                                fFactor = aLeft.getY() / aBase.getY();
+                            }
+
+                            if(fFactor >= 0.0 && fFactor <= 1.0)
+                            {
+                                bLeftEqualZero = true;
+                            }
+                        }
+
+                        if(!bRightEqualZero)
+                        {
+                            double fFactor;
+
+                            if(fabs(aBase.getX()) > fabs(aBase.getY()))
+                            {
+                                fFactor = aRight.getX() / -aBase.getX();
+                            }
+                            else
+                            {
+                                fFactor = aRight.getY() / -aBase.getY();
+                            }
+
+                            if(fFactor >= 0.0 && fFactor <= 1.0)
+                            {
+                                bRightEqualZero = true;
+                            }
+                        }
+
+                        if(bLeftEqualZero && bRightEqualZero)
+                        {
+                            nMaxRecursionDepth = 0;
+                        }
+                    }
+                }
+            }
+
+            if(nMaxRecursionDepth)
+            {
+                // divide at 0.5 ad test both edges for angle criteria
+                const B2DPoint aS1L(average(rfPA, rfEA));
+                const B2DPoint aS1C(average(rfEA, rfEB));
+                const B2DPoint aS1R(average(rfEB, rfPB));
+                const B2DPoint aS2L(average(aS1L, aS1C));
+                const B2DPoint aS2R(average(aS1C, aS1R));
+                const B2DPoint aS3C(average(aS2L, aS2R));
+
+                // test left
+                bool bAngleIsSmallerLeft(bAllParallel && bLeftEqualZero);
+                if(!bAngleIsSmallerLeft)
+                {
+                    const B2DVector aLeftLeft(bLeftEqualZero ? aS2L - aS1L : aS1L - rfPA); // #i72104#
+                    const B2DVector aRightLeft(aS2L - aS3C);
+                    const double fCurrentAngleLeft(aLeftLeft.angle(aRightLeft));
+                    bAngleIsSmallerLeft = (fabs(fCurrentAngleLeft) > (M_PI - rfAngleBound));
+                }
+
+                // test right
+                bool bAngleIsSmallerRight(bAllParallel && bRightEqualZero);
+                if(!bAngleIsSmallerRight)
+                {
+                    const B2DVector aLeftRight(aS2R - aS3C);
+                    const B2DVector aRightRight(bRightEqualZero ? aS2R - aS1R : aS1R - rfPB); // #i72104#
+                    const double fCurrentAngleRight(aLeftRight.angle(aRightRight));
+                    bAngleIsSmallerRight = (fabs(fCurrentAngleRight) > (M_PI - rfAngleBound));
+                }
+
+                if(bAngleIsSmallerLeft && bAngleIsSmallerRight)
+                {
+                    // no recursion necessary at all
+                    nMaxRecursionDepth = 0;
+                }
+                else
+                {
+                    // left
+                    if(bAngleIsSmallerLeft)
+                    {
+                        rTarget.append(aS3C);
+                    }
+                    else
+                    {
+                        ImpSubDivAngle(rfPA, aS1L, aS2L, aS3C, rTarget, rfAngleBound, true/*bAllowUnsharpen*/, nMaxRecursionDepth);
+                    }
+
+                    // right
+                    if(bAngleIsSmallerRight)
+                    {
+                        rTarget.append(rfPB);
+                    }
+                    else
+                    {
+                        ImpSubDivAngle(aS3C, aS2R, aS1R, rfPB, rTarget, rfAngleBound, true/*bAllowUnsharpen*/, nMaxRecursionDepth);
+                    }
+                }
+            }
+
+            if(!nMaxRecursionDepth)
+            {
+                rTarget.append(rfPB);
+            }
+        }
+
+        void ImpSubDivDistance(
+            const B2DPoint& rfPA,           // start point
+            const B2DPoint& rfEA,           // edge on A
+            const B2DPoint& rfEB,           // edge on B
+            const B2DPoint& rfPB,           // end point
+            B2DPolygon& rTarget,            // target polygon
+            double fDistanceBound2,         // quadratic distance criteria
+            double fLastDistanceError2,     // the last quadratic distance error
+            sal_uInt16 nMaxRecursionDepth)  // endless loop protection
+        {
+            if(nMaxRecursionDepth)
+            {
+                // decide if another recursion is needed. If not, set
+                // nMaxRecursionDepth to zero
+
+                // Perform bezier flatness test (lecture notes from R. Schaback,
+                // Mathematics of Computer-Aided Design, Uni Goettingen, 2000)
+
+                // ||P(t) - L(t)|| <= max     ||b_j - b_0 - j/n(b_n - b_0)||
+                //                    0<=j<=n
+
+                // What is calculated here is an upper bound to the distance from
+                // a line through b_0 and b_3 (rfPA and P4 in our notation) and the
+                // curve. We can drop 0 and n from the running indices, since the
+                // argument of max becomes zero for those cases.
+                const double fJ1x(rfEA.getX() - rfPA.getX() - 1.0/3.0*(rfPB.getX() - rfPA.getX()));
+                const double fJ1y(rfEA.getY() - rfPA.getY() - 1.0/3.0*(rfPB.getY() - rfPA.getY()));
+                const double fJ2x(rfEB.getX() - rfPA.getX() - 2.0/3.0*(rfPB.getX() - rfPA.getX()));
+                const double fJ2y(rfEB.getY() - rfPA.getY() - 2.0/3.0*(rfPB.getY() - rfPA.getY()));
+                const double fDistanceError2(std::max(fJ1x*fJ1x + fJ1y*fJ1y, fJ2x*fJ2x + fJ2y*fJ2y));
+
+                // stop if error measure does not improve anymore. This is a
+                // safety guard against floating point inaccuracies.
+                // stop if distance from line is guaranteed to be bounded by d
+                const bool bFurtherDivision(fLastDistanceError2 > fDistanceError2 && fDistanceError2 >= fDistanceBound2);
+
+                if(bFurtherDivision)
+                {
+                    // remember last error value
+                    fLastDistanceError2 = fDistanceError2;
+                }
+                else
+                {
+                    // stop recursion
+                    nMaxRecursionDepth = 0;
+                }
+            }
+
+            if(nMaxRecursionDepth)
+            {
+                // divide at 0.5
+                const B2DPoint aS1L(average(rfPA, rfEA));
+                const B2DPoint aS1C(average(rfEA, rfEB));
+                const B2DPoint aS1R(average(rfEB, rfPB));
+                const B2DPoint aS2L(average(aS1L, aS1C));
+                const B2DPoint aS2R(average(aS1C, aS1R));
+                const B2DPoint aS3C(average(aS2L, aS2R));
+
+                // left recursion
+                ImpSubDivDistance(rfPA, aS1L, aS2L, aS3C, rTarget, fDistanceBound2, fLastDistanceError2, nMaxRecursionDepth - 1);
+
+                // right recursion
+                ImpSubDivDistance(aS3C, aS2R, aS1R, rfPB, rTarget, fDistanceBound2, fLastDistanceError2, nMaxRecursionDepth - 1);
+            }
+            else
+            {
+                rTarget.append(rfPB);
+            }
+        }
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx
+{
+    B2DCubicBezier::B2DCubicBezier(const B2DCubicBezier&) = default;
+
+    B2DCubicBezier::B2DCubicBezier() = default;
+
+    B2DCubicBezier::B2DCubicBezier(const B2DPoint& rStart, const B2DPoint& rControlPointA, const B2DPoint& rControlPointB, const B2DPoint& rEnd)
+    :   maStartPoint(rStart),
+        maEndPoint(rEnd),
+        maControlPointA(rControlPointA),
+        maControlPointB(rControlPointB)
+    {
+    }
+
+    // assignment operator
+    B2DCubicBezier& B2DCubicBezier::operator=(const B2DCubicBezier&) = default;
+
+    // compare operators
+    bool B2DCubicBezier::operator==(const B2DCubicBezier& rBezier) const
+    {
+        return (
+            maStartPoint == rBezier.maStartPoint
+            && maEndPoint == rBezier.maEndPoint
+            && maControlPointA == rBezier.maControlPointA
+            && maControlPointB == rBezier.maControlPointB
+        );
+    }
+
+    bool B2DCubicBezier::operator!=(const B2DCubicBezier& rBezier) const
+    {
+        return (
+            maStartPoint != rBezier.maStartPoint
+            || maEndPoint != rBezier.maEndPoint
+            || maControlPointA != rBezier.maControlPointA
+            || maControlPointB != rBezier.maControlPointB
+        );
+    }
+
+    bool B2DCubicBezier::equal(const B2DCubicBezier& rBezier) const
+    {
+        return (
+            maStartPoint.equal(rBezier.maStartPoint)
+            && maEndPoint.equal(rBezier.maEndPoint)
+            && maControlPointA.equal(rBezier.maControlPointA)
+            && maControlPointB.equal(rBezier.maControlPointB)
+        );
+    }
+
+    // test if vectors are used
+    bool B2DCubicBezier::isBezier() const
+    {
+        return maControlPointA != maStartPoint || maControlPointB != maEndPoint;
+    }
+
+    void B2DCubicBezier::testAndSolveTrivialBezier()
+    {
+        if(maControlPointA == maStartPoint && maControlPointB == maEndPoint)
+            return;
+
+        const B2DVector aEdge(maEndPoint - maStartPoint);
+
+        // controls parallel to edge can be trivial. No edge -> not parallel -> control can
+        // still not be trivial (e.g. ballon loop)
+        if(aEdge.equalZero())
+            return;
+
+        // get control vectors
+        const B2DVector aVecA(maControlPointA - maStartPoint);
+        const B2DVector aVecB(maControlPointB - maEndPoint);
+
+        // check if trivial per se
+        bool bAIsTrivial(aVecA.equalZero());
+        bool bBIsTrivial(aVecB.equalZero());
+
+        // #i102241# prepare inverse edge length to normalize cross values;
+        // else the small compare value used in fTools::equalZero
+        // will be length dependent and this detection will work as less
+        // precise as longer the edge is. In principle, the length of the control
+        // vector would need to be used too, but to be trivial it is assumed to
+        // be of roughly equal length to the edge, so edge length can be used
+        // for both. Only needed when one of both is not trivial per se.
+        const double fInverseEdgeLength(bAIsTrivial && bBIsTrivial
+            ? 1.0
+            : 1.0 / aEdge.getLength());
+
+        // if A is not zero, check if it could be
+        if(!bAIsTrivial)
+        {
+            // #i102241# parallel to edge? Check aVecA, aEdge. Use cross() which does what
+            // we need here with the precision we need
+            const double fCross(aVecA.cross(aEdge) * fInverseEdgeLength);
+
+            if(fTools::equalZero(fCross))
+            {
+                // get scale to edge. Use bigger distance for numeric quality
+                const double fScale(fabs(aEdge.getX()) > fabs(aEdge.getY())
+                    ? aVecA.getX() / aEdge.getX()
+                    : aVecA.getY() / aEdge.getY());
+
+                // relative end point of vector in edge range?
+                if (fTools::betweenOrEqualEither(fScale, 0.0, 1.0))
+                {
+                    bAIsTrivial = true;
+                }
+            }
+        }
+
+        // if B is not zero, check if it could be, but only if A is already trivial;
+        // else solve to trivial will not be possible for whole edge
+        if(bAIsTrivial && !bBIsTrivial)
+        {
+            // parallel to edge? Check aVecB, aEdge
+            const double fCross(aVecB.cross(aEdge) * fInverseEdgeLength);
+
+            if(fTools::equalZero(fCross))
+            {
+                // get scale to edge. Use bigger distance for numeric quality
+                const double fScale(fabs(aEdge.getX()) > fabs(aEdge.getY())
+                    ? aVecB.getX() / aEdge.getX()
+                    : aVecB.getY() / aEdge.getY());
+
+                // end point of vector in edge range? Caution: controlB is directed AGAINST edge
+                if (fTools::betweenOrEqualEither(fScale, -1.0, 0.0))
+                {
+                    bBIsTrivial = true;
+                }
+            }
+        }
+
+        // if both are/can be reduced, do it.
+        // Not possible if only one is/can be reduced (!)
+        if(bAIsTrivial && bBIsTrivial)
+        {
+            maControlPointA = maStartPoint;
+            maControlPointB = maEndPoint;
+        }
+    }
+
+    namespace {
+        double impGetLength(const B2DCubicBezier& rEdge, double fDeviation, sal_uInt32 nRecursionWatch)
+        {
+            const double fEdgeLength(rEdge.getEdgeLength());
+            const double fControlPolygonLength(rEdge.getControlPolygonLength());
+            const double fCurrentDeviation(fTools::equalZero(fControlPolygonLength) ? 0.0 : 1.0 - (fEdgeLength / fControlPolygonLength));
+
+            if(!nRecursionWatch || fTools:: lessOrEqual(fCurrentDeviation, fDeviation))
+            {
+                return (fEdgeLength + fControlPolygonLength) * 0.5;
+            }
+            else
+            {
+                B2DCubicBezier aLeft, aRight;
+                const double fNewDeviation(fDeviation * 0.5);
+                const sal_uInt32 nNewRecursionWatch(nRecursionWatch - 1);
+
+                rEdge.split(0.5, &aLeft, &aRight);
+
+                return impGetLength(aLeft, fNewDeviation, nNewRecursionWatch)
+                    + impGetLength(aRight, fNewDeviation, nNewRecursionWatch);
+            }
+        }
+    }
+
+    double B2DCubicBezier::getLength(double fDeviation) const
+    {
+        if(isBezier())
+        {
+            if(fDeviation < 0.00000001)
+            {
+                fDeviation = 0.00000001;
+            }
+
+            return impGetLength(*this, fDeviation, 6);
+        }
+        else
+        {
+            return B2DVector(getEndPoint() - getStartPoint()).getLength();
+        }
+    }
+
+    double B2DCubicBezier::getEdgeLength() const
+    {
+        const B2DVector aEdge(maEndPoint - maStartPoint);
+        return aEdge.getLength();
+    }
+
+    double B2DCubicBezier::getControlPolygonLength() const
+    {
+        const B2DVector aVectorA(maControlPointA - maStartPoint);
+        const B2DVector aVectorB(maEndPoint - maControlPointB);
+
+        if(!aVectorA.equalZero() || !aVectorB.equalZero())
+        {
+            const B2DVector aTop(maControlPointB - maControlPointA);
+            return (aVectorA.getLength() + aVectorB.getLength() + aTop.getLength());
+        }
+        else
+        {
+            return getEdgeLength();
+        }
+    }
+
+    void B2DCubicBezier::adaptiveSubdivideByAngle(B2DPolygon& rTarget, double fAngleBound) const
+    {
+        if(isBezier())
+        {
+            // use support method #i37443# and allow unsharpen the criteria
+            ImpSubDivAngleStart(maStartPoint, maControlPointA, maControlPointB, maEndPoint, rTarget,
+                                deg2rad(fAngleBound));
+        }
+        else
+        {
+            rTarget.append(getEndPoint());
+        }
+    }
+
+    B2DVector B2DCubicBezier::getTangent(double t) const
+    {
+        if(fTools::lessOrEqual(t, 0.0))
+        {
+            // tangent in start point
+            B2DVector aTangent(getControlPointA() - getStartPoint());
+
+            if(!aTangent.equalZero())
+            {
+                return aTangent;
+            }
+
+            // start point and control vector are the same, fallback
+            // to implicit start vector to control point B
+            aTangent = (getControlPointB() - getStartPoint()) * 0.3;
+
+            if(!aTangent.equalZero())
+            {
+                return aTangent;
+            }
+
+            // not a bezier at all, return edge vector
+            return (getEndPoint() - getStartPoint()) * 0.3;
+        }
+        else if(fTools::moreOrEqual(t, 1.0))
+        {
+            // tangent in end point
+            B2DVector aTangent(getEndPoint() - getControlPointB());
+
+            if(!aTangent.equalZero())
+            {
+                return aTangent;
+            }
+
+            // end point and control vector are the same, fallback
+            // to implicit start vector from control point A
+            aTangent = (getEndPoint() - getControlPointA()) * 0.3;
+
+            if(!aTangent.equalZero())
+            {
+                return aTangent;
+            }
+
+            // not a bezier at all, return edge vector
+            return (getEndPoint() - getStartPoint()) * 0.3;
+        }
+        else
+        {
+            // t is in ]0.0 .. 1.0[. Split and extract
+            B2DCubicBezier aRight;
+            split(t, nullptr, &aRight);
+
+            return aRight.getControlPointA() - aRight.getStartPoint();
+        }
+    }
+
+    // #i37443# adaptive subdivide by nCount subdivisions
+    void B2DCubicBezier::adaptiveSubdivideByCount(B2DPolygon& rTarget, sal_uInt32 nCount) const
+    {
+        const double fLenFact(1.0 / static_cast< double >(nCount + 1));
+
+        for(sal_uInt32 a(1); a <= nCount; a++)
+        {
+            const double fPos(static_cast< double >(a) * fLenFact);
+            rTarget.append(interpolatePoint(fPos));
+        }
+
+        rTarget.append(getEndPoint());
+    }
+
+    // adaptive subdivide by distance
+    void B2DCubicBezier::adaptiveSubdivideByDistance(B2DPolygon& rTarget, double fDistanceBound, int nRecurseLimit) const
+    {
+        if(isBezier())
+        {
+            ImpSubDivDistance(maStartPoint, maControlPointA, maControlPointB, maEndPoint, rTarget,
+                fDistanceBound * fDistanceBound, std::numeric_limits<double>::max(), nRecurseLimit);
+        }
+        else
+        {
+            rTarget.append(getEndPoint());
+        }
+    }
+
+    B2DPoint B2DCubicBezier::interpolatePoint(double t) const
+    {
+        OSL_ENSURE(t >= 0.0 && t <= 1.0, "B2DCubicBezier::interpolatePoint: Access out of range (!)");
+
+        if(isBezier())
+        {
+            const B2DPoint aS1L(interpolate(maStartPoint, maControlPointA, t));
+            const B2DPoint aS1C(interpolate(maControlPointA, maControlPointB, t));
+            const B2DPoint aS1R(interpolate(maControlPointB, maEndPoint, t));
+            const B2DPoint aS2L(interpolate(aS1L, aS1C, t));
+            const B2DPoint aS2R(interpolate(aS1C, aS1R, t));
+
+            return interpolate(aS2L, aS2R, t);
+        }
+        else
+        {
+            return interpolate(maStartPoint, maEndPoint, t);
+        }
+    }
+
+    double B2DCubicBezier::getSmallestDistancePointToBezierSegment(const B2DPoint& rTestPoint, double& rCut) const
+    {
+        const sal_uInt32 nInitialDivisions(3);
+        B2DPolygon aInitialPolygon;
+
+        // as start make a fix division, creates nInitialDivisions + 2 points
+        aInitialPolygon.append(getStartPoint());
+        adaptiveSubdivideByCount(aInitialPolygon, nInitialDivisions);
+
+        // now look for the closest point
+        const sal_uInt32 nPointCount(aInitialPolygon.count());
+        B2DVector aVector(rTestPoint - aInitialPolygon.getB2DPoint(0));
+        double fQuadDist(aVector.getX() * aVector.getX() + aVector.getY() * aVector.getY());
+        double fNewQuadDist;
+        sal_uInt32 nSmallestIndex(0);
+
+        for(sal_uInt32 a(1); a < nPointCount; a++)
+        {
+            aVector = B2DVector(rTestPoint - aInitialPolygon.getB2DPoint(a));
+            fNewQuadDist = aVector.getX() * aVector.getX() + aVector.getY() * aVector.getY();
+
+            if(fNewQuadDist < fQuadDist)
+            {
+                fQuadDist = fNewQuadDist;
+                nSmallestIndex = a;
+            }
+        }
+
+        // look right and left for even smaller distances
+        double fStepValue(1.0 / static_cast<double>((nPointCount - 1) * 2)); // half the edge step width
+        double fPosition(static_cast<double>(nSmallestIndex) / static_cast<double>(nPointCount - 1));
+
+        while(true)
+        {
+            // test left
+            double fPosLeft(fPosition - fStepValue);
+
+            if(fPosLeft < 0.0)
+            {
+                fPosLeft = 0.0;
+                aVector = B2DVector(rTestPoint - maStartPoint);
+            }
+            else
+            {
+                aVector = B2DVector(rTestPoint - interpolatePoint(fPosLeft));
+            }
+
+            fNewQuadDist = aVector.getX() * aVector.getX() + aVector.getY() * aVector.getY();
+
+            if(fTools::less(fNewQuadDist, fQuadDist))
+            {
+                fQuadDist = fNewQuadDist;
+                fPosition = fPosLeft;
+            }
+            else
+            {
+                // test right
+                double fPosRight(fPosition + fStepValue);
+
+                if(fPosRight > 1.0)
+                {
+                    fPosRight = 1.0;
+                    aVector = B2DVector(rTestPoint - maEndPoint);
+                }
+                else
+                {
+                    aVector = B2DVector(rTestPoint - interpolatePoint(fPosRight));
+                }
+
+                fNewQuadDist = aVector.getX() * aVector.getX() + aVector.getY() * aVector.getY();
+
+                if(fTools::less(fNewQuadDist, fQuadDist))
+                {
+                    fQuadDist = fNewQuadDist;
+                    fPosition = fPosRight;
+                }
+                else
+                {
+                    // not less left or right, done
+                    break;
+                }
+            }
+
+            if(fPosition == 0.0 || fPosition == 1.0)
+            {
+                // if we are completely left or right, we are done
+                break;
+            }
+
+            // prepare next step value
+            fStepValue /= 2.0;
+        }
+
+        rCut = fPosition;
+        return sqrt(fQuadDist);
+    }
+
+    void B2DCubicBezier::split(double t, B2DCubicBezier* pBezierA, B2DCubicBezier* pBezierB) const
+    {
+        OSL_ENSURE(t >= 0.0 && t <= 1.0, "B2DCubicBezier::split: Access out of range (!)");
+
+        if(!pBezierA && !pBezierB)
+        {
+            return;
+        }
+
+        if(isBezier())
+        {
+            const B2DPoint aS1L(interpolate(maStartPoint, maControlPointA, t));
+            const B2DPoint aS1C(interpolate(maControlPointA, maControlPointB, t));
+            const B2DPoint aS1R(interpolate(maControlPointB, maEndPoint, t));
+            const B2DPoint aS2L(interpolate(aS1L, aS1C, t));
+            const B2DPoint aS2R(interpolate(aS1C, aS1R, t));
+            const B2DPoint aS3C(interpolate(aS2L, aS2R, t));
+
+            if(pBezierA)
+            {
+                pBezierA->setStartPoint(maStartPoint);
+                pBezierA->setEndPoint(aS3C);
+                pBezierA->setControlPointA(aS1L);
+                pBezierA->setControlPointB(aS2L);
+            }
+
+            if(pBezierB)
+            {
+                pBezierB->setStartPoint(aS3C);
+                pBezierB->setEndPoint(maEndPoint);
+                pBezierB->setControlPointA(aS2R);
+                pBezierB->setControlPointB(aS1R);
+            }
+        }
+        else
+        {
+            const B2DPoint aSplit(interpolate(maStartPoint, maEndPoint, t));
+
+            if(pBezierA)
+            {
+                pBezierA->setStartPoint(maStartPoint);
+                pBezierA->setEndPoint(aSplit);
+                pBezierA->setControlPointA(maStartPoint);
+                pBezierA->setControlPointB(aSplit);
+            }
+
+            if(pBezierB)
+            {
+                pBezierB->setStartPoint(aSplit);
+                pBezierB->setEndPoint(maEndPoint);
+                pBezierB->setControlPointA(aSplit);
+                pBezierB->setControlPointB(maEndPoint);
+            }
+        }
+    }
+
+    B2DCubicBezier B2DCubicBezier::snippet(double fStart, double fEnd) const
+    {
+        B2DCubicBezier aRetval;
+
+        if(fTools::more(fStart, 1.0))
+        {
+            fStart = 1.0;
+        }
+        else if(fTools::less(fStart, 0.0))
+        {
+            fStart = 0.0;
+        }
+
+        if(fTools::more(fEnd, 1.0))
+        {
+            fEnd = 1.0;
+        }
+        else if(fTools::less(fEnd, 0.0))
+        {
+            fEnd = 0.0;
+        }
+
+        if(fEnd <= fStart)
+        {
+            // empty or NULL, create single point at center
+            const double fSplit((fEnd + fStart) * 0.5);
+            const B2DPoint aPoint(interpolate(getStartPoint(), getEndPoint(), fSplit));
+            aRetval.setStartPoint(aPoint);
+            aRetval.setEndPoint(aPoint);
+            aRetval.setControlPointA(aPoint);
+            aRetval.setControlPointB(aPoint);
+        }
+        else
+        {
+            if(isBezier())
+            {
+                // copy bezier; cut off right, then cut off left. Do not forget to
+                // adapt cut value when both cuts happen
+                const bool bEndIsOne(fTools::equal(fEnd, 1.0));
+                const bool bStartIsZero(fTools::equalZero(fStart));
+                aRetval = *this;
+
+                if(!bEndIsOne)
+                {
+                    aRetval.split(fEnd, &aRetval, nullptr);
+
+                    if(!bStartIsZero)
+                    {
+                        fStart /= fEnd;
+                    }
+                }
+
+                if(!bStartIsZero)
+                {
+                    aRetval.split(fStart, nullptr, &aRetval);
+                }
+            }
+            else
+            {
+                // no bezier, create simple edge
+                const B2DPoint aPointA(interpolate(getStartPoint(), getEndPoint(), fStart));
+                const B2DPoint aPointB(interpolate(getStartPoint(), getEndPoint(), fEnd));
+                aRetval.setStartPoint(aPointA);
+                aRetval.setEndPoint(aPointB);
+                aRetval.setControlPointA(aPointA);
+                aRetval.setControlPointB(aPointB);
+            }
+        }
+
+        return aRetval;
+    }
+
+    B2DRange B2DCubicBezier::getRange() const
+    {
+        B2DRange aRetval(maStartPoint, maEndPoint);
+
+        aRetval.expand(maControlPointA);
+        aRetval.expand(maControlPointB);
+
+        return aRetval;
+    }
+
+    bool B2DCubicBezier::getMinimumExtremumPosition(double& rfResult) const
+    {
+        std::vector< double > aAllResults;
+
+        aAllResults.reserve(4);
+        getAllExtremumPositions(aAllResults);
+
+        const sal_uInt32 nCount(aAllResults.size());
+
+        if(!nCount)
+        {
+            return false;
+        }
+        else if(nCount == 1)
+        {
+            rfResult = aAllResults[0];
+            return true;
+        }
+        else
+        {
+            rfResult = *(std::min_element(aAllResults.begin(), aAllResults.end()));
+            return true;
+        }
+    }
+
+    namespace
+    {
+        void impCheckExtremumResult(double fCandidate, std::vector< double >& rResult)
+        {
+            // check for range ]0.0 .. 1.0[ with excluding 1.0 and 0.0 clearly
+            // by using the equalZero test, NOT ::more or ::less which will use the
+            // ApproxEqual() which is too exact here
+            if(fCandidate > 0.0 && !fTools::equalZero(fCandidate))
+            {
+                if(fCandidate < 1.0 && !fTools::equalZero(fCandidate - 1.0))
+                {
+                    rResult.push_back(fCandidate);
+                }
+            }
+        }
+    }
+
+    void B2DCubicBezier::getAllExtremumPositions(std::vector< double >& rResults) const
+    {
+        rResults.clear();
+
+        // calculate the x-extrema parameters by zeroing first x-derivative
+        // of the cubic bezier's parametric formula, which results in a
+        // quadratic equation: dBezier/dt = t*t*fAX - 2*t*fBX + fCX
+        const B2DPoint aControlDiff( maControlPointA - maControlPointB );
+        double fCX = maControlPointA.getX() - maStartPoint.getX();
+        const double fBX = fCX + aControlDiff.getX();
+        const double fAX = 3 * aControlDiff.getX() + (maEndPoint.getX() - maStartPoint.getX());
+
+        if(fTools::equalZero(fCX))
+        {
+            // detect fCX equal zero and truncate to real zero value in that case
+            fCX = 0.0;
+        }
+
+        if( !fTools::equalZero(fAX) )
+        {
+            // derivative is polynomial of order 2 => use binomial formula
+            const double fD = fBX*fBX - fAX*fCX;
+            if( fD >= 0.0 )
+            {
+                const double fS = sqrt(fD);
+                // calculate both roots (avoiding a numerically unstable subtraction)
+                const double fQ = fBX + ((fBX >= 0) ? +fS : -fS);
+                impCheckExtremumResult(fQ / fAX, rResults);
+                if( !fTools::equalZero(fS) ) // ignore root multiplicity
+                    impCheckExtremumResult(fCX / fQ, rResults);
+            }
+        }
+        else if( !fTools::equalZero(fBX) )
+        {
+            // derivative is polynomial of order 1 => one extrema
+            impCheckExtremumResult(fCX / (2 * fBX), rResults);
+        }
+
+        // calculate the y-extrema parameters by zeroing first y-derivative
+        double fCY = maControlPointA.getY() - maStartPoint.getY();
+        const double fBY = fCY + aControlDiff.getY();
+        const double fAY = 3 * aControlDiff.getY() + (maEndPoint.getY() - maStartPoint.getY());
+
+        if(fTools::equalZero(fCY))
+        {
+            // detect fCY equal zero and truncate to real zero value in that case
+            fCY = 0.0;
+        }
+
+        if( !fTools::equalZero(fAY) )
+        {
+            // derivative is polynomial of order 2 => use binomial formula
+            const double fD = fBY*fBY - fAY*fCY;
+            if( fD >= 0.0 )
+            {
+                const double fS = sqrt(fD);
+                // calculate both roots (avoiding a numerically unstable subtraction)
+                const double fQ = fBY + ((fBY >= 0) ? +fS : -fS);
+                impCheckExtremumResult(fQ / fAY, rResults);
+                if( !fTools::equalZero(fS) ) // ignore root multiplicity
+                    impCheckExtremumResult(fCY / fQ, rResults);
+            }
+        }
+        else if( !fTools::equalZero(fBY) )
+        {
+            // derivative is polynomial of order 1 => one extrema
+            impCheckExtremumResult(fCY / (2 * fBY), rResults);
+        }
+    }
+
+    void B2DCubicBezier::transform(const basegfx::B2DHomMatrix& rMatrix)
+    {
+        if(rMatrix.isIdentity())
+            return;
+
+        if(maControlPointA == maStartPoint)
+        {
+            maControlPointA = maStartPoint = rMatrix * maStartPoint;
+        }
+        else
+        {
+            maStartPoint *= rMatrix;
+            maControlPointA *= rMatrix;
+        }
+
+        if(maControlPointB == maEndPoint)
+        {
+            maControlPointB = maEndPoint = rMatrix * maEndPoint;
+        }
+        else
+        {
+            maEndPoint *= rMatrix;
+            maControlPointB *= rMatrix;
+        }
+    }
+
+    void B2DCubicBezier::fround()
+    {
+        if(maControlPointA == maStartPoint)
+        {
+            maControlPointA = maStartPoint = basegfx::B2DPoint(
+                basegfx::fround(maStartPoint.getX()),
+                basegfx::fround(maStartPoint.getY()));
+        }
+        else
+        {
+            maStartPoint = basegfx::B2DPoint(
+                basegfx::fround(maStartPoint.getX()),
+                basegfx::fround(maStartPoint.getY()));
+            maControlPointA = basegfx::B2DPoint(
+                basegfx::fround(maControlPointA.getX()),
+                basegfx::fround(maControlPointA.getY()));
+        }
+
+        if(maControlPointB == maEndPoint)
+        {
+            maControlPointB = maEndPoint = basegfx::B2DPoint(
+                basegfx::fround(maEndPoint.getX()),
+                basegfx::fround(maEndPoint.getY()));
+        }
+        else
+        {
+            maEndPoint = basegfx::B2DPoint(
+                basegfx::fround(maEndPoint.getX()),
+                basegfx::fround(maEndPoint.getY()));
+            maControlPointB = basegfx::B2DPoint(
+                basegfx::fround(maControlPointB.getX()),
+                basegfx::fround(maControlPointB.getY()));
+        }
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/inc/stringconversiontools.hxx b/basegfx/source/inc/stringconversiontools.hxx
new file mode 100644
index 0000000000..797697d203
--- /dev/null
+++ b/basegfx/source/inc/stringconversiontools.hxx
@@ -0,0 +1,64 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/config.h>
+
+#include <string_view>
+
+#include <sal/types.h>
+#include <rtl/ustring.hxx>
+
+namespace basegfx::internal
+    {
+        void skipSpaces(sal_Int32&      io_rPos,
+                        std::u16string_view rStr,
+                        const sal_Int32 nLen);
+
+        inline bool isOnNumberChar(const sal_Unicode aChar,
+                                   bool              bSignAllowed)
+        {
+            const bool bPredicate( (u'0' <= aChar && u'9' >= aChar)
+                                    || (bSignAllowed && u'+' == aChar)
+                                    || (bSignAllowed && u'-' == aChar)
+                                    || (u'.' == aChar));
+
+            return bPredicate;
+        }
+
+        inline bool isOnNumberChar(std::u16string_view rStr,
+                                   const sal_Int32 nPos)
+        {
+            return isOnNumberChar(rStr[nPos], true/*bSignAllowed*/);
+        }
+
+        bool importDoubleAndSpaces(double&          o_fRetval,
+                                   sal_Int32&       io_rPos,
+                                   std::u16string_view  rStr,
+                                   const sal_Int32  nLen );
+
+        bool importFlagAndSpaces(sal_Int32&      o_nRetval,
+                                 sal_Int32&      io_rPos,
+                                 std::u16string_view rStr,
+                                 const sal_Int32 nLen);
+
+} // namespace basegfx::internal
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/matrix/b2dhommatrix.cxx b/basegfx/source/matrix/b2dhommatrix.cxx
new file mode 100644
index 0000000000..e4a9dda9e3
--- /dev/null
+++ b/basegfx/source/matrix/b2dhommatrix.cxx
@@ -0,0 +1,430 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/matrix/hommatrixtemplate.hxx>
+#include <basegfx/tuple/b2dtuple.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+#include <memory>
+
+namespace basegfx
+{
+    constexpr int RowSize = 3;
+
+    void B2DHomMatrix::set3x2(double f_0x0, double f_0x1, double f_0x2, double f_1x0, double f_1x1, double f_1x2)
+    {
+        mfValues[0][0] = f_0x0;
+        mfValues[0][1] = f_0x1;
+        mfValues[0][2] = f_0x2;
+        mfValues[1][0] = f_1x0;
+        mfValues[1][1] = f_1x1;
+        mfValues[1][2] = f_1x2;
+    }
+
+    bool B2DHomMatrix::isIdentity() const
+    {
+        for(sal_uInt16 a(0); a < RowSize - 1; a++)
+        {
+            for(sal_uInt16 b(0); b < RowSize; b++)
+            {
+                const double fDefault(internal::implGetDefaultValue(a, b));
+                const double fValueAB(get(a, b));
+
+                if(!::basegfx::fTools::equal(fDefault, fValueAB))
+                {
+                    return false;
+                }
+            }
+        }
+
+        return true;
+    }
+
+    void B2DHomMatrix::identity()
+    {
+        for(sal_uInt16 a(0); a < RowSize - 1; a++)
+        {
+            for(sal_uInt16 b(0); b < RowSize; b++)
+                mfValues[a][b] = internal::implGetDefaultValue(a, b);
+        }
+    }
+
+    bool B2DHomMatrix::isInvertible() const
+    {
+        double dst[6];
+        /* Compute adjoint: */
+        computeAdjoint(dst);
+        /* Compute determinant: */
+        double det = computeDeterminant(dst);
+        if (fTools::equalZero(det))
+            return false;
+        return true;
+    }
+
+    bool B2DHomMatrix::invert()
+    {
+        if(isIdentity())
+            return true;
+
+        double dst[6];
+
+        /* Compute adjoint: */
+        computeAdjoint(dst);
+
+        /* Compute determinant: */
+        double det = computeDeterminant(dst);
+        if (fTools::equalZero(det))
+            return false;
+
+        /* Multiply adjoint with reciprocal of determinant: */
+        det = 1.0 / det;
+        mfValues[0][0] = dst[0] * det;
+        mfValues[0][1] = dst[1] * det;
+        mfValues[0][2] = dst[2] * det;
+        mfValues[1][0] = dst[3] * det;
+        mfValues[1][1] = dst[4] * det;
+        mfValues[1][2] = dst[5] * det;
+
+        return true;
+    }
+
+    /* Compute adjoint, optimised for the case where the last (not stored) row is { 0, 0, 1 } */
+    void B2DHomMatrix::computeAdjoint(double (&dst)[6]) const
+    {
+        dst[0] = + get(1, 1);
+        dst[1] = - get(0, 1);
+        dst[2] = + get(0, 1) * get(1, 2) - get(0, 2) * get(1, 1);
+        dst[3] = - get(1, 0);
+        dst[4] = + get(0, 0);
+        dst[5] = - get(0, 0) * get(1, 2) + get(0, 2) * get(1, 0);
+    }
+
+    /* Compute the determinant, given the adjoint matrix */
+    double B2DHomMatrix::computeDeterminant(double (&dst)[6]) const
+    {
+        return mfValues[0][0] * dst[0] + mfValues[0][1] * dst[3];
+    }
+
+    B2DHomMatrix& B2DHomMatrix::operator*=(const B2DHomMatrix& rMat)
+    {
+        if(rMat.isIdentity())
+        {
+            // multiply with identity, no change -> nothing to do
+        }
+        else if(isIdentity())
+        {
+            // we are identity, result will be rMat -> assign
+            *this = rMat;
+        }
+        else
+        {
+            // multiply
+            doMulMatrix(rMat);
+        }
+
+        return *this;
+    }
+
+    void B2DHomMatrix::doMulMatrix(const B2DHomMatrix& rMat)
+    {
+        // create a copy as source for the original values
+        const B2DHomMatrix aCopy(*this);
+
+        for(sal_uInt16 a(0); a < 2; ++a)
+        {
+            for(sal_uInt16 b(0); b < 3; ++b)
+            {
+                double fValue = 0.0;
+
+                for(sal_uInt16 c(0); c < 2; ++c)
+                    fValue += aCopy.mfValues[c][b] * rMat.mfValues[a][c];
+
+                mfValues[a][b] = fValue;
+            }
+            mfValues[a][2] += rMat.mfValues[a][2];
+        }
+    }
+
+    bool B2DHomMatrix::operator==(const B2DHomMatrix& rMat) const
+    {
+        if (&rMat == this)
+            return true;
+        for(sal_uInt16 a(0); a < 2; a++)
+        {
+            for(sal_uInt16 b(0); b < 3; b++)
+            {
+                const double fValueA(mfValues[a][b]);
+                const double fValueB(rMat.mfValues[a][b]);
+
+                if(!::basegfx::fTools::equal(fValueA, fValueB))
+                {
+                    return false;
+                }
+            }
+        }
+        return true;
+    }
+
+    bool B2DHomMatrix::operator!=(const B2DHomMatrix& rMat) const
+    {
+        return !(*this == rMat);
+    }
+
+    void B2DHomMatrix::rotate(double fRadiant)
+    {
+        if(fTools::equalZero(fRadiant))
+            return;
+
+        double fSin(0.0);
+        double fCos(1.0);
+
+        utils::createSinCosOrthogonal(fSin, fCos, fRadiant);
+        B2DHomMatrix aRotMat;
+
+        aRotMat.set(0, 0, fCos);
+        aRotMat.set(1, 1, fCos);
+        aRotMat.set(1, 0, fSin);
+        aRotMat.set(0, 1, -fSin);
+
+        doMulMatrix(aRotMat);
+    }
+
+    void B2DHomMatrix::translate(double fX, double fY)
+    {
+        if(!fTools::equalZero(fX) || !fTools::equalZero(fY))
+        {
+            B2DHomMatrix aTransMat;
+
+            aTransMat.set(0, 2, fX);
+            aTransMat.set(1, 2, fY);
+
+            doMulMatrix(aTransMat);
+        }
+    }
+
+    void B2DHomMatrix::translate(const B2DTuple& rTuple)
+    {
+        translate(rTuple.getX(), rTuple.getY());
+    }
+
+    void B2DHomMatrix::scale(double fX, double fY)
+    {
+        const double fOne(1.0);
+
+        if(!fTools::equal(fOne, fX) || !fTools::equal(fOne, fY))
+        {
+            B2DHomMatrix aScaleMat;
+
+            aScaleMat.set(0, 0, fX);
+            aScaleMat.set(1, 1, fY);
+
+            doMulMatrix(aScaleMat);
+        }
+    }
+
+    void B2DHomMatrix::scale(const B2DTuple& rTuple)
+    {
+        scale(rTuple.getX(), rTuple.getY());
+    }
+
+    void B2DHomMatrix::shearX(double fSx)
+    {
+        // #i76239# do not test against 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
+        if(!fTools::equalZero(fSx))
+        {
+            B2DHomMatrix aShearXMat;
+
+            aShearXMat.set(0, 1, fSx);
+
+            doMulMatrix(aShearXMat);
+        }
+    }
+
+    void B2DHomMatrix::shearY(double fSy)
+    {
+        // #i76239# do not test against 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
+        if(!fTools::equalZero(fSy))
+        {
+            B2DHomMatrix aShearYMat;
+
+            aShearYMat.set(1, 0, fSy);
+
+            doMulMatrix(aShearYMat);
+        }
+    }
+
+    /** Decomposition
+
+       New, optimized version with local shearX detection. Old version (keeping
+       below, is working well, too) used the 3D matrix decomposition when
+       shear was used. Keeping old version as comment below since it may get
+       necessary to add the determinant() test from there here, too.
+    */
+    bool B2DHomMatrix::decompose(B2DTuple& rScale, B2DTuple& rTranslate, double& rRotate, double& rShearX) const
+    {
+        // reset rotate and shear and copy translation values in every case
+        rRotate = rShearX = 0.0;
+        rTranslate.setX(get(0, 2));
+        rTranslate.setY(get(1, 2));
+
+        // test for rotation and shear
+        if(fTools::equalZero(get(0, 1)) && fTools::equalZero(get(1, 0)))
+        {
+            // no rotation and shear, copy scale values
+            rScale.setX(get(0, 0));
+            rScale.setY(get(1, 1));
+
+            // or is there?
+            if( rScale.getX() < 0 && rScale.getY() < 0 )
+            {
+                // there is - 180 degree rotated
+                rScale *= -1;
+                rRotate = M_PI;
+            }
+        }
+        else
+        {
+            // get the unit vectors of the transformation -> the perpendicular vectors
+            B2DVector aUnitVecX(get(0, 0), get(1, 0));
+            B2DVector aUnitVecY(get(0, 1), get(1, 1));
+            const double fScalarXY(aUnitVecX.scalar(aUnitVecY));
+
+            // Test if shear is zero. That's the case if the unit vectors in the matrix
+            // are perpendicular -> scalar is zero. This is also the case when one of
+            // the unit vectors is zero.
+            if(fTools::equalZero(fScalarXY))
+            {
+                // calculate unsigned scale values
+                rScale.setX(aUnitVecX.getLength());
+                rScale.setY(aUnitVecY.getLength());
+
+                // check unit vectors for zero lengths
+                const bool bXIsZero(fTools::equalZero(rScale.getX()));
+                const bool bYIsZero(fTools::equalZero(rScale.getY()));
+
+                if(bXIsZero || bYIsZero)
+                {
+                    // still extract as much as possible. Scalings are already set
+                    if(!bXIsZero)
+                    {
+                        // get rotation of X-Axis
+                        rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
+                    }
+                    else if(!bYIsZero)
+                    {
+                        // get rotation of X-Axis. When assuming X and Y perpendicular
+                        // and correct rotation, it's the Y-Axis rotation minus 90 degrees
+                        rRotate = atan2(aUnitVecY.getY(), aUnitVecY.getX()) - M_PI_2;
+                    }
+
+                    // one or both unit vectors do not exist, determinant is zero, no decomposition possible.
+                    // Eventually used rotations or shears are lost
+                    return false;
+                }
+                else
+                {
+                    // no shear
+                    // calculate rotation of X unit vector relative to (1, 0)
+                    rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
+
+                    // use orientation to evtl. correct sign of Y-Scale
+                    const double fCrossXY(aUnitVecX.cross(aUnitVecY));
+
+                    if(fCrossXY < 0.0)
+                    {
+                        rScale.setY(-rScale.getY());
+                    }
+                }
+            }
+            else
+            {
+                // fScalarXY is not zero, thus both unit vectors exist. No need to handle that here
+                // shear, extract it
+                double fCrossXY(aUnitVecX.cross(aUnitVecY));
+
+                // get rotation by calculating angle of X unit vector relative to (1, 0).
+                // This is before the parallel test following the motto to extract
+                // as much as possible
+                rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
+
+                // get unsigned scale value for X. It will not change and is useful
+                // for further corrections
+                rScale.setX(aUnitVecX.getLength());
+
+                if(fTools::equalZero(fCrossXY))
+                {
+                    // extract as much as possible
+                    rScale.setY(aUnitVecY.getLength());
+
+                    // unit vectors are parallel, thus not linear independent. No
+                    // useful decomposition possible. This should not happen since
+                    // the only way to get the unit vectors nearly parallel is
+                    // a very big shearing. Anyways, be prepared for hand-filled
+                    // matrices
+                    // Eventually used rotations or shears are lost
+                    return false;
+                }
+                else
+                {
+                    // calculate the contained shear
+                    rShearX = fScalarXY / fCrossXY;
+
+                    if(!fTools::equalZero(rRotate))
+                    {
+                        // To be able to correct the shear for aUnitVecY, rotation needs to be
+                        // removed first. Correction of aUnitVecX is easy, it will be rotated back to (1, 0).
+                        aUnitVecX.setX(rScale.getX());
+                        aUnitVecX.setY(0.0);
+
+                        // for Y correction we rotate the UnitVecY back about -rRotate
+                        const double fNegRotate(-rRotate);
+                        const double fSin(sin(fNegRotate));
+                        const double fCos(cos(fNegRotate));
+
+                        const double fNewX(aUnitVecY.getX() * fCos - aUnitVecY.getY() * fSin);
+                        const double fNewY(aUnitVecY.getX() * fSin + aUnitVecY.getY() * fCos);
+
+                        aUnitVecY.setX(fNewX);
+                        aUnitVecY.setY(fNewY);
+                    }
+
+                    // Correct aUnitVecY and fCrossXY to fShear=0. Rotation is already removed.
+                    // Shear correction can only work with removed rotation
+                    aUnitVecY.setX(aUnitVecY.getX() - (aUnitVecY.getY() * rShearX));
+                    fCrossXY = aUnitVecX.cross(aUnitVecY);
+
+                    // calculate unsigned scale value for Y, after the corrections since
+                    // the shear correction WILL change the length of aUnitVecY
+                    rScale.setY(aUnitVecY.getLength());
+
+                    // use orientation to set sign of Y-Scale
+                    if(fCrossXY < 0.0)
+                    {
+                        rScale.setY(-rScale.getY());
+                    }
+                }
+            }
+        }
+
+        return true;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/matrix/b2dhommatrixtools.cxx b/basegfx/source/matrix/b2dhommatrixtools.cxx
new file mode 100644
index 0000000000..7fb6bbe0cb
--- /dev/null
+++ b/basegfx/source/matrix/b2dhommatrixtools.cxx
@@ -0,0 +1,457 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+#include <basegfx/range/b2drange.hxx>
+
+#include <osl/diagnose.h>
+
+namespace basegfx::utils
+{
+        void createSinCosOrthogonal(double& o_rSin, double& o_rCos, double fRadiant)
+        {
+            if( fTools::equalZero( fmod( fRadiant, M_PI_2 ) ) )
+            {
+                // determine quadrant
+                const sal_Int32 nQuad(
+                    (4 + fround( M_2_PI*fmod( fRadiant, 2 * M_PI ) )) % 4 );
+                switch( nQuad )
+                {
+                    case 0: // -2pi,0,2pi
+                        o_rSin = 0.0;
+                        o_rCos = 1.0;
+                        break;
+
+                    case 1: // -3/2pi,1/2pi
+                        o_rSin = 1.0;
+                        o_rCos = 0.0;
+                        break;
+
+                    case 2: // -pi,pi
+                        o_rSin = 0.0;
+                        o_rCos = -1.0;
+                        break;
+
+                    case 3: // -1/2pi,3/2pi
+                        o_rSin = -1.0;
+                        o_rCos = 0.0;
+                        break;
+
+                    default:
+                        OSL_FAIL( "createSinCos: Impossible case reached" );
+                }
+            }
+            else
+            {
+                // TODO(P1): Maybe use glibc's sincos here (though
+                // that's kinda non-portable...)
+                o_rSin = sin(fRadiant);
+                o_rCos = cos(fRadiant);
+            }
+        }
+
+        B2DHomMatrix createScaleB2DHomMatrix(double fScaleX, double fScaleY)
+        {
+            B2DHomMatrix aRetval;
+            const double fOne(1.0);
+
+            if(!fTools::equal(fScaleX, fOne))
+            {
+                aRetval.set(0, 0, fScaleX);
+            }
+
+            if(!fTools::equal(fScaleY, fOne))
+            {
+                aRetval.set(1, 1, fScaleY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createShearXB2DHomMatrix(double fShearX)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fShearX))
+            {
+                aRetval.set(0, 1, fShearX);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createShearYB2DHomMatrix(double fShearY)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fShearY))
+            {
+                aRetval.set(1, 0, fShearY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createRotateB2DHomMatrix(double fRadiant)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fRadiant))
+            {
+                double fSin(0.0);
+                double fCos(1.0);
+
+                createSinCosOrthogonal(fSin, fCos, fRadiant);
+                aRetval.set(0, 0, fCos);
+                aRetval.set(1, 1, fCos);
+                aRetval.set(1, 0, fSin);
+                aRetval.set(0, 1, -fSin);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createTranslateB2DHomMatrix(double fTranslateX, double fTranslateY)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!(fTools::equalZero(fTranslateX) && fTools::equalZero(fTranslateY)))
+            {
+                aRetval.set(0, 2, fTranslateX);
+                aRetval.set(1, 2, fTranslateY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createScaleShearXRotateTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY)
+        {
+            const double fOne(1.0);
+
+            if(fTools::equal(fScaleX, fOne) && fTools::equal(fScaleY, fOne))
+            {
+                /// no scale, take shortcut
+                return createShearXRotateTranslateB2DHomMatrix(fShearX, fRadiant, fTranslateX, fTranslateY);
+            }
+            else
+            {
+                /// scale used
+                if(fTools::equalZero(fShearX))
+                {
+                    /// no shear
+                    if(fTools::equalZero(fRadiant))
+                    {
+                        /// no rotate, take shortcut
+                        return createScaleTranslateB2DHomMatrix(fScaleX, fScaleY, fTranslateX, fTranslateY);
+                    }
+                    else
+                    {
+                        /// rotate and scale used, no shear
+                        double fSin(0.0);
+                        double fCos(1.0);
+
+                        createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fCos * fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * -fSin,
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ fSin * fScaleX,
+                            /* Row 1, Column 1 */ fScaleY * fCos,
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                }
+                else
+                {
+                    /// scale and shear used
+                    if(fTools::equalZero(fRadiant))
+                    {
+                        /// scale and shear, but no rotate
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * fShearX,
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ 0.0,
+                            /* Row 1, Column 1 */ fScaleY,
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                    else
+                    {
+                        /// scale, shear and rotate used
+                        double fSin(0.0);
+                        double fCos(1.0);
+
+                        createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fCos * fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * ((fCos * fShearX) - fSin),
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ fSin * fScaleX,
+                            /* Row 1, Column 1 */ fScaleY * ((fSin * fShearX) + fCos),
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                }
+            }
+        }
+
+        B2DHomMatrix createShearXRotateTranslateB2DHomMatrix(
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY)
+        {
+            if(fTools::equalZero(fShearX))
+            {
+                /// no shear
+                if(fTools::equalZero(fRadiant))
+                {
+                    /// no shear, no rotate, take shortcut
+                    return createTranslateB2DHomMatrix(fTranslateX, fTranslateY);
+                }
+                else
+                {
+                    /// no shear, but rotate used
+                    double fSin(0.0);
+                    double fCos(1.0);
+
+                    createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fCos,
+                        /* Row 0, Column 1 */ -fSin,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ fSin,
+                        /* Row 1, Column 1 */ fCos,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+            else
+            {
+                /// shear used
+                if(fTools::equalZero(fRadiant))
+                {
+                    /// no rotate, but shear used
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ 1.0,
+                        /* Row 0, Column 1 */ fShearX,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ 0.0,
+                        /* Row 1, Column 1 */ 1.0,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+                else
+                {
+                    /// shear and rotate used
+                    double fSin(0.0);
+                    double fCos(1.0);
+
+                    createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fCos,
+                        /* Row 0, Column 1 */ (fCos * fShearX) - fSin,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ fSin,
+                        /* Row 1, Column 1 */ (fSin * fShearX) + fCos,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+        }
+
+        B2DHomMatrix createScaleTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fTranslateX, double fTranslateY)
+        {
+            const double fOne(1.0);
+
+            if(fTools::equal(fScaleX, fOne) && fTools::equal(fScaleY, fOne))
+            {
+                /// no scale, take shortcut
+                return createTranslateB2DHomMatrix(fTranslateX, fTranslateY);
+            }
+            else
+            {
+                /// scale used
+                if(fTools::equalZero(fTranslateX) && fTools::equalZero(fTranslateY))
+                {
+                    /// no translate, but scale.
+                    B2DHomMatrix aRetval;
+
+                    aRetval.set(0, 0, fScaleX);
+                    aRetval.set(1, 1, fScaleY);
+
+                    return aRetval;
+                }
+                else
+                {
+                    /// translate and scale
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fScaleX,
+                        /* Row 0, Column 1 */ 0.0,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ 0.0,
+                        /* Row 1, Column 1 */ fScaleY,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+        }
+
+        B2DHomMatrix createRotateAroundPoint(
+            double fPointX, double fPointY,
+            double fRadiant)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fRadiant))
+            {
+                double fSin(0.0);
+                double fCos(1.0);
+
+                createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                aRetval.set3x2(
+                    /* Row 0, Column 0 */ fCos,
+                    /* Row 0, Column 1 */ -fSin,
+                    /* Row 0, Column 2 */ (fPointX * (1.0 - fCos)) + (fSin * fPointY),
+                    /* Row 1, Column 0 */ fSin,
+                    /* Row 1, Column 1 */ fCos,
+                    /* Row 1, Column 2 */ (fPointY * (1.0 - fCos)) - (fSin * fPointX));
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createRotateAroundCenterKeepAspectRatioStayInsideRange(
+            const basegfx::B2DRange& rTargetRange,
+            double fRotate)
+        {
+            basegfx::B2DHomMatrix aRetval;
+
+            // RotGrfFlyFrame: Create a transformation that maps the range inside of itself
+            // so that it fits, takes as much space as possible and keeps the aspect ratio
+            if(0.0 != fRotate)
+            {
+                // Fit rotated graphic to center of available space, keeping page ratio:
+                // Adapt scaling ratio of unit object and rotate it
+                aRetval.scale(1.0, rTargetRange.getHeight() / rTargetRange.getWidth());
+                aRetval.rotate(fRotate);
+
+                // get the range to see where we are in unit coordinates
+                basegfx::B2DRange aFullRange(0.0, 0.0, 1.0, 1.0);
+                aFullRange.transform(aRetval);
+
+                // detect needed scales in X/Y and choose the smallest for staying inside the
+                // available space while keeping aspect ratio of the source
+                const double fScaleX(rTargetRange.getWidth() / aFullRange.getWidth());
+                const double fScaleY(rTargetRange.getHeight() / aFullRange.getHeight());
+                const double fScaleMin(std::min(fScaleX, fScaleY));
+
+                // TopLeft to zero, then scale, then move to center of available space
+                aRetval.translate(-aFullRange.getMinX(), -aFullRange.getMinY());
+                aRetval.scale(fScaleMin, fScaleMin);
+                aRetval.translate(
+                    rTargetRange.getCenterX() - (0.5 * fScaleMin * aFullRange.getWidth()),
+                    rTargetRange.getCenterY() - (0.5 * fScaleMin * aFullRange.getHeight()));
+            }
+            else
+            {
+                // just scale/translate needed
+                aRetval *= createScaleTranslateB2DHomMatrix(
+                    rTargetRange.getRange(),
+                    rTargetRange.getMinimum());
+            }
+
+            return aRetval;
+        }
+
+        /// special for the case to map from source range to target range
+        B2DHomMatrix createSourceRangeTargetRangeTransform(
+            const B2DRange& rSourceRange,
+            const B2DRange& rTargetRange)
+        {
+            B2DHomMatrix aRetval;
+
+            if(&rSourceRange == &rTargetRange)
+            {
+                return aRetval;
+            }
+
+            if(!fTools::equalZero(rSourceRange.getMinX()) || !fTools::equalZero(rSourceRange.getMinY()))
+            {
+                aRetval.set(0, 2, -rSourceRange.getMinX());
+                aRetval.set(1, 2, -rSourceRange.getMinY());
+            }
+
+            const double fSourceW(rSourceRange.getWidth());
+            const double fSourceH(rSourceRange.getHeight());
+            const bool bDivX(!fTools::equalZero(fSourceW) && !fTools::equal(fSourceW, 1.0));
+            const bool bDivY(!fTools::equalZero(fSourceH) && !fTools::equal(fSourceH, 1.0));
+            const double fScaleX(bDivX ? rTargetRange.getWidth() / fSourceW : rTargetRange.getWidth());
+            const double fScaleY(bDivY ? rTargetRange.getHeight() / fSourceH : rTargetRange.getHeight());
+
+            if(!fTools::equalZero(fScaleX) || !fTools::equalZero(fScaleY))
+            {
+                aRetval.scale(fScaleX, fScaleY);
+            }
+
+            if(!fTools::equalZero(rTargetRange.getMinX()) || !fTools::equalZero(rTargetRange.getMinY()))
+            {
+                aRetval.translate(
+                    rTargetRange.getMinX(),
+                    rTargetRange.getMinY());
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createCoordinateSystemTransform(
+            const B2DPoint& rOrigin,
+            const B2DVector& rX,
+            const B2DVector& rY)
+        {
+            return basegfx::B2DHomMatrix(
+                rX.getX(), rY.getX(), rOrigin.getX(),
+                rX.getY(), rY.getY(), rOrigin.getY());
+        }
+
+        B2DTuple getColumn(const B2DHomMatrix& rMatrix, sal_uInt16 nCol)
+        {
+            return B2DTuple(rMatrix.get(0, nCol), rMatrix.get(1, nCol));
+        }
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/matrix/b3dhommatrix.cxx b/basegfx/source/matrix/b3dhommatrix.cxx
new file mode 100644
index 0000000000..f9018c6979
--- /dev/null
+++ b/basegfx/source/matrix/b3dhommatrix.cxx
@@ -0,0 +1,546 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/matrix/hommatrixtemplate.hxx>
+#include <basegfx/vector/b3dvector.hxx>
+#include <memory>
+
+namespace basegfx
+{
+    typedef ::basegfx::internal::ImplHomMatrixTemplate< 4 >Impl3DHomMatrix_Base;
+    class Impl3DHomMatrix : public Impl3DHomMatrix_Base
+    {
+    };
+
+    B3DHomMatrix::B3DHomMatrix() = default;
+
+    B3DHomMatrix::B3DHomMatrix(const B3DHomMatrix&) = default;
+
+    B3DHomMatrix::B3DHomMatrix(B3DHomMatrix&&) = default;
+
+    B3DHomMatrix::~B3DHomMatrix() = default;
+
+    B3DHomMatrix& B3DHomMatrix::operator=(const B3DHomMatrix&) = default;
+
+    B3DHomMatrix& B3DHomMatrix::operator=(B3DHomMatrix&&) = default;
+
+    double B3DHomMatrix::get(sal_uInt16 nRow, sal_uInt16 nColumn) const
+    {
+        return mpImpl->get(nRow, nColumn);
+    }
+
+    void B3DHomMatrix::set(sal_uInt16 nRow, sal_uInt16 nColumn, double fValue)
+    {
+        mpImpl->set(nRow, nColumn, fValue);
+    }
+
+    bool B3DHomMatrix::isLastLineDefault() const
+    {
+        return mpImpl->isLastLineDefault();
+    }
+
+    bool B3DHomMatrix::isIdentity() const
+    {
+        return mpImpl->isIdentity();
+    }
+
+    void B3DHomMatrix::identity()
+    {
+        *mpImpl = Impl3DHomMatrix();
+    }
+
+    void B3DHomMatrix::invert()
+    {
+        Impl3DHomMatrix aWork(*mpImpl);
+        std::unique_ptr<sal_uInt16[]> pIndex( new sal_uInt16[Impl3DHomMatrix_Base::getEdgeLength()] );
+        sal_Int16 nParity;
+
+        if(aWork.ludcmp(pIndex.get(), nParity))
+        {
+            mpImpl->doInvert(aWork, pIndex.get());
+        }
+    }
+
+    double B3DHomMatrix::determinant() const
+    {
+        return mpImpl->doDeterminant();
+    }
+
+    B3DHomMatrix& B3DHomMatrix::operator+=(const B3DHomMatrix& rMat)
+    {
+        mpImpl->doAddMatrix(*rMat.mpImpl);
+        return *this;
+    }
+
+    B3DHomMatrix& B3DHomMatrix::operator-=(const B3DHomMatrix& rMat)
+    {
+        mpImpl->doSubMatrix(*rMat.mpImpl);
+        return *this;
+    }
+
+    B3DHomMatrix& B3DHomMatrix::operator*=(double fValue)
+    {
+        const double fOne(1.0);
+
+        if(!fTools::equal(fOne, fValue))
+            mpImpl->doMulMatrix(fValue);
+
+        return *this;
+    }
+
+    B3DHomMatrix& B3DHomMatrix::operator/=(double fValue)
+    {
+        const double fOne(1.0);
+
+        if(!fTools::equal(fOne, fValue))
+            mpImpl->doMulMatrix(1.0 / fValue);
+
+        return *this;
+    }
+
+    B3DHomMatrix& B3DHomMatrix::operator*=(const B3DHomMatrix& rMat)
+    {
+        if(rMat.isIdentity())
+        {
+            // multiply with identity, no change -> nothing to do
+        }
+        else if(isIdentity())
+        {
+            // we are identity, result will be rMat -> assign
+            *this = rMat;
+        }
+        else
+        {
+            // multiply
+            mpImpl->doMulMatrix(*rMat.mpImpl);
+        }
+        return *this;
+    }
+
+    bool B3DHomMatrix::operator==(const B3DHomMatrix& rMat) const
+    {
+        if(mpImpl.same_object(rMat.mpImpl))
+            return true;
+
+        return mpImpl->isEqual(*rMat.mpImpl);
+    }
+
+    bool B3DHomMatrix::operator!=(const B3DHomMatrix& rMat) const
+    {
+        return !(*this == rMat);
+    }
+
+    void B3DHomMatrix::rotate(double fAngleX,double fAngleY,double fAngleZ)
+    {
+        if(fTools::equalZero(fAngleX) && fTools::equalZero(fAngleY) && fTools::equalZero(fAngleZ))
+            return;
+
+        if(!fTools::equalZero(fAngleX))
+        {
+            Impl3DHomMatrix aRotMatX;
+            double fSin(sin(fAngleX));
+            double fCos(cos(fAngleX));
+
+            aRotMatX.set(1, 1, fCos);
+            aRotMatX.set(2, 2, fCos);
+            aRotMatX.set(2, 1, fSin);
+            aRotMatX.set(1, 2, -fSin);
+
+            mpImpl->doMulMatrix(aRotMatX);
+        }
+
+        if(!fTools::equalZero(fAngleY))
+        {
+            Impl3DHomMatrix aRotMatY;
+            double fSin(sin(fAngleY));
+            double fCos(cos(fAngleY));
+
+            aRotMatY.set(0, 0, fCos);
+            aRotMatY.set(2, 2, fCos);
+            aRotMatY.set(0, 2, fSin);
+            aRotMatY.set(2, 0, -fSin);
+
+            mpImpl->doMulMatrix(aRotMatY);
+        }
+
+        if(fTools::equalZero(fAngleZ))
+            return;
+
+        Impl3DHomMatrix aRotMatZ;
+        double fSin(sin(fAngleZ));
+        double fCos(cos(fAngleZ));
+
+        aRotMatZ.set(0, 0, fCos);
+        aRotMatZ.set(1, 1, fCos);
+        aRotMatZ.set(1, 0, fSin);
+        aRotMatZ.set(0, 1, -fSin);
+
+        mpImpl->doMulMatrix(aRotMatZ);
+    }
+
+    void B3DHomMatrix::rotate(const B3DTuple& rRotation)
+    {
+        rotate(rRotation.getX(), rRotation.getY(), rRotation.getZ());
+    }
+
+    void B3DHomMatrix::translate(double fX, double fY, double fZ)
+    {
+        if(!fTools::equalZero(fX) || !fTools::equalZero(fY) || !fTools::equalZero(fZ))
+        {
+            Impl3DHomMatrix aTransMat;
+
+            aTransMat.set(0, 3, fX);
+            aTransMat.set(1, 3, fY);
+            aTransMat.set(2, 3, fZ);
+
+            mpImpl->doMulMatrix(aTransMat);
+        }
+    }
+
+    void B3DHomMatrix::translate(const B3DTuple& rRotation)
+    {
+        translate(rRotation.getX(), rRotation.getY(), rRotation.getZ());
+    }
+
+    void B3DHomMatrix::scale(double fX, double fY, double fZ)
+    {
+        const double fOne(1.0);
+
+        if(!fTools::equal(fOne, fX) || !fTools::equal(fOne, fY) ||!fTools::equal(fOne, fZ))
+        {
+            Impl3DHomMatrix aScaleMat;
+
+            aScaleMat.set(0, 0, fX);
+            aScaleMat.set(1, 1, fY);
+            aScaleMat.set(2, 2, fZ);
+
+            mpImpl->doMulMatrix(aScaleMat);
+        }
+    }
+
+    void B3DHomMatrix::scale(const B3DTuple& rRotation)
+    {
+        scale(rRotation.getX(), rRotation.getY(), rRotation.getZ());
+    }
+
+    void B3DHomMatrix::shearXY(double fSx, double fSy)
+    {
+        // #i76239# do not test against 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
+        if(!fTools::equalZero(fSx) || !fTools::equalZero(fSy))
+        {
+            Impl3DHomMatrix aShearXYMat;
+
+            aShearXYMat.set(0, 2, fSx);
+            aShearXYMat.set(1, 2, fSy);
+
+            mpImpl->doMulMatrix(aShearXYMat);
+        }
+    }
+
+    void B3DHomMatrix::shearXZ(double fSx, double fSz)
+    {
+        // #i76239# do not test against 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
+        if(!fTools::equalZero(fSx) || !fTools::equalZero(fSz))
+        {
+            Impl3DHomMatrix aShearXZMat;
+
+            aShearXZMat.set(0, 1, fSx);
+            aShearXZMat.set(2, 1, fSz);
+
+            mpImpl->doMulMatrix(aShearXZMat);
+        }
+    }
+    void B3DHomMatrix::frustum(double fLeft, double fRight, double fBottom, double fTop, double fNear, double fFar)
+    {
+        const double fZero(0.0);
+        const double fOne(1.0);
+
+        if(!fTools::more(fNear, fZero))
+        {
+            fNear = 0.001;
+        }
+
+        if(!fTools::more(fFar, fZero))
+        {
+            fFar = fOne;
+        }
+
+        if(fTools::equal(fNear, fFar))
+        {
+            fFar = fNear + fOne;
+        }
+
+        if(fTools::equal(fLeft, fRight))
+        {
+            fLeft -= fOne;
+            fRight += fOne;
+        }
+
+        if(fTools::equal(fTop, fBottom))
+        {
+            fBottom -= fOne;
+            fTop += fOne;
+        }
+
+        Impl3DHomMatrix aFrustumMat;
+
+        aFrustumMat.set(0, 0, 2.0 * fNear / (fRight - fLeft));
+        aFrustumMat.set(1, 1, 2.0 * fNear / (fTop - fBottom));
+        aFrustumMat.set(0, 2, (fRight + fLeft) / (fRight - fLeft));
+        aFrustumMat.set(1, 2, (fTop + fBottom) / (fTop - fBottom));
+        aFrustumMat.set(2, 2, -fOne * ((fFar + fNear) / (fFar - fNear)));
+        aFrustumMat.set(3, 2, -fOne);
+        aFrustumMat.set(2, 3, -fOne * ((2.0 * fFar * fNear) / (fFar - fNear)));
+        aFrustumMat.set(3, 3, fZero);
+
+        mpImpl->doMulMatrix(aFrustumMat);
+    }
+
+    void B3DHomMatrix::ortho(double fLeft, double fRight, double fBottom, double fTop, double fNear, double fFar)
+    {
+        if(fTools::equal(fNear, fFar))
+        {
+            fFar = fNear + 1.0;
+        }
+
+        if(fTools::equal(fLeft, fRight))
+        {
+            fLeft -= 1.0;
+            fRight += 1.0;
+        }
+
+        if(fTools::equal(fTop, fBottom))
+        {
+            fBottom -= 1.0;
+            fTop += 1.0;
+        }
+
+        Impl3DHomMatrix aOrthoMat;
+
+        aOrthoMat.set(0, 0, 2.0 / (fRight - fLeft));
+        aOrthoMat.set(1, 1, 2.0 / (fTop - fBottom));
+        aOrthoMat.set(2, 2, -1.0 * (2.0 / (fFar - fNear)));
+        aOrthoMat.set(0, 3, -1.0 * ((fRight + fLeft) / (fRight - fLeft)));
+        aOrthoMat.set(1, 3, -1.0 * ((fTop + fBottom) / (fTop - fBottom)));
+        aOrthoMat.set(2, 3, -1.0 * ((fFar + fNear) / (fFar - fNear)));
+
+        mpImpl->doMulMatrix(aOrthoMat);
+    }
+
+    void B3DHomMatrix::orientation(const B3DPoint& rVRP, B3DVector aVPN, B3DVector aVUV)
+    {
+        Impl3DHomMatrix aOrientationMat;
+
+        // translate -VRP
+        aOrientationMat.set(0, 3, -rVRP.getX());
+        aOrientationMat.set(1, 3, -rVRP.getY());
+        aOrientationMat.set(2, 3, -rVRP.getZ());
+
+        // build rotation
+        aVUV.normalize();
+        aVPN.normalize();
+
+        // build x-axis as perpendicular from aVUV and aVPN
+        B3DVector aRx(aVUV.getPerpendicular(aVPN));
+        aRx.normalize();
+
+        // y-axis perpendicular to that
+        B3DVector aRy(aVPN.getPerpendicular(aRx));
+        aRy.normalize();
+
+        // the calculated normals are the line vectors of the rotation matrix,
+        // set them to create rotation
+        aOrientationMat.set(0, 0, aRx.getX());
+        aOrientationMat.set(0, 1, aRx.getY());
+        aOrientationMat.set(0, 2, aRx.getZ());
+        aOrientationMat.set(1, 0, aRy.getX());
+        aOrientationMat.set(1, 1, aRy.getY());
+        aOrientationMat.set(1, 2, aRy.getZ());
+        aOrientationMat.set(2, 0, aVPN.getX());
+        aOrientationMat.set(2, 1, aVPN.getY());
+        aOrientationMat.set(2, 2, aVPN.getZ());
+
+        mpImpl->doMulMatrix(aOrientationMat);
+    }
+
+    void B3DHomMatrix::decompose(B3DTuple& rScale, B3DTuple& rTranslate, B3DTuple& rRotate, B3DTuple& rShear) const
+    {
+        // when perspective is used, decompose is not made here
+        if(!mpImpl->isLastLineDefault())
+            return;
+
+        // If determinant is zero, decomposition is not possible
+        if(determinant() == 0.0)
+            return;
+
+        // isolate translation
+        rTranslate.setX(mpImpl->get(0, 3));
+        rTranslate.setY(mpImpl->get(1, 3));
+        rTranslate.setZ(mpImpl->get(2, 3));
+
+        // correct translate values
+        rTranslate.correctValues();
+
+        // get scale and shear
+        B3DVector aCol0(mpImpl->get(0, 0), mpImpl->get(1, 0), mpImpl->get(2, 0));
+        B3DVector aCol1(mpImpl->get(0, 1), mpImpl->get(1, 1), mpImpl->get(2, 1));
+        B3DVector aCol2(mpImpl->get(0, 2), mpImpl->get(1, 2), mpImpl->get(2, 2));
+        B3DVector aTemp;
+
+        // get ScaleX
+        rScale.setX(aCol0.getLength());
+        aCol0.normalize();
+
+        // get ShearXY
+        rShear.setX(aCol0.scalar(aCol1));
+
+        if(fTools::equalZero(rShear.getX()))
+        {
+            rShear.setX(0.0);
+        }
+        else
+        {
+            aTemp.setX(aCol1.getX() - rShear.getX() * aCol0.getX());
+            aTemp.setY(aCol1.getY() - rShear.getX() * aCol0.getY());
+            aTemp.setZ(aCol1.getZ() - rShear.getX() * aCol0.getZ());
+            aCol1 = aTemp;
+        }
+
+        // get ScaleY
+        rScale.setY(aCol1.getLength());
+        aCol1.normalize();
+
+        const double fShearX(rShear.getX());
+
+        if(!fTools::equalZero(fShearX))
+        {
+            rShear.setX(rShear.getX() / rScale.getY());
+        }
+
+        // get ShearXZ
+        rShear.setY(aCol0.scalar(aCol2));
+
+        if(fTools::equalZero(rShear.getY()))
+        {
+            rShear.setY(0.0);
+        }
+        else
+        {
+            aTemp.setX(aCol2.getX() - rShear.getY() * aCol0.getX());
+            aTemp.setY(aCol2.getY() - rShear.getY() * aCol0.getY());
+            aTemp.setZ(aCol2.getZ() - rShear.getY() * aCol0.getZ());
+            aCol2 = aTemp;
+        }
+
+        // get ShearYZ
+        rShear.setZ(aCol1.scalar(aCol2));
+
+        if(fTools::equalZero(rShear.getZ()))
+        {
+            rShear.setZ(0.0);
+        }
+        else
+        {
+            aTemp.setX(aCol2.getX() - rShear.getZ() * aCol1.getX());
+            aTemp.setY(aCol2.getY() - rShear.getZ() * aCol1.getY());
+            aTemp.setZ(aCol2.getZ() - rShear.getZ() * aCol1.getZ());
+            aCol2 = aTemp;
+        }
+
+        // get ScaleZ
+        rScale.setZ(aCol2.getLength());
+        aCol2.normalize();
+
+        const double fShearY(rShear.getY());
+
+        if(!fTools::equalZero(fShearY))
+        {
+            // coverity[copy_paste_error : FALSE] - this is correct getZ, not getY
+            rShear.setY(rShear.getY() / rScale.getZ());
+        }
+
+        const double fShearZ(rShear.getZ());
+
+        if(!fTools::equalZero(fShearZ))
+        {
+            // coverity[original] - this is not an original copy-and-paste source for ^^^
+            rShear.setZ(rShear.getZ() / rScale.getZ());
+        }
+
+        // correct shear values
+        rShear.correctValues();
+
+        // Coordinate system flip?
+        if(0.0 > aCol0.scalar(aCol1.getPerpendicular(aCol2)))
+        {
+            rScale = -rScale;
+            aCol0 = -aCol0;
+            aCol1 = -aCol1;
+            aCol2 = -aCol2;
+        }
+
+        // correct scale values
+        rScale.correctValues(1.0);
+
+        // Get rotations
+        {
+            double fy=0;
+            double cy=0;
+
+            if( ::basegfx::fTools::equal( aCol0.getZ(), 1.0 )
+                || aCol0.getZ() > 1.0 )
+            {
+                fy = -M_PI/2.0;
+                cy = 0.0;
+            }
+            else if( ::basegfx::fTools::equal( aCol0.getZ(), -1.0 )
+                || aCol0.getZ() < -1.0 )
+            {
+                fy = M_PI/2.0;
+                cy = 0.0;
+            }
+            else
+            {
+                fy = asin( -aCol0.getZ() );
+                cy = cos(fy);
+            }
+
+            rRotate.setY(fy);
+            if( ::basegfx::fTools::equalZero( cy ) )
+            {
+                if( aCol0.getZ() > 0.0 )
+                    rRotate.setX(atan2(-1.0*aCol1.getX(), aCol1.getY()));
+                else
+                    rRotate.setX(atan2(aCol1.getX(), aCol1.getY()));
+                rRotate.setZ(0.0);
+            }
+            else
+            {
+                rRotate.setX(atan2(aCol1.getZ(), aCol2.getZ()));
+                rRotate.setZ(atan2(aCol0.getY(), aCol0.getX()));
+            }
+
+            // correct rotate values
+            rRotate.correctValues();
+        }
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/matrix/b3dhommatrixtools.cxx b/basegfx/source/matrix/b3dhommatrixtools.cxx
new file mode 100644
index 0000000000..9125aca4e0
--- /dev/null
+++ b/basegfx/source/matrix/b3dhommatrixtools.cxx
@@ -0,0 +1,71 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/matrix/b3dhommatrixtools.hxx>
+#include <com/sun/star/drawing/HomogenMatrix.hpp>
+
+namespace basegfx::utils
+{
+B3DHomMatrix UnoHomogenMatrixToB3DHomMatrix(const com::sun::star::drawing::HomogenMatrix& rMatrixIn)
+{
+    B3DHomMatrix aRetval;
+
+    aRetval.set(0, 0, rMatrixIn.Line1.Column1);
+    aRetval.set(0, 1, rMatrixIn.Line1.Column2);
+    aRetval.set(0, 2, rMatrixIn.Line1.Column3);
+    aRetval.set(0, 3, rMatrixIn.Line1.Column4);
+    aRetval.set(1, 0, rMatrixIn.Line2.Column1);
+    aRetval.set(1, 1, rMatrixIn.Line2.Column2);
+    aRetval.set(1, 2, rMatrixIn.Line2.Column3);
+    aRetval.set(1, 3, rMatrixIn.Line2.Column4);
+    aRetval.set(2, 0, rMatrixIn.Line3.Column1);
+    aRetval.set(2, 1, rMatrixIn.Line3.Column2);
+    aRetval.set(2, 2, rMatrixIn.Line3.Column3);
+    aRetval.set(2, 3, rMatrixIn.Line3.Column4);
+    aRetval.set(3, 0, rMatrixIn.Line4.Column1);
+    aRetval.set(3, 1, rMatrixIn.Line4.Column2);
+    aRetval.set(3, 2, rMatrixIn.Line4.Column3);
+    aRetval.set(3, 3, rMatrixIn.Line4.Column4);
+
+    return aRetval;
+}
+
+void B3DHomMatrixToUnoHomogenMatrix(const B3DHomMatrix& rMatrixIn,
+                                    com::sun::star::drawing::HomogenMatrix& rMatrixOut)
+{
+    rMatrixOut.Line1.Column1 = rMatrixIn.get(0, 0);
+    rMatrixOut.Line1.Column2 = rMatrixIn.get(0, 1);
+    rMatrixOut.Line1.Column3 = rMatrixIn.get(0, 2);
+    rMatrixOut.Line1.Column4 = rMatrixIn.get(0, 3);
+    rMatrixOut.Line2.Column1 = rMatrixIn.get(1, 0);
+    rMatrixOut.Line2.Column2 = rMatrixIn.get(1, 1);
+    rMatrixOut.Line2.Column3 = rMatrixIn.get(1, 2);
+    rMatrixOut.Line2.Column4 = rMatrixIn.get(1, 3);
+    rMatrixOut.Line3.Column1 = rMatrixIn.get(2, 0);
+    rMatrixOut.Line3.Column2 = rMatrixIn.get(2, 1);
+    rMatrixOut.Line3.Column3 = rMatrixIn.get(2, 2);
+    rMatrixOut.Line3.Column4 = rMatrixIn.get(2, 3);
+    rMatrixOut.Line4.Column1 = rMatrixIn.get(3, 0);
+    rMatrixOut.Line4.Column2 = rMatrixIn.get(3, 1);
+    rMatrixOut.Line4.Column3 = rMatrixIn.get(3, 2);
+    rMatrixOut.Line4.Column4 = rMatrixIn.get(3, 3);
+}
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/numeric/ftools.cxx b/basegfx/source/numeric/ftools.cxx
new file mode 100644
index 0000000000..246d8d548a
--- /dev/null
+++ b/basegfx/source/numeric/ftools.cxx
@@ -0,0 +1,135 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    double snapToNearestMultiple(double v, const double fStep)
+    {
+        if(fTools::equalZero(fStep))
+        {
+            // with a zero step, all snaps to 0.0
+            return 0.0;
+        }
+        else
+        {
+            const double fHalfStep(fStep * 0.5);
+            const double fChange(fHalfStep - fmod(v + fHalfStep, fStep));
+
+            if(basegfx::fTools::equal(fabs(v), fabs(fChange)))
+            {
+                return 0.0;
+            }
+            else
+            {
+                return v + fChange;
+            }
+        }
+    }
+
+    double snapToZeroRange(double v, double fWidth)
+    {
+        if(fTools::equalZero(fWidth))
+        {
+            // with no range all snaps to range bound
+            return 0.0;
+        }
+        else
+        {
+            if(v < 0.0 || v > fWidth)
+            {
+                double fRetval(fmod(v, fWidth));
+
+                if(fRetval < 0.0)
+                {
+                    fRetval += fWidth;
+                }
+
+                return fRetval;
+            }
+            else
+            {
+                return v;
+            }
+        }
+    }
+
+    double snapToRange(double v, double fLow, double fHigh)
+    {
+        if(fTools::equal(fLow, fHigh))
+        {
+            // with no range all snaps to range bound
+            return 0.0;
+        }
+        else
+        {
+            if(fLow > fHigh)
+            {
+                // correct range order. Evtl. assert this (?)
+                std::swap(fLow, fHigh);
+            }
+
+            if(v < fLow || v > fHigh)
+            {
+                return snapToZeroRange(v - fLow, fHigh - fLow) + fLow;
+            }
+            else
+            {
+                return v;
+            }
+        }
+    }
+
+    double normalizeToRange(double v, const double fRange)
+    {
+        if(fTools::lessOrEqual(fRange, 0.0))
+        {
+            // with a zero (or less) range, all normalizes to 0.0
+            return 0.0;
+        }
+
+        const bool bNegative(fTools::less(v, 0.0));
+
+        if(bNegative)
+        {
+            if(fTools::moreOrEqual(v, -fRange))
+            {
+                // in range [-fRange, 0.0[, shift one step
+                return v + fRange;
+            }
+
+            // re-calculate
+            return v - (floor(v/fRange)*fRange);
+        }
+        else
+        {
+            if(fTools::less(v, fRange))
+            {
+                // already in range [0.0, fRange[, nothing to do
+                return v;
+            }
+
+            // re-calculate
+            return v - (floor(v/fRange)*fRange);
+        }
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/point/b2dpoint.cxx b/basegfx/source/point/b2dpoint.cxx
new file mode 100644
index 0000000000..d12c3dd04c
--- /dev/null
+++ b/basegfx/source/point/b2dpoint.cxx
@@ -0,0 +1,51 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    B2DPoint& B2DPoint::operator*=( const ::basegfx::B2DHomMatrix& rMat )
+    {
+        double fTempX(
+            rMat.get(0, 0) * mnX +
+            rMat.get(0, 1) * mnY +
+            rMat.get(0, 2));
+        double fTempY(
+            rMat.get(1, 0) * mnX +
+            rMat.get(1, 1) * mnY +
+            rMat.get(1, 2));
+
+        mnX = fTempX;
+        mnY = fTempY;
+
+        return *this;
+    }
+
+    B2DPoint operator*( const ::basegfx::B2DHomMatrix& rMat, const B2DPoint& rPoint )
+    {
+        B2DPoint aRes( rPoint );
+        aRes *= rMat;
+        return aRes;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/point/b2ipoint.cxx b/basegfx/source/point/b2ipoint.cxx
new file mode 100644
index 0000000000..2790fe3a18
--- /dev/null
+++ b/basegfx/source/point/b2ipoint.cxx
@@ -0,0 +1,51 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/point/b2ipoint.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    B2IPoint& B2IPoint::operator=( const ::basegfx::B2ITuple& rPoint )
+    {
+        mnX = rPoint.getX();
+        mnY = rPoint.getY();
+        return *this;
+    }
+
+    B2IPoint& B2IPoint::operator*=( const ::basegfx::B2DHomMatrix& rMat )
+    {
+        double fTempX(
+            rMat.get(0, 0) * mnX +
+            rMat.get(0, 1) * mnY +
+            rMat.get(0, 2));
+        double fTempY(
+            rMat.get(1, 0) * mnX +
+            rMat.get(1, 1) * mnY +
+            rMat.get(1, 2));
+
+        mnX = fround(fTempX);
+        mnY = fround(fTempY);
+
+        return *this;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/point/b3dpoint.cxx b/basegfx/source/point/b3dpoint.cxx
new file mode 100644
index 0000000000..7d2d4cf4a2
--- /dev/null
+++ b/basegfx/source/point/b3dpoint.cxx
@@ -0,0 +1,76 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/point/b3dpoint.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    B3DPoint& B3DPoint::operator*=( const ::basegfx::B3DHomMatrix& rMat )
+    {
+        double fTempX(
+            rMat.get(0, 0) * mnX +
+            rMat.get(0, 1) * mnY +
+            rMat.get(0, 2) * mnZ +
+            rMat.get(0, 3));
+        double fTempY(
+            rMat.get(1, 0) * mnX +
+            rMat.get(1, 1) * mnY +
+            rMat.get(1, 2) * mnZ +
+            rMat.get(1, 3));
+        double fTempZ(
+            rMat.get(2, 0) * mnX +
+            rMat.get(2, 1) * mnY +
+            rMat.get(2, 2) * mnZ +
+            rMat.get(2, 3));
+
+        if(!rMat.isLastLineDefault())
+        {
+            const double fOne(1.0);
+            const double fTempM(
+                rMat.get(3, 0) * mnX +
+                rMat.get(3, 1) * mnY +
+                rMat.get(3, 2) * mnZ +
+                rMat.get(3, 3));
+
+            if(!fTools::equalZero(fTempM) && !fTools::equal(fOne, fTempM))
+            {
+                fTempX /= fTempM;
+                fTempY /= fTempM;
+                fTempZ /= fTempM;
+            }
+        }
+
+        mnX = fTempX;
+        mnY = fTempY;
+        mnZ = fTempZ;
+
+        return *this;
+    }
+
+    B3DPoint operator*( const ::basegfx::B3DHomMatrix& rMat, const B3DPoint& rPoint )
+    {
+        B3DPoint aRes( rPoint );
+        aRes *= rMat;
+        return aRes;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/WaveLine.cxx b/basegfx/source/polygon/WaveLine.cxx
new file mode 100644
index 0000000000..bc85c45362
--- /dev/null
+++ b/basegfx/source/polygon/WaveLine.cxx
@@ -0,0 +1,52 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ */
+
+#include <basegfx/polygon/WaveLine.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+
+namespace basegfx
+{
+BASEGFX_DLLPUBLIC B2DPolygon createWaveLinePolygon(basegfx::B2DRectangle const& rRectangle)
+{
+    basegfx::B2DPolygon aPolygon;
+
+    double fWaveHeight = rRectangle.getHeight();
+    // Wavelength depends on the wave height so it looks nice
+    double fHalfWaveLength = fWaveHeight + 1.0;
+    double fWaveAmplitude = fWaveHeight / 2.0;
+
+    double fLastX = rRectangle.getMinX();
+    double fBaseY = rRectangle.getMinY() + fWaveAmplitude;
+    double fDirection = 1.0;
+
+    // In quadratic bezier the curve is 1/2 of the control height
+    // so we need to compensate for that.
+    constexpr double fHeightCompensation = 2.0;
+
+    aPolygon.append(basegfx::B2DPoint(fLastX, fBaseY));
+
+    for (double fI = fHalfWaveLength; fI <= rRectangle.getWidth(); fI += fHalfWaveLength)
+    {
+        basegfx::B2DPoint aPoint(fLastX + fHalfWaveLength, fBaseY);
+        basegfx::B2DPoint aControl(fLastX + (fHalfWaveLength / 2.0),
+                                   fBaseY + fDirection * fWaveAmplitude * fHeightCompensation);
+
+        aPolygon.appendQuadraticBezierSegment(aControl, aPoint);
+
+        fLastX = aPoint.getX(); // next iteration
+        fDirection *= -1.0; // fDirection iterates between 1 and -1
+    }
+
+    return aPolygon;
+}
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dlinegeometry.cxx b/basegfx/source/polygon/b2dlinegeometry.cxx
new file mode 100644
index 0000000000..437ebcbb49
--- /dev/null
+++ b/basegfx/source/polygon/b2dlinegeometry.cxx
@@ -0,0 +1,998 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <osl/diagnose.h>
+#include <sal/log.hxx>
+#include <basegfx/polygon/b2dlinegeometry.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+#include <com/sun/star/drawing/LineCap.hpp>
+#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
+#include <basegfx/polygon/b2dpolygontriangulator.hxx>
+
+namespace basegfx::utils
+{
+        B2DPolyPolygon createAreaGeometryForLineStartEnd(
+            const B2DPolygon& rCandidate,
+            const B2DPolyPolygon& rArrow,
+            bool bStart,
+            double fWidth,
+            double fCandidateLength,
+            double fDockingPosition, // 0->top, 1->bottom
+            double* pConsumedLength,
+            double fShift)
+        {
+            B2DPolyPolygon aRetval;
+            assert((rCandidate.count() > 1) && "createAreaGeometryForLineStartEnd: Line polygon has too few points");
+            assert((rArrow.count() > 0) && "createAreaGeometryForLineStartEnd: Empty arrow utils::PolyPolygon");
+            assert((fWidth > 0.0) && "createAreaGeometryForLineStartEnd: Width too small");
+            assert((fDockingPosition >= 0.0 && fDockingPosition <= 1.0) &&
+                "createAreaGeometryForLineStartEnd: fDockingPosition out of range [0.0 .. 1.0]");
+
+            if(fWidth < 0.0)
+            {
+                fWidth = -fWidth;
+            }
+
+            if(rCandidate.count() > 1 && rArrow.count() && !fTools::equalZero(fWidth))
+            {
+                if(fDockingPosition < 0.0)
+                {
+                    fDockingPosition = 0.0;
+                }
+                else if(fDockingPosition > 1.0)
+                {
+                    fDockingPosition = 1.0;
+                }
+
+                // init return value from arrow
+                aRetval.append(rArrow);
+
+                // get size of the arrow
+                const B2DRange aArrowSize(getRange(rArrow));
+
+                // build ArrowTransform; center in X, align with axis in Y
+                B2DHomMatrix aArrowTransform(basegfx::utils::createTranslateB2DHomMatrix(
+                    -aArrowSize.getCenter().getX(), -aArrowSize.getMinimum().getY()));
+
+                // scale to target size
+                const double fArrowScale(fWidth / (aArrowSize.getWidth()));
+                aArrowTransform.scale(fArrowScale, fArrowScale);
+
+                // get arrow size in Y
+                B2DPoint aUpperCenter(aArrowSize.getCenter().getX(), aArrowSize.getMaximum().getY());
+                aUpperCenter *= aArrowTransform;
+                const double fArrowYLength(B2DVector(aUpperCenter).getLength());
+
+                // move arrow to have docking position centered
+                aArrowTransform.translate(0.0, -fArrowYLength * fDockingPosition + fShift);
+
+                // prepare polygon length
+                if(fTools::equalZero(fCandidateLength))
+                {
+                    fCandidateLength = getLength(rCandidate);
+                }
+
+                // get the polygon vector we want to plant this arrow on
+                const double fConsumedLength(fArrowYLength * (1.0 - fDockingPosition) - fShift);
+                const B2DVector aHead(rCandidate.getB2DPoint(bStart ? 0 : rCandidate.count() - 1));
+                const B2DVector aTail(getPositionAbsolute(rCandidate,
+                    bStart ? fConsumedLength : fCandidateLength - fConsumedLength, fCandidateLength));
+
+                // from that vector, take the needed rotation and add rotate for arrow to transformation
+                const B2DVector aTargetDirection(aHead - aTail);
+                const double fRotation(atan2(aTargetDirection.getY(), aTargetDirection.getX()) + M_PI_2);
+
+                // rotate around docking position
+                aArrowTransform.rotate(fRotation);
+
+                // move arrow docking position to polygon head
+                aArrowTransform.translate(aHead.getX(), aHead.getY());
+
+                // transform retval and close
+                aRetval.transform(aArrowTransform);
+                aRetval.setClosed(true);
+
+                // if pConsumedLength is asked for, fill it
+                if(pConsumedLength)
+                {
+                    *pConsumedLength = fConsumedLength;
+                }
+            }
+
+            return aRetval;
+        }
+} // end of namespace
+
+namespace basegfx
+{
+    // anonymous namespace for local helpers
+    namespace
+    {
+        bool impIsSimpleEdge(const B2DCubicBezier& rCandidate, double fMaxCosQuad, double fMaxPartOfEdgeQuad)
+        {
+            // isBezier() is true, already tested by caller
+            const B2DVector aEdge(rCandidate.getEndPoint() - rCandidate.getStartPoint());
+
+            if(aEdge.equalZero())
+            {
+                // start and end point the same, but control vectors used -> balloon curve loop
+                // is not a simple edge
+                return false;
+            }
+
+            // get tangentA and scalar with edge
+            const B2DVector aTangentA(rCandidate.getTangent(0.0));
+            const double fScalarAE(aEdge.scalar(aTangentA));
+
+            if(fTools::lessOrEqual(fScalarAE, 0.0))
+            {
+                // angle between TangentA and Edge is bigger or equal 90 degrees
+                return false;
+            }
+
+            // get self-scalars for E and A
+            const double fScalarE(aEdge.scalar(aEdge));
+            const double fScalarA(aTangentA.scalar(aTangentA));
+            const double fLengthCompareE(fScalarE * fMaxPartOfEdgeQuad);
+
+            if(fTools::moreOrEqual(fScalarA, fLengthCompareE))
+            {
+                // length of TangentA is more than fMaxPartOfEdge of length of edge
+                return false;
+            }
+
+            if(fTools::lessOrEqual(fScalarAE * fScalarAE, fScalarA * fScalarE * fMaxCosQuad))
+            {
+                // angle between TangentA and Edge is bigger or equal angle defined by fMaxCos
+                return false;
+            }
+
+            // get tangentB and scalar with edge
+            const B2DVector aTangentB(rCandidate.getTangent(1.0));
+            const double fScalarBE(aEdge.scalar(aTangentB));
+
+            if(fTools::lessOrEqual(fScalarBE, 0.0))
+            {
+                // angle between TangentB and Edge is bigger or equal 90 degrees
+                return false;
+            }
+
+            // get self-scalar for B
+            const double fScalarB(aTangentB.scalar(aTangentB));
+
+            if(fTools::moreOrEqual(fScalarB, fLengthCompareE))
+            {
+                // length of TangentB is more than fMaxPartOfEdge of length of edge
+                return false;
+            }
+
+            if(fTools::lessOrEqual(fScalarBE * fScalarBE, fScalarB * fScalarE * fMaxCosQuad))
+            {
+                // angle between TangentB and Edge is bigger or equal defined by fMaxCos
+                return false;
+            }
+
+            return true;
+        }
+
+        void impSubdivideToSimple(const B2DCubicBezier& rCandidate, B2DPolygon& rTarget, double fMaxCosQuad, double fMaxPartOfEdgeQuad, sal_uInt32 nMaxRecursionDepth)
+        {
+            if(!nMaxRecursionDepth || impIsSimpleEdge(rCandidate, fMaxCosQuad, fMaxPartOfEdgeQuad))
+            {
+                rTarget.appendBezierSegment(rCandidate.getControlPointA(), rCandidate.getControlPointB(), rCandidate.getEndPoint());
+            }
+            else
+            {
+                B2DCubicBezier aLeft, aRight;
+                rCandidate.split(0.5, &aLeft, &aRight);
+
+                impSubdivideToSimple(aLeft, rTarget, fMaxCosQuad, fMaxPartOfEdgeQuad, nMaxRecursionDepth - 1);
+                impSubdivideToSimple(aRight, rTarget, fMaxCosQuad, fMaxPartOfEdgeQuad, nMaxRecursionDepth - 1);
+            }
+        }
+
+        B2DPolygon subdivideToSimple(const B2DPolygon& rCandidate, double fMaxCosQuad, double fMaxPartOfEdgeQuad)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(rCandidate.areControlPointsUsed() && nPointCount)
+            {
+                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                B2DPolygon aRetval;
+                B2DCubicBezier aEdge;
+
+                // prepare edge for loop
+                aEdge.setStartPoint(rCandidate.getB2DPoint(0));
+                aRetval.append(aEdge.getStartPoint());
+
+                for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                {
+                    // fill B2DCubicBezier
+                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                    aEdge.setControlPointA(rCandidate.getNextControlPoint(a));
+                    aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                    aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+
+                    // get rid of unnecessary bezier segments
+                    aEdge.testAndSolveTrivialBezier();
+
+                    if(aEdge.isBezier())
+                    {
+                        // before splitting recursively with internal simple criteria, use
+                        // ExtremumPosFinder to remove those
+                        std::vector< double > aExtremumPositions;
+
+                        aExtremumPositions.reserve(4);
+                        aEdge.getAllExtremumPositions(aExtremumPositions);
+
+                        const sal_uInt32 nCount(aExtremumPositions.size());
+
+                        if(nCount)
+                        {
+                            if(nCount > 1)
+                            {
+                                // create order from left to right
+                                std::sort(aExtremumPositions.begin(), aExtremumPositions.end());
+                            }
+
+                            for(sal_uInt32 b(0); b < nCount;)
+                            {
+                                // split aEdge at next split pos
+                                B2DCubicBezier aLeft;
+                                const double fSplitPos(aExtremumPositions[b++]);
+
+                                aEdge.split(fSplitPos, &aLeft, &aEdge);
+                                aLeft.testAndSolveTrivialBezier();
+
+                                // consume left part
+                                if(aLeft.isBezier())
+                                {
+                                    impSubdivideToSimple(aLeft, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
+                                }
+                                else
+                                {
+                                    aRetval.append(aLeft.getEndPoint());
+                                }
+
+                                if(b < nCount)
+                                {
+                                    // correct the remaining split positions to fit to shortened aEdge
+                                    const double fScaleFactor(1.0 / (1.0 - fSplitPos));
+
+                                    for(sal_uInt32 c(b); c < nCount; c++)
+                                    {
+                                        aExtremumPositions[c] = (aExtremumPositions[c] - fSplitPos) * fScaleFactor;
+                                    }
+                                }
+                            }
+
+                            // test the shortened rest of aEdge
+                            aEdge.testAndSolveTrivialBezier();
+
+                            // consume right part
+                            if(aEdge.isBezier())
+                            {
+                                impSubdivideToSimple(aEdge, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
+                            }
+                            else
+                            {
+                                aRetval.append(aEdge.getEndPoint());
+                            }
+                        }
+                        else
+                        {
+                            impSubdivideToSimple(aEdge, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
+                        }
+                    }
+                    else
+                    {
+                        // straight edge, add point
+                        aRetval.append(aEdge.getEndPoint());
+                    }
+
+                    // prepare edge for next step
+                    aEdge.setStartPoint(aEdge.getEndPoint());
+                }
+
+                // copy closed flag and check for double points
+                aRetval.setClosed(rCandidate.isClosed());
+                aRetval.removeDoublePoints();
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolygon createAreaGeometryForEdge(
+            const B2DCubicBezier& rEdge,
+            double fHalfLineWidth,
+            bool bStartRound,
+            bool bEndRound,
+            bool bStartSquare,
+            bool bEndSquare,
+            basegfx::triangulator::B2DTriangleVector* pTriangles)
+        {
+            // create polygon for edge
+            // Unfortunately, while it would be geometrically correct to not add
+            // the in-between points EdgeEnd and EdgeStart, it leads to rounding
+            // errors when converting to integer polygon coordinates for painting
+            if(rEdge.isBezier())
+            {
+                // prepare target and data common for upper and lower
+                B2DPolygon aBezierPolygon;
+                const B2DVector aPureEdgeVector(rEdge.getEndPoint() - rEdge.getStartPoint());
+                const double fEdgeLength(aPureEdgeVector.getLength());
+                const bool bIsEdgeLengthZero(fTools::equalZero(fEdgeLength));
+                B2DVector aTangentA(rEdge.getTangent(0.0)); aTangentA.normalize();
+                B2DVector aTangentB(rEdge.getTangent(1.0)); aTangentB.normalize();
+                const B2DVector aNormalizedPerpendicularA(getPerpendicular(aTangentA));
+                const B2DVector aNormalizedPerpendicularB(getPerpendicular(aTangentB));
+
+                // create upper displacement vectors and check if they cut
+                const B2DVector aPerpendStartA(aNormalizedPerpendicularA * -fHalfLineWidth);
+                const B2DVector aPerpendEndA(aNormalizedPerpendicularB * -fHalfLineWidth);
+                double fCutA(0.0);
+                const CutFlagValue aCutA(utils::findCut(
+                    rEdge.getStartPoint(), aPerpendStartA,
+                    rEdge.getEndPoint(), aPerpendEndA,
+                    CutFlagValue::ALL, &fCutA));
+                const bool bCutA(aCutA != CutFlagValue::NONE);
+
+                // create lower displacement vectors and check if they cut
+                const B2DVector aPerpendStartB(aNormalizedPerpendicularA * fHalfLineWidth);
+                const B2DVector aPerpendEndB(aNormalizedPerpendicularB * fHalfLineWidth);
+                double fCutB(0.0);
+                const CutFlagValue aCutB(utils::findCut(
+                    rEdge.getEndPoint(), aPerpendEndB,
+                    rEdge.getStartPoint(), aPerpendStartB,
+                    CutFlagValue::ALL, &fCutB));
+                const bool bCutB(aCutB != CutFlagValue::NONE);
+
+                // check if cut happens
+                const bool bCut(bCutA || bCutB);
+                B2DPoint aCutPoint;
+
+                // create left edge
+                if(bStartRound || bStartSquare)
+                {
+                    if(bStartRound)
+                    {
+                        basegfx::B2DPolygon aStartPolygon(utils::createHalfUnitCircle());
+
+                        aStartPolygon.transform(
+                            utils::createScaleShearXRotateTranslateB2DHomMatrix(
+                                fHalfLineWidth, fHalfLineWidth,
+                                0.0,
+                                atan2(aTangentA.getY(), aTangentA.getX()) + M_PI_2,
+                                rEdge.getStartPoint().getX(), rEdge.getStartPoint().getY()));
+                        aBezierPolygon.append(aStartPolygon);
+                    }
+                    else // bStartSquare
+                    {
+                        const basegfx::B2DPoint aStart(rEdge.getStartPoint() - (aTangentA * fHalfLineWidth));
+
+                        if(bCutB)
+                        {
+                            aBezierPolygon.append(rEdge.getStartPoint() + aPerpendStartB);
+                        }
+
+                        aBezierPolygon.append(aStart + aPerpendStartB);
+                        aBezierPolygon.append(aStart + aPerpendStartA);
+
+                        if(bCutA)
+                        {
+                            aBezierPolygon.append(rEdge.getStartPoint() + aPerpendStartA);
+                        }
+                    }
+                }
+                else
+                {
+                    // append original in-between point
+                    aBezierPolygon.append(rEdge.getStartPoint());
+                }
+
+                // create upper edge.
+                {
+                    if(bCutA)
+                    {
+                        // calculate cut point and add
+                        aCutPoint = rEdge.getStartPoint() + (aPerpendStartA * fCutA);
+                        aBezierPolygon.append(aCutPoint);
+                    }
+                    else
+                    {
+                        // create scaled bezier segment
+                        const B2DPoint aStart(rEdge.getStartPoint() + aPerpendStartA);
+                        const B2DPoint aEnd(rEdge.getEndPoint() + aPerpendEndA);
+                        const B2DVector aEdge(aEnd - aStart);
+                        const double fLength(aEdge.getLength());
+                        const double fScale(bIsEdgeLengthZero ? 1.0 : fLength / fEdgeLength);
+                        const B2DVector fRelNext(rEdge.getControlPointA() - rEdge.getStartPoint());
+                        const B2DVector fRelPrev(rEdge.getControlPointB() - rEdge.getEndPoint());
+
+                        aBezierPolygon.append(aStart);
+                        aBezierPolygon.appendBezierSegment(aStart + (fRelNext * fScale), aEnd + (fRelPrev * fScale), aEnd);
+                    }
+                }
+
+                // create right edge
+                if(bEndRound || bEndSquare)
+                {
+                    if(bEndRound)
+                    {
+                        basegfx::B2DPolygon aEndPolygon(utils::createHalfUnitCircle());
+
+                        aEndPolygon.transform(
+                            utils::createScaleShearXRotateTranslateB2DHomMatrix(
+                                fHalfLineWidth, fHalfLineWidth,
+                                0.0,
+                                atan2(aTangentB.getY(), aTangentB.getX()) - M_PI_2,
+                                rEdge.getEndPoint().getX(), rEdge.getEndPoint().getY()));
+                        aBezierPolygon.append(aEndPolygon);
+                    }
+                    else // bEndSquare
+                    {
+                        const basegfx::B2DPoint aEnd(rEdge.getEndPoint() + (aTangentB * fHalfLineWidth));
+
+                        if(bCutA)
+                        {
+                            aBezierPolygon.append(rEdge.getEndPoint() + aPerpendEndA);
+                        }
+
+                        aBezierPolygon.append(aEnd + aPerpendEndA);
+                        aBezierPolygon.append(aEnd + aPerpendEndB);
+
+                        if(bCutB)
+                        {
+                            aBezierPolygon.append(rEdge.getEndPoint() + aPerpendEndB);
+                        }
+                    }
+                }
+                else
+                {
+                    // append original in-between point
+                    aBezierPolygon.append(rEdge.getEndPoint());
+                }
+
+                // create lower edge.
+                {
+                    if(bCutB)
+                    {
+                        // calculate cut point and add
+                        aCutPoint = rEdge.getEndPoint() + (aPerpendEndB * fCutB);
+                        aBezierPolygon.append(aCutPoint);
+                    }
+                    else
+                    {
+                        // create scaled bezier segment
+                        const B2DPoint aStart(rEdge.getEndPoint() + aPerpendEndB);
+                        const B2DPoint aEnd(rEdge.getStartPoint() + aPerpendStartB);
+                        const B2DVector aEdge(aEnd - aStart);
+                        const double fLength(aEdge.getLength());
+                        const double fScale(bIsEdgeLengthZero ? 1.0 : fLength / fEdgeLength);
+                        const B2DVector fRelNext(rEdge.getControlPointB() - rEdge.getEndPoint());
+                        const B2DVector fRelPrev(rEdge.getControlPointA() - rEdge.getStartPoint());
+
+                        aBezierPolygon.append(aStart);
+                        aBezierPolygon.appendBezierSegment(aStart + (fRelNext * fScale), aEnd + (fRelPrev * fScale), aEnd);
+                    }
+                }
+
+                // close
+                aBezierPolygon.setClosed(true);
+
+                if(bStartRound || bEndRound)
+                {
+                    // double points possible when round caps are used at start or end
+                    aBezierPolygon.removeDoublePoints();
+                }
+
+                if(bCut && ((bStartRound || bStartSquare) && (bEndRound || bEndSquare)))
+                {
+                    // When cut exists and both ends are extended with caps, a self-intersecting polygon
+                    // is created; one cut point is known, but there is a 2nd one in the caps geometry.
+                    // Solve by using tooling.
+                    // Remark: This nearly never happens due to curve preparations to extreme points
+                    // and maximum angle turning, but I constructed a test case and checked that it is
+                    // working properly.
+                    const B2DPolyPolygon aTemp(utils::solveCrossovers(aBezierPolygon));
+                    const sal_uInt32 nTempCount(aTemp.count());
+
+                    if(nTempCount)
+                    {
+                        if(nTempCount > 1)
+                        {
+                            // as expected, multiple polygons (with same orientation). Remove
+                            // the one which contains aCutPoint, or better take the one without
+                            for (sal_uInt32 a(0); a < nTempCount; a++)
+                            {
+                                aBezierPolygon = aTemp.getB2DPolygon(a);
+
+                                const sal_uInt32 nCandCount(aBezierPolygon.count());
+
+                                for(sal_uInt32 b(0); b < nCandCount; b++)
+                                {
+                                    if(aCutPoint.equal(aBezierPolygon.getB2DPoint(b)))
+                                    {
+                                        aBezierPolygon.clear();
+                                        break;
+                                    }
+                                }
+
+                                if(aBezierPolygon.count())
+                                {
+                                    break;
+                                }
+                            }
+
+                            OSL_ENSURE(aBezierPolygon.count(), "Error in line geometry creation, could not solve self-intersection (!)");
+                        }
+                        else
+                        {
+                            // none found, use result
+                            aBezierPolygon = aTemp.getB2DPolygon(0);
+                        }
+                    }
+                    else
+                    {
+                        OSL_ENSURE(false, "Error in line geometry creation, could not solve self-intersection (!)");
+                    }
+                }
+
+                if(nullptr != pTriangles)
+                {
+                    const basegfx::triangulator::B2DTriangleVector aResult(
+                        basegfx::triangulator::triangulate(
+                            aBezierPolygon));
+                    pTriangles->insert(pTriangles->end(), aResult.begin(), aResult.end());
+                    aBezierPolygon.clear();
+                }
+
+                // return
+                return aBezierPolygon;
+            }
+            else
+            {
+                // Get start and  end point, create tangent and set to needed length
+                B2DVector aTangent(rEdge.getEndPoint() - rEdge.getStartPoint());
+                aTangent.setLength(fHalfLineWidth);
+
+                // prepare return value
+                B2DPolygon aEdgePolygon;
+
+                // buffered angle
+                double fAngle(0.0);
+                bool bAngle(false);
+
+                // buffered perpendicular
+                B2DVector aPerpend;
+                bool bPerpend(false);
+
+                // create left vertical
+                if(bStartRound)
+                {
+                    aEdgePolygon = utils::createHalfUnitCircle();
+                    fAngle = atan2(aTangent.getY(), aTangent.getX());
+                    bAngle = true;
+                    aEdgePolygon.transform(
+                        utils::createScaleShearXRotateTranslateB2DHomMatrix(
+                            fHalfLineWidth, fHalfLineWidth,
+                            0.0,
+                            fAngle + M_PI_2,
+                            rEdge.getStartPoint().getX(), rEdge.getStartPoint().getY()));
+                }
+                else
+                {
+                    aPerpend.setX(-aTangent.getY());
+                    aPerpend.setY(aTangent.getX());
+                    bPerpend = true;
+
+                    if(bStartSquare)
+                    {
+                        const basegfx::B2DPoint aStart(rEdge.getStartPoint() - aTangent);
+
+                        aEdgePolygon.append(aStart + aPerpend);
+                        aEdgePolygon.append(aStart - aPerpend);
+                    }
+                    else
+                    {
+                        aEdgePolygon.append(rEdge.getStartPoint() + aPerpend);
+                        aEdgePolygon.append(rEdge.getStartPoint()); // keep the in-between point for numerical reasons
+                        aEdgePolygon.append(rEdge.getStartPoint() - aPerpend);
+                    }
+                }
+
+                // create right vertical
+                if(bEndRound)
+                {
+                    basegfx::B2DPolygon aEndPolygon(utils::createHalfUnitCircle());
+
+                    if(!bAngle)
+                    {
+                        fAngle = atan2(aTangent.getY(), aTangent.getX());
+                    }
+
+                    aEndPolygon.transform(
+                        utils::createScaleShearXRotateTranslateB2DHomMatrix(
+                            fHalfLineWidth, fHalfLineWidth,
+                            0.0,
+                            fAngle - M_PI_2,
+                            rEdge.getEndPoint().getX(), rEdge.getEndPoint().getY()));
+                    aEdgePolygon.append(aEndPolygon);
+                }
+                else
+                {
+                    if(!bPerpend)
+                    {
+                        aPerpend.setX(-aTangent.getY());
+                        aPerpend.setY(aTangent.getX());
+                    }
+
+                    if(bEndSquare)
+                    {
+                        const basegfx::B2DPoint aEnd(rEdge.getEndPoint() + aTangent);
+
+                        aEdgePolygon.append(aEnd - aPerpend);
+                        aEdgePolygon.append(aEnd + aPerpend);
+                    }
+                    else
+                    {
+                        aEdgePolygon.append(rEdge.getEndPoint() - aPerpend);
+                        aEdgePolygon.append(rEdge.getEndPoint()); // keep the in-between point for numerical reasons
+                        aEdgePolygon.append(rEdge.getEndPoint() + aPerpend);
+                    }
+                }
+
+                // close and return
+                aEdgePolygon.setClosed(true);
+
+                if(nullptr != pTriangles)
+                {
+                    const basegfx::triangulator::B2DTriangleVector aResult(
+                        basegfx::triangulator::triangulate(
+                            aEdgePolygon));
+                    pTriangles->insert(pTriangles->end(), aResult.begin(), aResult.end());
+                    aEdgePolygon.clear();
+                }
+
+                return aEdgePolygon;
+            }
+        }
+
+        B2DPolygon createAreaGeometryForJoin(
+            const B2DVector& rTangentPrev,
+            const B2DVector& rTangentEdge,
+            const B2DVector& rPerpendPrev,
+            const B2DVector& rPerpendEdge,
+            const B2DPoint& rPoint,
+            double fHalfLineWidth,
+            B2DLineJoin eJoin,
+            double fMiterMinimumAngle)
+        {
+            SAL_WARN_IF(fHalfLineWidth <= 0.0,"basegfx","createAreaGeometryForJoin: LineWidth too small (!)");
+            assert((eJoin != B2DLineJoin::NONE) && "createAreaGeometryForJoin: B2DLineJoin::NONE not allowed (!)");
+
+            // LineJoin from tangent rPerpendPrev to tangent rPerpendEdge in rPoint
+            B2DPolygon aEdgePolygon;
+            const B2DPoint aStartPoint(rPoint + rPerpendPrev);
+            const B2DPoint aEndPoint(rPoint + rPerpendEdge);
+
+            // test if for Miter, the angle is too small and the fallback
+            // to bevel needs to be used
+            if(eJoin == B2DLineJoin::Miter)
+            {
+                const double fAngle(fabs(rPerpendPrev.angle(rPerpendEdge)));
+
+                if((M_PI - fAngle) < fMiterMinimumAngle)
+                {
+                    // fallback to bevel
+                    eJoin = B2DLineJoin::Bevel;
+                }
+            }
+
+            switch(eJoin)
+            {
+                case B2DLineJoin::Miter :
+                {
+                    aEdgePolygon.append(aEndPoint);
+                    aEdgePolygon.append(rPoint);
+                    aEdgePolygon.append(aStartPoint);
+
+                    // Look for the cut point between start point along rTangentPrev and
+                    // end point along rTangentEdge. -rTangentEdge should be used, but since
+                    // the cut value is used for interpolating along the first edge, the negation
+                    // is not needed since the same fCut will be found on the first edge.
+                    // If it exists, insert it to complete the mitered fill polygon.
+                    double fCutPos(0.0);
+                    utils::findCut(aStartPoint, rTangentPrev, aEndPoint, rTangentEdge, CutFlagValue::ALL, &fCutPos);
+
+                    if(fCutPos != 0.0)
+                    {
+                        const B2DPoint aCutPoint(aStartPoint + (rTangentPrev * fCutPos));
+                        aEdgePolygon.append(aCutPoint);
+                    }
+
+                    break;
+                }
+                case B2DLineJoin::Round :
+                {
+                    // use tooling to add needed EllipseSegment
+                    double fAngleStart(atan2(rPerpendPrev.getY(), rPerpendPrev.getX()));
+                    double fAngleEnd(atan2(rPerpendEdge.getY(), rPerpendEdge.getX()));
+
+                    // atan2 results are [-PI .. PI], consolidate to [0.0 .. 2PI]
+                    if(fAngleStart < 0.0)
+                    {
+                        fAngleStart += 2 * M_PI;
+                    }
+
+                    if(fAngleEnd < 0.0)
+                    {
+                        fAngleEnd += 2 * M_PI;
+                    }
+
+                    const B2DPolygon aBow(utils::createPolygonFromEllipseSegment(rPoint, fHalfLineWidth, fHalfLineWidth, fAngleStart, fAngleEnd));
+
+                    if(aBow.count() > 1)
+                    {
+                        // #i101491#
+                        // use the original start/end positions; the ones from bow creation may be numerically
+                        // different due to their different creation. To guarantee good merging quality with edges
+                        // and edge roundings (and to reduce point count)
+                        aEdgePolygon = aBow;
+                        aEdgePolygon.setB2DPoint(0, aStartPoint);
+                        aEdgePolygon.setB2DPoint(aEdgePolygon.count() - 1, aEndPoint);
+                        aEdgePolygon.append(rPoint);
+
+                        break;
+                    }
+                    else
+                    {
+                        [[fallthrough]]; // wanted fall-through to default
+                    }
+                }
+                default: // B2DLineJoin::Bevel
+                {
+                    aEdgePolygon.append(aEndPoint);
+                    aEdgePolygon.append(rPoint);
+                    aEdgePolygon.append(aStartPoint);
+
+                    break;
+                }
+            }
+
+            // create last polygon part for edge
+            aEdgePolygon.setClosed(true);
+
+            return aEdgePolygon;
+        }
+    } // end of anonymous namespace
+
+    namespace utils
+    {
+        B2DPolyPolygon createAreaGeometry(
+            const B2DPolygon& rCandidate,
+            double fHalfLineWidth,
+            B2DLineJoin eJoin,
+            css::drawing::LineCap eCap,
+            double fMaxAllowedAngle,
+            double fMaxPartOfEdge,
+            double fMiterMinimumAngle)
+        {
+            if(fMaxAllowedAngle > M_PI_2)
+            {
+                fMaxAllowedAngle = M_PI_2;
+            }
+            else if(fMaxAllowedAngle < 0.01 * M_PI_2)
+            {
+                fMaxAllowedAngle = 0.01 * M_PI_2;
+            }
+
+            if(fMaxPartOfEdge > 1.0)
+            {
+                fMaxPartOfEdge = 1.0;
+            }
+            else if(fMaxPartOfEdge < 0.01)
+            {
+                fMaxPartOfEdge = 0.01;
+            }
+
+            if(fMiterMinimumAngle > M_PI)
+            {
+                fMiterMinimumAngle = M_PI;
+            }
+            else if(fMiterMinimumAngle < 0.01 * M_PI)
+            {
+                fMiterMinimumAngle = 0.01 * M_PI;
+            }
+
+            B2DPolygon aCandidate(rCandidate);
+            const double fMaxCos(cos(fMaxAllowedAngle));
+
+            aCandidate.removeDoublePoints();
+            aCandidate = subdivideToSimple(aCandidate, fMaxCos * fMaxCos, fMaxPartOfEdge * fMaxPartOfEdge);
+
+            const sal_uInt32 nPointCount(aCandidate.count());
+
+            if(nPointCount)
+            {
+                B2DPolyPolygon aRetval;
+                const bool bIsClosed(aCandidate.isClosed());
+                const sal_uInt32 nEdgeCount(bIsClosed ? nPointCount : nPointCount - 1);
+                const bool bLineCap(!bIsClosed && eCap != css::drawing::LineCap_BUTT);
+
+                if(nEdgeCount)
+                {
+                    B2DCubicBezier aEdge;
+                    B2DCubicBezier aPrev;
+
+                    const bool bEventuallyCreateLineJoin(eJoin != B2DLineJoin::NONE);
+                    // prepare edge
+                    aEdge.setStartPoint(aCandidate.getB2DPoint(0));
+
+                    if(bIsClosed && bEventuallyCreateLineJoin)
+                    {
+                        // prepare previous edge
+                        const sal_uInt32 nPrevIndex(nPointCount - 1);
+                        aPrev.setStartPoint(aCandidate.getB2DPoint(nPrevIndex));
+                        aPrev.setControlPointA(aCandidate.getNextControlPoint(nPrevIndex));
+                        aPrev.setControlPointB(aCandidate.getPrevControlPoint(0));
+                        aPrev.setEndPoint(aEdge.getStartPoint());
+                    }
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        // fill current Edge
+                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                        aEdge.setControlPointA(aCandidate.getNextControlPoint(a));
+                        aEdge.setControlPointB(aCandidate.getPrevControlPoint(nNextIndex));
+                        aEdge.setEndPoint(aCandidate.getB2DPoint(nNextIndex));
+
+                        // check and create linejoin
+                        if(bEventuallyCreateLineJoin && (bIsClosed || a != 0))
+                        {
+                            B2DVector aTangentPrev(aPrev.getTangent(1.0)); aTangentPrev.normalize();
+                            B2DVector aTangentEdge(aEdge.getTangent(0.0)); aTangentEdge.normalize();
+                            B2VectorOrientation aOrientation(getOrientation(aTangentPrev, aTangentEdge));
+
+                            if(aOrientation == B2VectorOrientation::Neutral)
+                            {
+                                // they are parallel or empty; if they are both not zero and point
+                                // in opposite direction, a half-circle is needed
+                                if(!aTangentPrev.equalZero() && !aTangentEdge.equalZero())
+                                {
+                                    const double fAngle(fabs(aTangentPrev.angle(aTangentEdge)));
+
+                                    if(fTools::equal(fAngle, M_PI))
+                                    {
+                                        // for half-circle production, fallback to positive
+                                        // orientation
+                                        aOrientation = B2VectorOrientation::Positive;
+                                    }
+                                }
+                            }
+
+                            if(aOrientation == B2VectorOrientation::Positive)
+                            {
+                                const B2DVector aPerpendPrev(getPerpendicular(aTangentPrev) * -fHalfLineWidth);
+                                const B2DVector aPerpendEdge(getPerpendicular(aTangentEdge) * -fHalfLineWidth);
+
+                                aRetval.append(
+                                    createAreaGeometryForJoin(
+                                        aTangentPrev,
+                                        aTangentEdge,
+                                        aPerpendPrev,
+                                        aPerpendEdge,
+                                        aEdge.getStartPoint(),
+                                        fHalfLineWidth,
+                                        eJoin,
+                                        fMiterMinimumAngle));
+                            }
+                            else if(aOrientation == B2VectorOrientation::Negative)
+                            {
+                                const B2DVector aPerpendPrev(getPerpendicular(aTangentPrev) * fHalfLineWidth);
+                                const B2DVector aPerpendEdge(getPerpendicular(aTangentEdge) * fHalfLineWidth);
+
+                                aRetval.append(
+                                    createAreaGeometryForJoin(
+                                        aTangentEdge,
+                                        aTangentPrev,
+                                        aPerpendEdge,
+                                        aPerpendPrev,
+                                        aEdge.getStartPoint(),
+                                        fHalfLineWidth,
+                                        eJoin,
+                                        fMiterMinimumAngle));
+                            }
+                        }
+
+                        // create geometry for edge
+                        const bool bLast(a + 1 == nEdgeCount);
+
+                        if(bLineCap)
+                        {
+                            const bool bFirst(!a);
+
+                            aRetval.append(
+                                createAreaGeometryForEdge(
+                                    aEdge,
+                                    fHalfLineWidth,
+                                    bFirst && eCap == css::drawing::LineCap_ROUND,
+                                    bLast && eCap == css::drawing::LineCap_ROUND,
+                                    bFirst && eCap == css::drawing::LineCap_SQUARE,
+                                    bLast && eCap == css::drawing::LineCap_SQUARE,
+                                    nullptr));
+                        }
+                        else
+                        {
+                            aRetval.append(
+                                createAreaGeometryForEdge(
+                                    aEdge,
+                                    fHalfLineWidth,
+                                    false,
+                                    false,
+                                    false,
+                                    false,
+                                    nullptr));
+                        }
+
+                        // prepare next step
+                        if(!bLast)
+                        {
+                            if(bEventuallyCreateLineJoin)
+                            {
+                                aPrev = aEdge;
+                            }
+
+                            aEdge.setStartPoint(aEdge.getEndPoint());
+                        }
+                    }
+                }
+                else
+                {
+                    // point count, but no edge count -> single point
+                    const basegfx::B2DPolygon aCircle(
+                        createPolygonFromCircle(
+                            aCandidate.getB2DPoint(0),
+                            fHalfLineWidth));
+
+                    aRetval.append(aCircle);
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return B2DPolyPolygon(rCandidate);
+            }
+        }
+    } // end of namespace utils
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolygon.cxx b/basegfx/source/polygon/b2dpolygon.cxx
new file mode 100644
index 0000000000..cf7309d20d
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygon.cxx
@@ -0,0 +1,1455 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <sal/config.h>
+
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/utils/systemdependentdata.hxx>
+#include <memory>
+#include <vector>
+
+namespace
+{
+
+class CoordinateDataArray2D
+{
+private:
+    std::vector<basegfx::B2DPoint> maVector;
+
+public:
+    explicit CoordinateDataArray2D(sal_uInt32 nCount)
+    :   maVector(nCount)
+    {
+    }
+
+    CoordinateDataArray2D(const CoordinateDataArray2D& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   maVector(rOriginal.maVector.begin() + nIndex, rOriginal.maVector.begin() + (nIndex + nCount))
+    {
+    }
+
+    sal_uInt32 count() const
+    {
+        return maVector.size();
+    }
+
+    bool operator==(const CoordinateDataArray2D& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    const basegfx::B2DPoint& getCoordinate(sal_uInt32 nIndex) const
+    {
+        assert(nIndex < maVector.size());
+        return maVector[nIndex];
+    }
+
+    void setCoordinate(sal_uInt32 nIndex, const basegfx::B2DPoint& rValue)
+    {
+        assert(nIndex < maVector.size());
+        maVector[nIndex] = rValue;
+    }
+
+    void reserve(sal_uInt32 nCount)
+    {
+        maVector.reserve(nCount);
+    }
+
+    void append(const basegfx::B2DPoint& rValue)
+    {
+        maVector.push_back(rValue);
+    }
+
+    void insert(sal_uInt32 nIndex, const basegfx::B2DPoint& rValue, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex <= maVector.size());
+        // add nCount copies of rValue
+        maVector.insert(maVector.begin() + nIndex, nCount, rValue);
+    }
+
+    void insert(sal_uInt32 nIndex, const CoordinateDataArray2D& rSource)
+    {
+        assert(rSource.maVector.size() > 0);
+        assert(nIndex <= maVector.size());
+        // insert data
+        auto aIndex = maVector.begin();
+        aIndex += nIndex;
+        auto aStart = rSource.maVector.cbegin();
+        auto aEnd = rSource.maVector.cend();
+        maVector.insert(aIndex, aStart, aEnd);
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex + nCount <= maVector.size());
+        // remove point data
+        const auto aStart = maVector.begin() + nIndex;
+        const auto aEnd = aStart + nCount;
+        maVector.erase(aStart, aEnd);
+    }
+
+    void flip(bool bIsClosed)
+    {
+        assert(maVector.size() > 1);
+
+        // to keep the same point at index 0, just flip all points except the
+        // first one when closed
+        const sal_uInt32 nHalfSize(bIsClosed ? (maVector.size() - 1) >> 1 : maVector.size() >> 1);
+        auto aStart = bIsClosed ? maVector.begin() + 1 : maVector.begin();
+        auto aEnd = maVector.end() - 1;
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            std::swap(*aStart, *aEnd);
+            ++aStart;
+            --aEnd;
+        }
+    }
+
+    void removeDoublePointsAtBeginEnd()
+    {
+        // remove from end as long as there are at least two points
+        // and begin/end are equal
+        while((maVector.size() > 1) && (maVector[0] == maVector[maVector.size() - 1]))
+        {
+            maVector.pop_back();
+        }
+    }
+
+    void removeDoublePointsWholeTrack()
+    {
+        sal_uInt32 nIndex(0);
+
+        // test as long as there are at least two points and as long as the index
+        // is smaller or equal second last point
+        while((maVector.size() > 1) && (nIndex <= maVector.size() - 2))
+        {
+            if(maVector[nIndex] == maVector[nIndex + 1])
+            {
+                // if next is same as index, delete next
+                maVector.erase(maVector.begin() + (nIndex + 1));
+            }
+            else
+            {
+                // if different, step forward
+                nIndex++;
+            }
+        }
+    }
+
+    void transform(const basegfx::B2DHomMatrix& rMatrix)
+    {
+        for (auto& point : maVector)
+        {
+            point *= rMatrix;
+        }
+    }
+};
+
+class ControlVectorPair2D
+{
+    basegfx::B2DVector                          maPrevVector;
+    basegfx::B2DVector                          maNextVector;
+
+public:
+    explicit ControlVectorPair2D() {}
+
+    const basegfx::B2DVector& getPrevVector() const
+    {
+        return maPrevVector;
+    }
+
+    void setPrevVector(const basegfx::B2DVector& rValue)
+    {
+        if(rValue != maPrevVector)
+            maPrevVector = rValue;
+    }
+
+    const basegfx::B2DVector& getNextVector() const
+    {
+        return maNextVector;
+    }
+
+    void setNextVector(const basegfx::B2DVector& rValue)
+    {
+        if(rValue != maNextVector)
+            maNextVector = rValue;
+    }
+
+    bool operator==(const ControlVectorPair2D& rData) const
+    {
+        return (maPrevVector == rData.getPrevVector() && maNextVector == rData.getNextVector());
+    }
+
+    void flip()
+    {
+        std::swap(maPrevVector, maNextVector);
+    }
+};
+
+class ControlVectorArray2D
+{
+    typedef std::vector< ControlVectorPair2D > ControlVectorPair2DVector;
+
+    ControlVectorPair2DVector                           maVector;
+    sal_uInt32                                          mnUsedVectors;
+
+public:
+    explicit ControlVectorArray2D(sal_uInt32 nCount)
+    :   maVector(nCount),
+        mnUsedVectors(0)
+    {}
+
+    ControlVectorArray2D(const ControlVectorArray2D& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   mnUsedVectors(0)
+    {
+        assert(nIndex + nCount <= rOriginal.maVector.size());
+        auto aStart(rOriginal.maVector.begin() + nIndex);
+        auto aEnd(aStart + nCount);
+        maVector.reserve(nCount);
+
+        for(; aStart != aEnd; ++aStart)
+        {
+            if(!aStart->getPrevVector().equalZero())
+                mnUsedVectors++;
+
+            if(!aStart->getNextVector().equalZero())
+                mnUsedVectors++;
+
+            maVector.push_back(*aStart);
+        }
+    }
+
+    bool operator==(const ControlVectorArray2D& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    bool isUsed() const
+    {
+        return (mnUsedVectors != 0);
+    }
+
+    const basegfx::B2DVector& getPrevVector(sal_uInt32 nIndex) const
+    {
+        assert(nIndex < maVector.size());
+        return maVector[nIndex].getPrevVector();
+    }
+
+    void setPrevVector(sal_uInt32 nIndex, const basegfx::B2DVector& rValue)
+    {
+        bool bWasUsed(mnUsedVectors && !maVector[nIndex].getPrevVector().equalZero());
+        bool bIsUsed(!rValue.equalZero());
+
+        if(bWasUsed)
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex].setPrevVector(rValue);
+            }
+            else
+            {
+                maVector[nIndex].setPrevVector(basegfx::B2DVector::getEmptyVector());
+                mnUsedVectors--;
+            }
+        }
+        else
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex].setPrevVector(rValue);
+                mnUsedVectors++;
+            }
+        }
+    }
+
+    const basegfx::B2DVector& getNextVector(sal_uInt32 nIndex) const
+    {
+        assert(nIndex < maVector.size());
+        return maVector[nIndex].getNextVector();
+    }
+
+    void setNextVector(sal_uInt32 nIndex, const basegfx::B2DVector& rValue)
+    {
+        bool bWasUsed(mnUsedVectors && !maVector[nIndex].getNextVector().equalZero());
+        bool bIsUsed(!rValue.equalZero());
+
+        if(bWasUsed)
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex].setNextVector(rValue);
+            }
+            else
+            {
+                maVector[nIndex].setNextVector(basegfx::B2DVector::getEmptyVector());
+                mnUsedVectors--;
+            }
+        }
+        else
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex].setNextVector(rValue);
+                mnUsedVectors++;
+            }
+        }
+    }
+
+    void append(const ControlVectorPair2D& rValue)
+    {
+        maVector.push_back(rValue);
+
+        if(!rValue.getPrevVector().equalZero())
+            mnUsedVectors += 1;
+
+        if(!rValue.getNextVector().equalZero())
+            mnUsedVectors += 1;
+    }
+
+    void insert(sal_uInt32 nIndex, const ControlVectorPair2D& rValue, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex <= maVector.size());
+
+        // add nCount copies of rValue
+        maVector.insert(maVector.begin() + nIndex, nCount, rValue);
+
+        if(!rValue.getPrevVector().equalZero())
+            mnUsedVectors += nCount;
+
+        if(!rValue.getNextVector().equalZero())
+            mnUsedVectors += nCount;
+    }
+
+    void insert(sal_uInt32 nIndex, const ControlVectorArray2D& rSource)
+    {
+        assert(rSource.maVector.size() > 0);
+        assert(nIndex <= maVector.size());
+
+        // insert data
+        ControlVectorPair2DVector::iterator aIndex(maVector.begin() + nIndex);
+        ControlVectorPair2DVector::const_iterator aStart(rSource.maVector.begin());
+        ControlVectorPair2DVector::const_iterator aEnd(rSource.maVector.end());
+        maVector.insert(aIndex, aStart, aEnd);
+
+        for(; aStart != aEnd; ++aStart)
+        {
+            if(!aStart->getPrevVector().equalZero())
+                mnUsedVectors++;
+
+            if(!aStart->getNextVector().equalZero())
+                mnUsedVectors++;
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex + nCount <= maVector.size());
+
+        const ControlVectorPair2DVector::iterator aDeleteStart(maVector.begin() + nIndex);
+        const ControlVectorPair2DVector::iterator aDeleteEnd(aDeleteStart + nCount);
+        ControlVectorPair2DVector::const_iterator aStart(aDeleteStart);
+
+        for(; mnUsedVectors && aStart != aDeleteEnd; ++aStart)
+        {
+            if(!aStart->getPrevVector().equalZero())
+                mnUsedVectors--;
+
+            if(mnUsedVectors && !aStart->getNextVector().equalZero())
+                mnUsedVectors--;
+        }
+
+        // remove point data
+        maVector.erase(aDeleteStart, aDeleteEnd);
+    }
+
+    void flip(bool bIsClosed)
+    {
+        assert(maVector.size() > 1);
+
+        // to keep the same point at index 0, just flip all points except the
+        // first one when closed
+        const sal_uInt32 nHalfSize(bIsClosed ? (maVector.size() - 1) >> 1 : maVector.size() >> 1);
+        ControlVectorPair2DVector::iterator aStart(bIsClosed ? maVector.begin() + 1 : maVector.begin());
+        ControlVectorPair2DVector::iterator aEnd(maVector.end() - 1);
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            // swap Prev and Next
+            aStart->flip();
+            aEnd->flip();
+
+            // swap entries
+            std::swap(*aStart, *aEnd);
+
+            ++aStart;
+            --aEnd;
+        }
+
+        if(aStart == aEnd)
+        {
+            // swap Prev and Next at middle element (if exists)
+            aStart->flip();
+        }
+
+        if(bIsClosed)
+        {
+            // swap Prev and Next at start element
+            maVector.begin()->flip();
+        }
+    }
+};
+
+class ImplBufferedData : public basegfx::SystemDependentDataHolder
+{
+private:
+    // Possibility to hold the last subdivision
+    mutable std::optional< basegfx::B2DPolygon >  mpDefaultSubdivision;
+
+    // Possibility to hold the last B2DRange calculation
+    mutable std::optional< basegfx::B2DRange > moB2DRange;
+
+public:
+    ImplBufferedData()
+    {
+    }
+
+    const basegfx::B2DPolygon& getDefaultAdaptiveSubdivision(const basegfx::B2DPolygon& rSource) const
+    {
+        if(!mpDefaultSubdivision)
+        {
+            mpDefaultSubdivision = basegfx::utils::adaptiveSubdivideByAngle(rSource);
+        }
+
+        return *mpDefaultSubdivision;
+    }
+
+    const basegfx::B2DRange& getB2DRange(const basegfx::B2DPolygon& rSource) const
+    {
+        if(!moB2DRange)
+        {
+            basegfx::B2DRange aNewRange;
+            const sal_uInt32 nPointCount(rSource.count());
+
+            if(nPointCount)
+            {
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    aNewRange.expand(rSource.getB2DPoint(a));
+                }
+
+                if(rSource.areControlPointsUsed())
+                {
+                    const sal_uInt32 nEdgeCount(rSource.isClosed() ? nPointCount : nPointCount - 1);
+
+                    if(nEdgeCount)
+                    {
+                        basegfx::B2DCubicBezier aEdge;
+                        aEdge.setStartPoint(rSource.getB2DPoint(0));
+
+                        for(sal_uInt32 b(0); b < nEdgeCount; b++)
+                        {
+                            const sal_uInt32 nNextIndex((b + 1) % nPointCount);
+                            aEdge.setControlPointA(rSource.getNextControlPoint(b));
+                            aEdge.setControlPointB(rSource.getPrevControlPoint(nNextIndex));
+                            aEdge.setEndPoint(rSource.getB2DPoint(nNextIndex));
+
+                            if(aEdge.isBezier())
+                            {
+                                const basegfx::B2DRange aBezierRangeWithControlPoints(aEdge.getRange());
+
+                                if(!aNewRange.isInside(aBezierRangeWithControlPoints))
+                                {
+                                    // the range with control points of the current edge is not completely
+                                    // inside the current range without control points. Expand current range by
+                                    // subdividing the bezier segment.
+                                    // Ideal here is a subdivision at the extreme values, so use
+                                    // getAllExtremumPositions to get all extremas in one run
+                                    std::vector< double > aExtremas;
+
+                                    aExtremas.reserve(4);
+                                    aEdge.getAllExtremumPositions(aExtremas);
+
+                                    const sal_uInt32 nExtremaCount(aExtremas.size());
+
+                                    for(sal_uInt32 c(0); c < nExtremaCount; c++)
+                                    {
+                                        aNewRange.expand(aEdge.interpolatePoint(aExtremas[c]));
+                                    }
+                                }
+                            }
+
+                            // prepare next edge
+                            aEdge.setStartPoint(aEdge.getEndPoint());
+                        }
+                    }
+                }
+            }
+
+            moB2DRange = aNewRange;
+        }
+
+        return *moB2DRange;
+    }
+};
+
+}
+
+class ImplB2DPolygon
+{
+private:
+    // The point vector. This vector exists always and defines the
+    // count of members.
+    CoordinateDataArray2D                         maPoints;
+
+    // The control point vectors. This vectors are created on demand
+    // and may be zero.
+    std::optional< ControlVectorArray2D >         moControlVector;
+
+    // buffered data for e.g. default subdivision and range
+    // we do not want to 'modify' the ImplB2DPolygon,
+    // but add buffered data that is valid for all referencing instances
+    mutable std::unique_ptr<ImplBufferedData> mpBufferedData;
+
+    // flag which decides if this polygon is opened or closed
+    bool                                          mbIsClosed;
+
+public:
+    const basegfx::B2DPolygon& getDefaultAdaptiveSubdivision(const basegfx::B2DPolygon& rSource) const
+    {
+        if(!moControlVector || !moControlVector->isUsed())
+        {
+            return rSource;
+        }
+
+        if(!mpBufferedData)
+        {
+            mpBufferedData.reset(new ImplBufferedData);
+        }
+
+        return mpBufferedData->getDefaultAdaptiveSubdivision(rSource);
+    }
+
+    const basegfx::B2DRange& getB2DRange(const basegfx::B2DPolygon& rSource) const
+    {
+        if(!mpBufferedData)
+        {
+            mpBufferedData.reset(new ImplBufferedData);
+        }
+
+        return mpBufferedData->getB2DRange(rSource);
+    }
+
+    ImplB2DPolygon()
+    :   maPoints(0),
+        mbIsClosed(false)
+    {}
+
+    ImplB2DPolygon(const ImplB2DPolygon& rToBeCopied)
+    :   maPoints(rToBeCopied.maPoints),
+        mbIsClosed(rToBeCopied.mbIsClosed)
+    {
+        // complete initialization using copy
+        if(rToBeCopied.moControlVector && rToBeCopied.moControlVector->isUsed())
+        {
+            moControlVector.emplace( *rToBeCopied.moControlVector );
+        }
+    }
+
+    ImplB2DPolygon(const ImplB2DPolygon& rToBeCopied, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   maPoints(rToBeCopied.maPoints, nIndex, nCount),
+        mbIsClosed(rToBeCopied.mbIsClosed)
+    {
+        // complete initialization using partly copy
+        if(rToBeCopied.moControlVector && rToBeCopied.moControlVector->isUsed())
+        {
+            moControlVector.emplace( *rToBeCopied.moControlVector, nIndex, nCount );
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+    }
+
+    ImplB2DPolygon& operator=(const ImplB2DPolygon& rOther)
+    {
+        if (this != &rOther)
+        {
+            moControlVector.reset();
+            mpBufferedData.reset();
+            maPoints = rOther.maPoints;
+            mbIsClosed = rOther.mbIsClosed;
+            if (rOther.moControlVector && rOther.moControlVector->isUsed())
+            {
+                moControlVector.emplace( *rOther.moControlVector );
+
+                if(!moControlVector->isUsed())
+                    moControlVector.reset();
+            }
+        }
+        return *this;
+    }
+
+    sal_uInt32 count() const
+    {
+        return maPoints.count();
+    }
+
+    bool isClosed() const
+    {
+        return mbIsClosed;
+    }
+
+    void setClosed(bool bNew)
+    {
+        if(bNew != mbIsClosed)
+        {
+            mpBufferedData.reset();
+            mbIsClosed = bNew;
+        }
+    }
+
+    bool operator==(const ImplB2DPolygon& rCandidate) const
+    {
+        if(mbIsClosed != rCandidate.mbIsClosed)
+            return false;
+        if(!(maPoints == rCandidate.maPoints))
+            return false;
+        bool bControlVectorsAreEqual(true);
+
+        if(moControlVector)
+        {
+            if(rCandidate.moControlVector)
+            {
+                bControlVectorsAreEqual = ((*moControlVector) == (*rCandidate.moControlVector));
+            }
+            else
+            {
+                // candidate has no control vector, so it's assumed all unused.
+                bControlVectorsAreEqual = !moControlVector->isUsed();
+            }
+        }
+        else
+        {
+            if(rCandidate.moControlVector)
+            {
+                // we have no control vector, so it's assumed all unused.
+                bControlVectorsAreEqual = !rCandidate.moControlVector->isUsed();
+            }
+        }
+
+        return bControlVectorsAreEqual;
+    }
+
+    const basegfx::B2DPoint& getPoint(sal_uInt32 nIndex) const
+    {
+        return maPoints.getCoordinate(nIndex);
+    }
+
+    void setPoint(sal_uInt32 nIndex, const basegfx::B2DPoint& rValue)
+    {
+        mpBufferedData.reset();
+        maPoints.setCoordinate(nIndex, rValue);
+    }
+
+    void reserve(sal_uInt32 nCount)
+    {
+        maPoints.reserve(nCount);
+    }
+
+    void append(const basegfx::B2DPoint& rPoint)
+    {
+        mpBufferedData.reset(); // TODO: is this needed?
+        const auto aCoordinate = rPoint;
+        maPoints.append(aCoordinate);
+
+        if(moControlVector)
+        {
+            const ControlVectorPair2D aVectorPair;
+            moControlVector->append(aVectorPair);
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const basegfx::B2DPoint& rPoint, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        mpBufferedData.reset();
+        auto aCoordinate = rPoint;
+        maPoints.insert(nIndex, aCoordinate, nCount);
+
+        if(moControlVector)
+        {
+            ControlVectorPair2D aVectorPair;
+            moControlVector->insert(nIndex, aVectorPair, nCount);
+        }
+    }
+
+    void append(const basegfx::B2DPoint& rPoint, sal_uInt32 nCount)
+    {
+        insert(count(), rPoint, nCount);
+    }
+
+    const basegfx::B2DVector& getPrevControlVector(sal_uInt32 nIndex) const
+    {
+        if(moControlVector)
+        {
+            return moControlVector->getPrevVector(nIndex);
+        }
+        else
+        {
+            return basegfx::B2DVector::getEmptyVector();
+        }
+    }
+
+    void setPrevControlVector(sal_uInt32 nIndex, const basegfx::B2DVector& rValue)
+    {
+        if(!moControlVector)
+        {
+            if(!rValue.equalZero())
+            {
+                mpBufferedData.reset();
+                moControlVector.emplace(maPoints.count());
+                moControlVector->setPrevVector(nIndex, rValue);
+            }
+        }
+        else
+        {
+            mpBufferedData.reset();
+            moControlVector->setPrevVector(nIndex, rValue);
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+    }
+
+    const basegfx::B2DVector& getNextControlVector(sal_uInt32 nIndex) const
+    {
+        if(moControlVector)
+        {
+            return moControlVector->getNextVector(nIndex);
+        }
+        else
+        {
+            return basegfx::B2DVector::getEmptyVector();
+        }
+    }
+
+    void setNextControlVector(sal_uInt32 nIndex, const basegfx::B2DVector& rValue)
+    {
+        if(!moControlVector)
+        {
+            if(!rValue.equalZero())
+            {
+                mpBufferedData.reset();
+                moControlVector.emplace(maPoints.count());
+                moControlVector->setNextVector(nIndex, rValue);
+            }
+        }
+        else
+        {
+            mpBufferedData.reset();
+            moControlVector->setNextVector(nIndex, rValue);
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+    }
+
+    bool areControlPointsUsed() const
+    {
+        return (moControlVector && moControlVector->isUsed());
+    }
+
+    void resetControlVectors()
+    {
+        mpBufferedData.reset();
+        moControlVector.reset();
+    }
+
+    void setControlVectors(sal_uInt32 nIndex, const basegfx::B2DVector& rPrev, const basegfx::B2DVector& rNext)
+    {
+        setPrevControlVector(nIndex, rPrev);
+        setNextControlVector(nIndex, rNext);
+    }
+
+    void appendBezierSegment(const basegfx::B2DVector& rNext, const basegfx::B2DVector& rPrev, const basegfx::B2DPoint& rPoint)
+    {
+        mpBufferedData.reset();
+        const sal_uInt32 nCount(maPoints.count());
+
+        if(nCount)
+        {
+            setNextControlVector(nCount - 1, rNext);
+        }
+
+        insert(nCount, rPoint, 1);
+        setPrevControlVector(nCount, rPrev);
+    }
+
+    void append(const ImplB2DPolygon& rSource)
+    {
+        assert(rSource.maPoints.count() > 0);
+        const sal_uInt32 nIndex = count();
+
+        mpBufferedData.reset();
+
+        maPoints.insert(nIndex, rSource.maPoints);
+
+        if(rSource.moControlVector)
+        {
+            if (!moControlVector)
+                moControlVector.emplace(nIndex);
+            moControlVector->insert(nIndex, *rSource.moControlVector);
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+        else if(moControlVector)
+        {
+            ControlVectorPair2D aVectorPair;
+            moControlVector->insert(nIndex, aVectorPair, rSource.count());
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        mpBufferedData.reset();
+        maPoints.remove(nIndex, nCount);
+
+        if(moControlVector)
+        {
+            moControlVector->remove(nIndex, nCount);
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+    }
+
+    void flip()
+    {
+        assert(maPoints.count() > 1);
+
+        mpBufferedData.reset();
+
+        // flip points
+        maPoints.flip(mbIsClosed);
+
+        if(moControlVector)
+        {
+            // flip control vector
+            moControlVector->flip(mbIsClosed);
+        }
+    }
+
+    bool hasDoublePoints() const
+    {
+        if(mbIsClosed)
+        {
+            // check for same start and end point
+            const sal_uInt32 nIndex(maPoints.count() - 1);
+
+            if(maPoints.getCoordinate(0) == maPoints.getCoordinate(nIndex))
+            {
+                if(moControlVector)
+                {
+                    if(moControlVector->getNextVector(nIndex).equalZero() && moControlVector->getPrevVector(0).equalZero())
+                    {
+                        return true;
+                    }
+                }
+                else
+                {
+                    return true;
+                }
+            }
+        }
+
+        // test for range
+        for(sal_uInt32 a(0); a < maPoints.count() - 1; a++)
+        {
+            if(maPoints.getCoordinate(a) == maPoints.getCoordinate(a + 1))
+            {
+                if(moControlVector)
+                {
+                    if(moControlVector->getNextVector(a).equalZero() && moControlVector->getPrevVector(a + 1).equalZero())
+                    {
+                        return true;
+                    }
+                }
+                else
+                {
+                    return true;
+                }
+            }
+        }
+
+        return false;
+    }
+
+    void removeDoublePointsAtBeginEnd()
+    {
+        // Only remove DoublePoints at Begin and End when poly is closed
+        if(!mbIsClosed)
+            return;
+
+        mpBufferedData.reset();
+
+        if(moControlVector)
+        {
+            bool bRemove;
+
+            do
+            {
+                bRemove = false;
+
+                if(maPoints.count() > 1)
+                {
+                    const sal_uInt32 nIndex(maPoints.count() - 1);
+
+                    if(maPoints.getCoordinate(0) == maPoints.getCoordinate(nIndex))
+                    {
+                        if(moControlVector)
+                        {
+                            if(moControlVector->getNextVector(nIndex).equalZero() && moControlVector->getPrevVector(0).equalZero())
+                            {
+                                bRemove = true;
+                            }
+                        }
+                        else
+                        {
+                            bRemove = true;
+                        }
+                    }
+                }
+
+                if(bRemove)
+                {
+                    const sal_uInt32 nIndex(maPoints.count() - 1);
+
+                    if(moControlVector && !moControlVector->getPrevVector(nIndex).equalZero())
+                    {
+                        moControlVector->setPrevVector(0, moControlVector->getPrevVector(nIndex));
+                    }
+
+                    remove(nIndex, 1);
+                }
+            }
+            while(bRemove);
+        }
+        else
+        {
+            maPoints.removeDoublePointsAtBeginEnd();
+        }
+    }
+
+    void removeDoublePointsWholeTrack()
+    {
+        mpBufferedData.reset();
+
+        if(moControlVector)
+        {
+            sal_uInt32 nIndex(0);
+
+            // test as long as there are at least two points and as long as the index
+            // is smaller or equal second last point
+            while((maPoints.count() > 1) && (nIndex <= maPoints.count() - 2))
+            {
+                bool bRemove(maPoints.getCoordinate(nIndex) == maPoints.getCoordinate(nIndex + 1));
+
+                if(bRemove && moControlVector)
+                {
+                    if(!moControlVector->getNextVector(nIndex).equalZero() || !moControlVector->getPrevVector(nIndex + 1).equalZero())
+                    {
+                        bRemove = false;
+                    }
+                }
+
+                if(bRemove)
+                {
+                    if(moControlVector && !moControlVector->getPrevVector(nIndex).equalZero())
+                    {
+                        moControlVector->setPrevVector(nIndex + 1, moControlVector->getPrevVector(nIndex));
+                    }
+
+                    // if next is same as index and the control vectors are unused, delete index
+                    remove(nIndex, 1);
+                }
+                else
+                {
+                    // if different, step forward
+                    nIndex++;
+                }
+            }
+        }
+        else
+        {
+            maPoints.removeDoublePointsWholeTrack();
+        }
+    }
+
+    void transform(const basegfx::B2DHomMatrix& rMatrix)
+    {
+        mpBufferedData.reset();
+
+        if(moControlVector)
+        {
+            for(sal_uInt32 a(0); a < maPoints.count(); a++)
+            {
+                basegfx::B2DPoint aCandidate = maPoints.getCoordinate(a);
+
+                if(moControlVector->isUsed())
+                {
+                    const basegfx::B2DVector& rPrevVector(moControlVector->getPrevVector(a));
+                    const basegfx::B2DVector& rNextVector(moControlVector->getNextVector(a));
+
+                    if(!rPrevVector.equalZero())
+                    {
+                        basegfx::B2DVector aPrevVector(rMatrix * rPrevVector);
+                        moControlVector->setPrevVector(a, aPrevVector);
+                    }
+
+                    if(!rNextVector.equalZero())
+                    {
+                        basegfx::B2DVector aNextVector(rMatrix * rNextVector);
+                        moControlVector->setNextVector(a, aNextVector);
+                    }
+                }
+
+                aCandidate *= rMatrix;
+                maPoints.setCoordinate(a, aCandidate);
+            }
+
+            if(!moControlVector->isUsed())
+                moControlVector.reset();
+        }
+        else
+        {
+            maPoints.transform(rMatrix);
+        }
+    }
+
+    void addOrReplaceSystemDependentData(basegfx::SystemDependentData_SharedPtr& rData) const
+    {
+        if(!mpBufferedData)
+        {
+            mpBufferedData.reset(new ImplBufferedData);
+        }
+
+        mpBufferedData->addOrReplaceSystemDependentData(rData);
+    }
+
+    basegfx::SystemDependentData_SharedPtr getSystemDependentData(size_t hash_code) const
+    {
+        if(mpBufferedData)
+        {
+            return mpBufferedData->getSystemDependentData(hash_code);
+        }
+
+        return basegfx::SystemDependentData_SharedPtr();
+    }
+};
+
+namespace basegfx
+{
+    static o3tl::cow_wrapper<ImplB2DPolygon> DEFAULT;
+
+    B2DPolygon::B2DPolygon()
+        : mpPolygon(DEFAULT) {}
+
+    B2DPolygon::B2DPolygon(std::initializer_list<basegfx::B2DPoint> aPoints)
+    {
+        for (const basegfx::B2DPoint& rPoint : aPoints)
+        {
+            append(rPoint);
+        }
+    }
+
+    B2DPolygon::B2DPolygon(const B2DPolygon&) = default;
+
+    B2DPolygon::B2DPolygon(B2DPolygon&&) = default;
+
+    B2DPolygon::B2DPolygon(const B2DPolygon& rPolygon, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   mpPolygon(ImplB2DPolygon(*rPolygon.mpPolygon, nIndex, nCount))
+    {
+    }
+
+    B2DPolygon::~B2DPolygon() = default;
+
+    B2DPolygon& B2DPolygon::operator=(const B2DPolygon&) = default;
+
+    B2DPolygon& B2DPolygon::operator=(B2DPolygon&&) = default;
+
+    void B2DPolygon::makeUnique()
+    {
+        mpPolygon.make_unique();
+    }
+
+    bool B2DPolygon::operator==(const B2DPolygon& rPolygon) const
+    {
+        if(mpPolygon.same_object(rPolygon.mpPolygon))
+            return true;
+
+        return ((*mpPolygon) == (*rPolygon.mpPolygon));
+    }
+
+    sal_uInt32 B2DPolygon::count() const
+    {
+        return mpPolygon->count();
+    }
+
+    B2DPoint const & B2DPolygon::getB2DPoint(sal_uInt32 nIndex) const
+    {
+        return mpPolygon->getPoint(nIndex);
+    }
+
+    void B2DPolygon::setB2DPoint(sal_uInt32 nIndex, const B2DPoint& rValue)
+    {
+        if(getB2DPoint(nIndex) != rValue)
+        {
+            mpPolygon->setPoint(nIndex, rValue);
+        }
+    }
+
+    void B2DPolygon::reserve(sal_uInt32 nCount)
+    {
+        mpPolygon->reserve(nCount);
+    }
+
+    void B2DPolygon::insert(sal_uInt32 nIndex, const B2DPoint& rPoint, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            mpPolygon->insert(nIndex, rPoint, nCount);
+        }
+    }
+
+    void B2DPolygon::append(const B2DPoint& rPoint, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            mpPolygon->append(rPoint, nCount);
+        }
+    }
+
+    void B2DPolygon::append(const B2DPoint& rPoint)
+    {
+        mpPolygon->append(rPoint);
+    }
+
+    const basegfx::B2DVector& B2DPolygon::getPrevControlVector(sal_uInt32 nIndex) const
+    {
+        return mpPolygon->getPrevControlVector(nIndex);
+    }
+
+    const basegfx::B2DVector& B2DPolygon::getNextControlVector(sal_uInt32 nIndex) const
+    {
+        return mpPolygon->getNextControlVector(nIndex);
+    }
+
+    B2DPoint B2DPolygon::getPrevControlPoint(sal_uInt32 nIndex) const
+    {
+        if(areControlPointsUsed())
+        {
+            return getB2DPoint(nIndex) + getPrevControlVector(nIndex);
+        }
+        else
+        {
+            return getB2DPoint(nIndex);
+        }
+    }
+
+    B2DPoint B2DPolygon::getNextControlPoint(sal_uInt32 nIndex) const
+    {
+        if(areControlPointsUsed())
+        {
+            return getB2DPoint(nIndex) + getNextControlVector(nIndex);
+        }
+        else
+        {
+            return getB2DPoint(nIndex);
+        }
+    }
+
+    void B2DPolygon::setPrevControlPoint(sal_uInt32 nIndex, const B2DPoint& rValue)
+    {
+        const basegfx::B2DVector aNewVector(rValue - getB2DPoint(nIndex));
+
+        if(getPrevControlVector(nIndex) != aNewVector)
+        {
+            mpPolygon->setPrevControlVector(nIndex, aNewVector);
+        }
+    }
+
+    void B2DPolygon::setNextControlPoint(sal_uInt32 nIndex, const B2DPoint& rValue)
+    {
+        const basegfx::B2DVector aNewVector(rValue - getB2DPoint(nIndex));
+
+        if(getNextControlVector(nIndex) != aNewVector)
+        {
+            mpPolygon->setNextControlVector(nIndex, aNewVector);
+        }
+    }
+
+    void B2DPolygon::setControlPoints(sal_uInt32 nIndex, const basegfx::B2DPoint& rPrev, const basegfx::B2DPoint& rNext)
+    {
+        const B2DPoint aPoint(getB2DPoint(nIndex));
+        const basegfx::B2DVector aNewPrev(rPrev - aPoint);
+        const basegfx::B2DVector aNewNext(rNext - aPoint);
+
+        if(getPrevControlVector(nIndex) != aNewPrev || getNextControlVector(nIndex) != aNewNext)
+        {
+            mpPolygon->setControlVectors(nIndex, aNewPrev, aNewNext);
+        }
+    }
+
+    void B2DPolygon::resetPrevControlPoint(sal_uInt32 nIndex)
+    {
+        if(areControlPointsUsed() && !getPrevControlVector(nIndex).equalZero())
+        {
+            mpPolygon->setPrevControlVector(nIndex, B2DVector::getEmptyVector());
+        }
+    }
+
+    void B2DPolygon::resetNextControlPoint(sal_uInt32 nIndex)
+    {
+        if(areControlPointsUsed() && !getNextControlVector(nIndex).equalZero())
+        {
+            mpPolygon->setNextControlVector(nIndex, B2DVector::getEmptyVector());
+        }
+    }
+
+    void B2DPolygon::resetControlPoints()
+    {
+        if(areControlPointsUsed())
+        {
+            mpPolygon->resetControlVectors();
+        }
+    }
+
+    void B2DPolygon::appendBezierSegment(
+        const B2DPoint& rNextControlPoint,
+        const B2DPoint& rPrevControlPoint,
+        const B2DPoint& rPoint)
+    {
+        const B2DVector aNewNextVector(count() ? B2DVector(rNextControlPoint - getB2DPoint(count() - 1)) : B2DVector::getEmptyVector());
+        const B2DVector aNewPrevVector(rPrevControlPoint - rPoint);
+
+        if(aNewNextVector.equalZero() && aNewPrevVector.equalZero())
+        {
+            mpPolygon->append(rPoint);
+        }
+        else
+        {
+            mpPolygon->appendBezierSegment(aNewNextVector, aNewPrevVector, rPoint);
+        }
+    }
+
+    void B2DPolygon::appendQuadraticBezierSegment(const B2DPoint& rControlPoint, const B2DPoint& rPoint)
+    {
+        if (count() == 0)
+        {
+            mpPolygon->append(rPoint);
+            const double nX((rControlPoint.getX() * 2.0 + rPoint.getX()) / 3.0);
+            const double nY((rControlPoint.getY() * 2.0 + rPoint.getY()) / 3.0);
+            setPrevControlPoint(0, B2DPoint(nX, nY));
+        }
+        else
+        {
+            const B2DPoint aPreviousPoint(getB2DPoint(count() - 1));
+
+            const double nX1((rControlPoint.getX() * 2.0 + aPreviousPoint.getX()) / 3.0);
+            const double nY1((rControlPoint.getY() * 2.0 + aPreviousPoint.getY()) / 3.0);
+            const double nX2((rControlPoint.getX() * 2.0 + rPoint.getX()) / 3.0);
+            const double nY2((rControlPoint.getY() * 2.0 + rPoint.getY()) / 3.0);
+
+            appendBezierSegment(B2DPoint(nX1, nY1), B2DPoint(nX2, nY2), rPoint);
+        }
+    }
+
+    bool B2DPolygon::areControlPointsUsed() const
+    {
+        return mpPolygon->areControlPointsUsed();
+    }
+
+    bool B2DPolygon::isPrevControlPointUsed(sal_uInt32 nIndex) const
+    {
+        return (areControlPointsUsed() && !getPrevControlVector(nIndex).equalZero());
+    }
+
+    bool B2DPolygon::isNextControlPointUsed(sal_uInt32 nIndex) const
+    {
+        return (areControlPointsUsed() && !getNextControlVector(nIndex).equalZero());
+    }
+
+    B2VectorContinuity B2DPolygon::getContinuityInPoint(sal_uInt32 nIndex) const
+    {
+        if(areControlPointsUsed())
+        {
+            const B2DVector& rPrev(getPrevControlVector(nIndex));
+            const B2DVector& rNext(getNextControlVector(nIndex));
+
+            return getContinuity(rPrev, rNext);
+        }
+        else
+        {
+            return B2VectorContinuity::NONE;
+        }
+    }
+
+    void B2DPolygon::getBezierSegment(sal_uInt32 nIndex, B2DCubicBezier& rTarget) const
+    {
+        const bool bNextIndexValidWithoutClose(nIndex + 1 < count());
+
+        if(bNextIndexValidWithoutClose || isClosed())
+        {
+            const sal_uInt32 nNextIndex(bNextIndexValidWithoutClose ? nIndex + 1 : 0);
+            rTarget.setStartPoint(getB2DPoint(nIndex));
+            rTarget.setEndPoint(getB2DPoint(nNextIndex));
+
+            if(areControlPointsUsed())
+            {
+                rTarget.setControlPointA(rTarget.getStartPoint() + getNextControlVector(nIndex));
+                rTarget.setControlPointB(rTarget.getEndPoint() + getPrevControlVector(nNextIndex));
+            }
+            else
+            {
+                // no bezier, reset control points at rTarget
+                rTarget.setControlPointA(rTarget.getStartPoint());
+                rTarget.setControlPointB(rTarget.getEndPoint());
+            }
+        }
+        else
+        {
+            // no valid edge at all, reset rTarget to current point
+            const B2DPoint aPoint(getB2DPoint(nIndex));
+            rTarget.setStartPoint(aPoint);
+            rTarget.setEndPoint(aPoint);
+            rTarget.setControlPointA(aPoint);
+            rTarget.setControlPointB(aPoint);
+        }
+    }
+
+    B2DPolygon const & B2DPolygon::getDefaultAdaptiveSubdivision() const
+    {
+        return mpPolygon->getDefaultAdaptiveSubdivision(*this);
+    }
+
+    B2DRange const & B2DPolygon::getB2DRange() const
+    {
+        return mpPolygon->getB2DRange(*this);
+    }
+
+    void B2DPolygon::append(const B2DPolygon& rPoly, sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        assert(nIndex + nCount <= rPoly.count());
+
+        if(!nCount)
+        {
+            nCount = rPoly.count() - nIndex;
+            if (!nCount)
+                return;
+        }
+
+        if(nIndex == 0 && nCount == rPoly.count())
+        {
+            mpPolygon->append(*rPoly.mpPolygon);
+        }
+        else
+        {
+            mpPolygon->append(ImplB2DPolygon(*rPoly.mpPolygon, nIndex, nCount));
+        }
+    }
+
+    void B2DPolygon::remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            mpPolygon->remove(nIndex, nCount);
+        }
+    }
+
+    void B2DPolygon::clear()
+    {
+        *mpPolygon = ImplB2DPolygon();
+    }
+
+    bool B2DPolygon::isClosed() const
+    {
+        return mpPolygon->isClosed();
+    }
+
+    void B2DPolygon::setClosed(bool bNew)
+    {
+        if(isClosed() != bNew)
+        {
+            mpPolygon->setClosed(bNew);
+        }
+    }
+
+    void B2DPolygon::flip()
+    {
+        if(count() > 1)
+        {
+            mpPolygon->flip();
+        }
+    }
+
+    bool B2DPolygon::hasDoublePoints() const
+    {
+        return (count() > 1 && mpPolygon->hasDoublePoints());
+    }
+
+    void B2DPolygon::removeDoublePoints()
+    {
+        if(hasDoublePoints())
+        {
+            mpPolygon->removeDoublePointsAtBeginEnd();
+            mpPolygon->removeDoublePointsWholeTrack();
+        }
+    }
+
+    void B2DPolygon::transform(const B2DHomMatrix& rMatrix)
+    {
+        if(count() && !rMatrix.isIdentity())
+        {
+            mpPolygon->transform(rMatrix);
+        }
+    }
+
+    void B2DPolygon::addOrReplaceSystemDependentDataInternal(SystemDependentData_SharedPtr& rData) const
+    {
+        mpPolygon->addOrReplaceSystemDependentData(rData);
+    }
+
+    SystemDependentData_SharedPtr B2DPolygon::getSystemDependantDataInternal(size_t hash_code) const
+    {
+        return mpPolygon->getSystemDependentData(hash_code);
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolygonclipper.cxx b/basegfx/source/polygon/b2dpolygonclipper.cxx
new file mode 100644
index 0000000000..e2f1f06038
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygonclipper.cxx
@@ -0,0 +1,824 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dpolygonclipper.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
+#include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/utils/rectcliptools.hxx>
+#include <sal/log.hxx>
+
+namespace basegfx::utils
+{
+        B2DPolyPolygon clipPolygonOnParallelAxis(const B2DPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count())
+            {
+                const B2DRange aCandidateRange(getRange(rCandidate));
+
+                if(bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinY(), fValueOnOtherAxis))
+                {
+                    // completely above and on the clip line. also true for curves.
+                    if(bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxY(), fValueOnOtherAxis))
+                {
+                    // completely below and on the clip line. also true for curves.
+                    if(!bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(!bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinX(), fValueOnOtherAxis))
+                {
+                    // completely right of and on the clip line. also true for curves.
+                    if(bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(!bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxX(), fValueOnOtherAxis))
+                {
+                    // completely left of and on the clip line. also true for curves.
+                    if(!bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else
+                {
+                    // add cuts with axis to polygon, including bezier segments
+                    // Build edge to cut with. Make it a little big longer than needed for
+                    // numerical stability. We want to cut against the edge seen as endless
+                    // ray here, but addPointsAtCuts() will limit itself to the
+                    // edge's range ]0.0 .. 1.0[.
+                    const double fSmallExtension((aCandidateRange.getWidth() + aCandidateRange.getHeight()) * (0.5 * 0.1));
+                    const B2DPoint aStart(
+                        bParallelToXAxis ? aCandidateRange.getMinX() - fSmallExtension : fValueOnOtherAxis,
+                        bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMinY() - fSmallExtension);
+                    const B2DPoint aEnd(
+                        bParallelToXAxis ? aCandidateRange.getMaxX() + fSmallExtension : fValueOnOtherAxis,
+                        bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMaxY() + fSmallExtension);
+                    const B2DPolygon aCandidate(addPointsAtCuts(rCandidate, aStart, aEnd));
+                    const sal_uInt32 nPointCount(aCandidate.count());
+                    const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    B2DCubicBezier aEdge;
+                    B2DPolygon aRun;
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        aCandidate.getBezierSegment(a, aEdge);
+                        const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
+                        const bool bInside(bParallelToXAxis ?
+                            fTools::moreOrEqual(aTestPoint.getY(), fValueOnOtherAxis) == bAboveAxis :
+                            fTools::moreOrEqual(aTestPoint.getX(), fValueOnOtherAxis) == bAboveAxis);
+
+                        if(bInside)
+                        {
+                            if(!aRun.count() || !aRun.getB2DPoint(aRun.count() - 1).equal(aEdge.getStartPoint()))
+                            {
+                                aRun.append(aEdge.getStartPoint());
+                            }
+
+                            if(aEdge.isBezier())
+                            {
+                                aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
+                            }
+                            else
+                            {
+                                aRun.append(aEdge.getEndPoint());
+                            }
+                        }
+                        else
+                        {
+                            if(bStroke && aRun.count())
+                            {
+                                aRetval.append(aRun);
+                                aRun.clear();
+                            }
+                        }
+                    }
+
+                    if(aRun.count())
+                    {
+                        if(bStroke)
+                        {
+                            // try to merge this last and first polygon; they may have been
+                            // the former polygon's start/end point
+                            if(aRetval.count())
+                            {
+                                const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
+
+                                if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
+                                {
+                                    // append start polygon to aRun, remove from result set
+                                    aRun.append(aStartPolygon); aRun.removeDoublePoints();
+                                    aRetval.remove(0);
+                                }
+                            }
+
+                            aRetval.append(aRun);
+                        }
+                        else
+                        {
+                            // set closed flag and correct last point (which is added double now).
+                            closeWithGeometryChange(aRun);
+                            aRetval.append(aRun);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnParallelAxis(const B2DPolyPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(const auto& rB2DPolygon : rCandidate )
+            {
+                const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnParallelAxis(rB2DPolygon, bParallelToXAxis, bAboveAxis, fValueOnOtherAxis, bStroke));
+
+                if(aClippedPolyPolygon.count())
+                {
+                    aRetval.append(aClippedPolyPolygon);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolygonOnRange(const B2DPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+            B2DPolyPolygon aRetval;
+
+            if(!nCount)
+            {
+                // source is empty
+                return aRetval;
+            }
+
+            if(rRange.isEmpty())
+            {
+                if(bInside)
+                {
+                    // nothing is inside an empty range
+                    return aRetval;
+                }
+                else
+                {
+                    // everything is outside an empty range
+                    return B2DPolyPolygon(rCandidate);
+                }
+            }
+
+            const B2DRange aCandidateRange(getRange(rCandidate));
+
+            if(rRange.isInside(aCandidateRange))
+            {
+                  // candidate is completely inside given range
+                if(bInside)
+                {
+                    // nothing to do
+                    return B2DPolyPolygon(rCandidate);
+                }
+                else
+                {
+                    // nothing is outside, then
+                    return aRetval;
+                }
+            }
+
+            if(!bInside)
+            {
+                // cutting off the outer parts of filled polygons at parallel
+                // lines to the axes is only possible for the inner part, not for
+                // the outer part which means cutting a hole into the original polygon.
+                // This is because the inner part is a logical AND-operation of
+                // the four implied half-planes, but the outer part is not.
+                // It is possible for strokes, but with creating unnecessary extra
+                // cuts, so using clipPolygonOnPolyPolygon is better there, too.
+                // This needs to be done with the topology knowledge and is unfortunately
+                // more expensive, too.
+                const B2DPolygon aClip(createPolygonFromRect(rRange));
+
+                return clipPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
+            }
+
+            // clip against the four axes of the range
+            // against X-Axis, lower value
+            aRetval = clipPolygonOnParallelAxis(rCandidate, true, bInside, rRange.getMinY(), bStroke);
+
+            if(aRetval.count())
+            {
+                // against Y-Axis, lower value
+                if(aRetval.count() == 1)
+                {
+                    aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), false, bInside, rRange.getMinX(), bStroke);
+                }
+                else
+                {
+                    aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, bInside, rRange.getMinX(), bStroke);
+                }
+
+                if(aRetval.count())
+                {
+                    // against X-Axis, higher value
+                    if(aRetval.count() == 1)
+                    {
+                        aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), true, false, rRange.getMaxY(), bStroke);
+                    }
+                    else
+                    {
+                        aRetval = clipPolyPolygonOnParallelAxis(aRetval, true, false, rRange.getMaxY(), bStroke);
+                    }
+
+                    if(aRetval.count())
+                    {
+                        // against Y-Axis, higher value
+                        if(aRetval.count() == 1)
+                        {
+                            aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), false, false, rRange.getMaxX(), bStroke);
+                        }
+                        else
+                        {
+                            aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, false, rRange.getMaxX(), bStroke);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnRange(const B2DPolyPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(!rCandidate.count())
+            {
+                // source is empty
+                return aRetval;
+            }
+
+            if(rRange.isEmpty())
+            {
+                if(bInside)
+                {
+                    // nothing is inside an empty range
+                    return aRetval;
+                }
+                else
+                {
+                    // everything is outside an empty range
+                    return rCandidate;
+                }
+            }
+
+            if(bInside)
+            {
+                for( const auto& rClippedPoly : rCandidate)
+                {
+                    const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnRange(rClippedPoly , rRange, bInside, bStroke));
+
+                    if(aClippedPolyPolygon.count())
+                    {
+                        aRetval.append(aClippedPolyPolygon);
+                    }
+                }
+            }
+            else
+            {
+                // for details, see comment in clipPolygonOnRange for the "cutting off
+                // the outer parts of filled polygons at parallel lines" explanations
+                const B2DPolygon aClip(createPolygonFromRect(rRange));
+
+                return clipPolyPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnPolyPolygon(const B2DPolyPolygon& rCandidate, const B2DPolyPolygon& rClip,
+                                                    bool bInside, bool bStroke, size_t* pPointLimit)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count() && rClip.count())
+            {
+                // one or both are no rectangle - go the hard way and clip PolyPolygon
+                // against PolyPolygon...
+                if(bStroke)
+                {
+                    // line clipping, create line snippets by first adding all cut points and
+                    // then marching along the edges and detecting if they are inside or outside
+                    // the clip polygon
+                    for(const auto& rPolygon : rCandidate)
+                    {
+                        // add cuts with clip to polygon, including bezier segments
+                        const B2DPolygon aCandidate(addPointsAtCuts(rPolygon, rClip));
+                        const sal_uInt32 nPointCount(aCandidate.count());
+                        const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                        B2DCubicBezier aEdge;
+                        B2DPolygon aRun;
+
+                        for(sal_uInt32 b(0); b < nEdgeCount; b++)
+                        {
+                            aCandidate.getBezierSegment(b, aEdge);
+                            const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
+                            const bool bIsInside(utils::isInside(rClip, aTestPoint) == bInside);
+
+                            if(bIsInside)
+                            {
+                                if(!aRun.count())
+                                {
+                                    aRun.append(aEdge.getStartPoint());
+                                }
+
+                                if(aEdge.isBezier())
+                                {
+                                    aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
+                                }
+                                else
+                                {
+                                    aRun.append(aEdge.getEndPoint());
+                                }
+                            }
+                            else
+                            {
+                                if(aRun.count())
+                                {
+                                    aRetval.append(aRun);
+                                    aRun.clear();
+                                }
+                            }
+                        }
+
+                        if(aRun.count())
+                        {
+                            // try to merge this last and first polygon; they may have been
+                            // the former polygon's start/end point
+                            if(aRetval.count())
+                            {
+                                const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
+
+                                if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
+                                {
+                                    // append start polygon to aRun, remove from result set
+                                    aRun.append(aStartPolygon); aRun.removeDoublePoints();
+                                    aRetval.remove(0);
+                                }
+                            }
+
+                            aRetval.append(aRun);
+                        }
+                    }
+                }
+                else
+                {
+                    // check for simplification with ranges if !bStroke (handling as stroke is more simple),
+                    // but also only when bInside, else the simplification may lead to recursive calls (see
+                    // calls to clipPolyPolygonOnPolyPolygon in clipPolyPolygonOnRange and clipPolygonOnRange)
+                    if (bInside && basegfx::utils::isRectangle(rClip))
+                    {
+                        // #i125349# detect if both given PolyPolygons are indeed ranges
+                        if (basegfx::utils::isRectangle(rCandidate))
+                        {
+                            // both are rectangle
+                            if(rCandidate.getB2DRange().equal(rClip.getB2DRange()))
+                            {
+                                // if both are equal -> no change
+                                return rCandidate;
+                            }
+                            else
+                            {
+                                // not equal -> create new intersection from both ranges,
+                                // but much cheaper based on the ranges
+                                basegfx::B2DRange aIntersectionRange(rCandidate.getB2DRange());
+
+                                aIntersectionRange.intersect(rClip.getB2DRange());
+
+                                if(aIntersectionRange.isEmpty())
+                                {
+                                    // no common IntersectionRange -> the clip will be empty
+                                    return B2DPolyPolygon();
+                                }
+                                else
+                                {
+                                    // use common aIntersectionRange as result, convert
+                                    // to expected utils::PolyPolygon form
+                                    return basegfx::B2DPolyPolygon(
+                                        basegfx::utils::createPolygonFromRect(aIntersectionRange));
+                                }
+                            }
+                        }
+                        else
+                        {
+                            // rClip is rectangle -> clip rCandidate on rRectangle, use the much
+                            // cheaper and numerically more stable clipping against a range
+                            return clipPolyPolygonOnRange(rCandidate, rClip.getB2DRange(), bInside, bStroke);
+                        }
+                    }
+
+                    // area clipping
+
+                    // First solve all polygon-self and polygon-polygon intersections.
+                    // Also get rid of some not-needed polygons (neutral, no area -> when
+                    // no intersections, these are tubes).
+                    // Now it is possible to correct the orientations in the cut-free
+                    // polygons to values corresponding to painting the utils::PolyPolygon with
+                    // a XOR-WindingRule.
+                    B2DPolyPolygon aMergePolyPolygonA = solveCrossovers(rClip);
+                    aMergePolyPolygonA = stripNeutralPolygons(aMergePolyPolygonA);
+                    aMergePolyPolygonA = correctOrientations(aMergePolyPolygonA);
+
+                    if(!bInside)
+                    {
+                        // if we want to get the outside of the clip polygon, make
+                        // it a 'Hole' in topological sense
+                        aMergePolyPolygonA.flip();
+                    }
+
+
+                    // prepare 2nd source polygon in same way
+                    B2DPolyPolygon aMergePolyPolygonB = solveCrossovers(rCandidate, pPointLimit);
+
+                    if (pPointLimit && !*pPointLimit)
+                    {
+                        SAL_WARN("basegfx", "clipPolyPolygonOnPolyPolygon hit point limit");
+                        return aRetval;
+                    }
+
+                    aMergePolyPolygonB = stripNeutralPolygons(aMergePolyPolygonB);
+                    aMergePolyPolygonB = correctOrientations(aMergePolyPolygonB);
+
+                    // to clip against each other, concatenate and solve all
+                    // polygon-polygon crossovers. polygon-self do not need to
+                    // be solved again, they were solved in the preparation.
+                    aRetval.append(aMergePolyPolygonA);
+                    aRetval.append(aMergePolyPolygonB);
+                    aRetval = solveCrossovers(aRetval, pPointLimit);
+
+                    // now remove neutral polygons (closed, but no area). In a last
+                    // step throw away all polygons which have a depth of less than 1
+                    // which means there was no logical AND at their position. For the
+                    // not-inside solution, the clip was flipped to define it as 'Hole',
+                    // so the removal rule is different here; remove all with a depth
+                    // of less than 0 (aka holes).
+                    aRetval = stripNeutralPolygons(aRetval);
+                    aRetval = stripDispensablePolygons(aRetval, bInside);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolygonOnPolyPolygon(const B2DPolygon& rCandidate, const B2DPolyPolygon& rClip, bool bInside, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count() && rClip.count())
+            {
+                aRetval = clipPolyPolygonOnPolyPolygon(B2DPolyPolygon(rCandidate), rClip, bInside, bStroke);
+            }
+
+            return aRetval;
+        }
+
+        namespace {
+
+        /*
+        * let a plane be defined as
+        *
+        *     v.n+d=0
+        *
+        * and a ray be defined as
+        *
+        *     a+(b-a)*t=0
+        *
+        * substitute and rearranging yields
+        *
+        *     t = -(a.n+d)/(n.(b-a))
+        *
+        * if the denominator is zero, the line is either
+        * contained in the plane or parallel to the plane.
+        * in either case, there is no intersection.
+        * if numerator and denominator are both zero, the
+        * ray is contained in the plane.
+        *
+        */
+        struct scissor_plane {
+            double nx,ny;           // plane normal
+            double d;               // [-] minimum distance from origin
+            sal_uInt32 clipmask;    // clipping mask, e.g. 1000 1000
+        };
+
+        }
+
+        /*
+        *
+        * polygon clipping rules  (straight out of Foley and Van Dam)
+        * ===========================================================
+        * current   |next       |emit
+        * ____________________________________
+        * inside    |inside     |next
+        * inside    |outside    |intersect with clip plane
+        * outside   |outside    |nothing
+        * outside   |inside     |intersect with clip plane followed by next
+        *
+        */
+        static sal_uInt32 scissorLineSegment( ::basegfx::B2DPoint           *in_vertex,    // input buffer
+                                       sal_uInt32                     in_count,     // number of verts in input buffer
+                                       ::basegfx::B2DPoint           *out_vertex,   // output buffer
+                                       scissor_plane const           *pPlane,       // scissoring plane
+                                       const ::basegfx::B2DRectangle &rR )          // clipping rectangle
+        {
+
+            sal_uInt32 out_count=0;
+
+            // process all the verts
+            for(sal_uInt32 i=0; i<in_count; i++) {
+
+                // vertices are relative to the coordinate
+                // system defined by the rectangle.
+                ::basegfx::B2DPoint *curr = &in_vertex[i];
+                ::basegfx::B2DPoint *next = &in_vertex[(i+1)%in_count];
+
+                // perform clipping judgement & mask against current plane.
+                sal_uInt32 clip = pPlane->clipmask & ((getCohenSutherlandClipFlags(*curr,rR)<<4)|getCohenSutherlandClipFlags(*next,rR));
+
+                if(clip==0) { // both verts are inside
+                    out_vertex[out_count++] = *next;
+                }
+                else if((clip&0x0f) && (clip&0xf0)) { // both verts are outside
+                }
+                else if((clip&0x0f) && (clip&0xf0)==0) { // curr is inside, next is outside
+
+                    // direction vector from 'current' to 'next', *not* normalized
+                    // to bring 't' into the [0<=x<=1] interval.
+                    ::basegfx::B2DPoint dir((*next)-(*curr));
+
+                    double denominator = pPlane->nx*dir.getX() +
+                                         pPlane->ny*dir.getY();
+                    double numerator =  pPlane->nx*curr->getX() +
+                                        pPlane->ny*curr->getY() +
+                                        pPlane->d;
+                    double t = -numerator/denominator;
+
+                    // calculate the actual point of intersection
+                    ::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
+                                                    curr->getY()+t*dir.getY() );
+
+                    out_vertex[out_count++] = intersection;
+                }
+                else if((clip&0x0f)==0 && (clip&0xf0)) { // curr is outside, next is inside
+
+                    // direction vector from 'current' to 'next', *not* normalized
+                    // to bring 't' into the [0<=x<=1] interval.
+                    ::basegfx::B2DPoint dir((*next)-(*curr));
+
+                    double denominator = pPlane->nx*dir.getX() +
+                                         pPlane->ny*dir.getY();
+                    double numerator =  pPlane->nx*curr->getX() +
+                                        pPlane->ny*curr->getY() +
+                                        pPlane->d;
+                    double t = -numerator/denominator;
+
+                    // calculate the actual point of intersection
+                    ::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
+                                                    curr->getY()+t*dir.getY() );
+
+                    out_vertex[out_count++] = intersection;
+                    out_vertex[out_count++] = *next;
+                }
+            }
+
+            return out_count;
+        }
+
+        B2DPolygon clipTriangleListOnRange( const B2DPolygon& rCandidate,
+                                            const B2DRange&   rRange )
+        {
+            B2DPolygon aResult;
+
+            if( !(rCandidate.count()%3) )
+            {
+                const int scissor_plane_count = 4;
+
+                scissor_plane sp[scissor_plane_count];
+
+                sp[0].nx = +1.0;
+                sp[0].ny = +0.0;
+                sp[0].d = -(rRange.getMinX());
+                sp[0].clipmask = (RectClipFlags::LEFT << 4) | RectClipFlags::LEFT; // 0001 0001
+                sp[1].nx = -1.0;
+                sp[1].ny = +0.0;
+                sp[1].d = +(rRange.getMaxX());
+                sp[1].clipmask = (RectClipFlags::RIGHT << 4) | RectClipFlags::RIGHT; // 0010 0010
+                sp[2].nx = +0.0;
+                sp[2].ny = +1.0;
+                sp[2].d = -(rRange.getMinY());
+                sp[2].clipmask = (RectClipFlags::TOP << 4) | RectClipFlags::TOP; // 0100 0100
+                sp[3].nx = +0.0;
+                sp[3].ny = -1.0;
+                sp[3].d = +(rRange.getMaxY());
+                sp[3].clipmask = (RectClipFlags::BOTTOM << 4) | RectClipFlags::BOTTOM; // 1000 1000
+
+                // retrieve the number of vertices of the triangulated polygon
+                const sal_uInt32 nVertexCount = rCandidate.count();
+
+                if(nVertexCount)
+                {
+                    // Upper bound for the maximal number of vertices when intersecting an
+                    // axis-aligned rectangle with a triangle in E2
+
+                    // The rectangle and the triangle are in general position, and have 4 and 3
+                    // vertices, respectively.
+
+                    //   Lemma: Since the rectangle is a convex polygon ( see
+                    //   http://mathworld.wolfram.com/ConvexPolygon.html for a definition), and
+                    //   has no holes, it follows that any straight line will intersect the
+                    //   rectangle's border line at utmost two times (with the usual
+                    //   tie-breaking rule, if the intersection exactly hits an already existing
+                    //   rectangle vertex, that this intersection is only attributed to one of
+                    //   the adjoining edges). Thus, having a rectangle intersected with
+                    //   a half-plane (one side of a straight line denotes 'inside', the
+                    //   other 'outside') will at utmost add _one_  vertex to the resulting
+                    //   intersection polygon (adding two intersection vertices, and removing at
+                    //   least one rectangle vertex):
+
+                    //         *
+                    //     +--+-----------------+
+                    //     | *                  |
+                    //     |*                   |
+                    //     +                    |
+                    //    *|                    |
+                    //   * |                    |
+                    //     +--------------------+
+
+                    //   Proof: If the straight line intersects the rectangle two
+                    //   times, it does so for distinct edges, i.e. the intersection has
+                    //   minimally one of the rectangle's vertices on either side of the straight
+                    //   line (but maybe more). Thus, the intersection with a half-plane has
+                    //   minimally _one_ rectangle vertex removed from the resulting clip
+                    //   polygon, and therefore, a clip against a half-plane has the net effect
+                    //   of adding at utmost _one_ vertex to the resulting clip polygon.
+
+                    // Theorem: The intersection of a rectangle and a triangle results in a
+                    // polygon with at utmost 7 vertices.
+
+                    // Proof: The inside of the triangle can be described as the consecutive
+                    // intersection with three half-planes. Together with the lemma above, this
+                    // results in at utmost 3 additional vertices added to the already existing 4
+                    // rectangle vertices.
+
+                    // This upper bound is attained with the following example configuration:
+
+                    //                               *
+                    //                             ***
+                    //                           ** *
+                    //                         **  *
+                    //                       **   *
+                    //                     **    *
+                    //                   **     *
+                    //                 **      *
+                    //               **       *
+                    //             **        *
+                    //           **         *
+                    //     ----*2--------3 *
+                    //     | **          |*
+                    //     1*            4
+                    //   **|            *|
+                    // **  |           * |
+                    //   **|          *  |
+                    //     7*        *   |
+                    //     --*6-----5-----
+                    //         **  *
+                    //           **
+
+                    // As we need to scissor all triangles against the
+                    // output rectangle we employ an output buffer for the
+                    // resulting vertices.  the question is how large this
+                    // buffer needs to be compared to the number of
+                    // incoming vertices.  this buffer needs to hold at
+                    // most the number of original vertices times '7'. see
+                    // figure above for an example.  scissoring triangles
+                    // with the cohen-sutherland line clipping algorithm
+                    // as implemented here will result in a triangle fan
+                    // which will be rendered as separate triangles to
+                    // avoid pipeline stalls for each scissored
+                    // triangle. creating separate triangles from a
+                    // triangle fan produces (n-2)*3 vertices where n is
+                    // the number of vertices of the original triangle
+                    // fan.  for the maximum number of 7 vertices of
+                    // resulting triangle fans we therefore need 15 times
+                    // the number of original vertices.
+
+                    //const size_t nBufferSize = sizeof(vertex)*(nVertexCount*16);
+                    //vertex *pVertices = (vertex*)alloca(nBufferSize);
+                    //sal_uInt32 nNumOutput = 0;
+
+                    // we need to clip this triangle against the output rectangle
+                    // to ensure that the resulting texture coordinates are in
+                    // the valid range from [0<=st<=1]. under normal circumstances
+                    // we could use the BORDERCOLOR renderstate but some cards
+                    // seem to ignore this feature.
+                    ::basegfx::B2DPoint stack[3];
+                    unsigned int clipflag = 0;
+
+                    for(sal_uInt32 nIndex=0; nIndex<nVertexCount; ++nIndex)
+                    {
+                        // rotate stack
+                        stack[0] = stack[1];
+                        stack[1] = stack[2];
+                        stack[2] = rCandidate.getB2DPoint(nIndex);
+
+                        // clipping judgement
+                        clipflag |= unsigned(!(rRange.isInside(stack[2])));
+
+                        if(nIndex > 1)
+                        {
+                            // consume vertices until a single separate triangle has been visited.
+                            if(!((nIndex+1)%3))
+                            {
+                                // if any of the last three vertices was outside
+                                // we need to scissor against the destination rectangle
+                                if(clipflag & 7)
+                                {
+                                    ::basegfx::B2DPoint buf0[16];
+                                    ::basegfx::B2DPoint buf1[16];
+
+                                    sal_uInt32 vertex_count = 3;
+
+                                    // clip against all 4 planes passing the result of
+                                    // each plane as the input to the next using a double buffer
+                                    vertex_count = scissorLineSegment(stack,vertex_count,buf1,&sp[0],rRange);
+                                    vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[1],rRange);
+                                    vertex_count = scissorLineSegment(buf0,vertex_count,buf1,&sp[2],rRange);
+                                    vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[3],rRange);
+
+                                    if(vertex_count >= 3)
+                                    {
+                                        // convert triangle fan back to triangle list.
+                                        ::basegfx::B2DPoint v0(buf0[0]);
+                                        ::basegfx::B2DPoint v1(buf0[1]);
+                                        for(sal_uInt32 i=2; i<vertex_count; ++i)
+                                        {
+                                            ::basegfx::B2DPoint v2(buf0[i]);
+                                            aResult.append(v0);
+                                            aResult.append(v1);
+                                            aResult.append(v2);
+                                            v1 = v2;
+                                        }
+                                    }
+                                }
+                                else
+                                {
+                                    // the last triangle has not been altered, simply copy to result
+                                    for(const basegfx::B2DPoint & i : stack)
+                                        aResult.append(i);
+                                }
+                            }
+                        }
+
+                        clipflag <<= 1;
+                    }
+                }
+            }
+
+            return aResult;
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolygoncutandtouch.cxx b/basegfx/source/polygon/b2dpolygoncutandtouch.cxx
new file mode 100644
index 0000000000..c91f0ec48f
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygoncutandtouch.cxx
@@ -0,0 +1,1077 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
+#include <osl/diagnose.h>
+#include <sal/log.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+
+#include <vector>
+#include <algorithm>
+#include <memory>
+
+#define SUBDIVIDE_FOR_CUT_TEST_COUNT        (50)
+
+namespace basegfx
+{
+    namespace
+    {
+
+        class temporaryPoint
+        {
+            B2DPoint                            maPoint;        // the new point
+            sal_uInt32                          mnIndex;        // index after which to insert
+            double                              mfCut;          // parametric cut description [0.0 .. 1.0]
+
+        public:
+            temporaryPoint(const B2DPoint& rNewPoint, sal_uInt32 nIndex, double fCut)
+            :   maPoint(rNewPoint),
+                mnIndex(nIndex),
+                mfCut(fCut)
+            {
+            }
+
+            bool operator<(const temporaryPoint& rComp) const
+            {
+                if(mnIndex == rComp.mnIndex)
+                {
+                    return (mfCut < rComp.mfCut);
+                }
+
+                return (mnIndex < rComp.mnIndex);
+            }
+
+            const B2DPoint& getPoint() const { return maPoint; }
+            sal_uInt32 getIndex() const { return mnIndex; }
+            double getCut() const { return mfCut; }
+        };
+
+        typedef std::vector< temporaryPoint > temporaryPointVector;
+
+        class temporaryPolygonData
+        {
+            B2DPolygon                              maPolygon;
+            B2DRange                                maRange;
+            temporaryPointVector                    maPoints;
+
+        public:
+            const B2DPolygon& getPolygon() const { return maPolygon; }
+            void setPolygon(const B2DPolygon& rNew) { maPolygon = rNew; maRange = utils::getRange(maPolygon); }
+            const B2DRange& getRange() const { return maRange; }
+            temporaryPointVector& getTemporaryPointVector() { return maPoints; }
+        };
+
+        B2DPolygon mergeTemporaryPointsAndPolygon(const B2DPolygon& rCandidate, temporaryPointVector& rTempPoints)
+        {
+            // #i76891# mergeTemporaryPointsAndPolygon redesigned to be able to correctly handle
+            // single edges with/without control points
+            // #i101491# added counter for non-changing element count
+            const sal_uInt32 nTempPointCount(rTempPoints.size());
+
+            if(nTempPointCount)
+            {
+                B2DPolygon aRetval;
+                const sal_uInt32 nCount(rCandidate.count());
+
+                if(nCount)
+                {
+                    // sort temp points to assure increasing fCut values and increasing indices
+                    std::sort(rTempPoints.begin(), rTempPoints.end());
+
+                    // prepare loop
+                    B2DCubicBezier aEdge;
+                    sal_uInt32 nNewInd(0);
+
+                    // add start point
+                    aRetval.append(rCandidate.getB2DPoint(0));
+
+                    for(sal_uInt32 a(0); a < nCount; a++)
+                    {
+                        // get edge
+                        rCandidate.getBezierSegment(a, aEdge);
+
+                        if(aEdge.isBezier())
+                        {
+                            // control vectors involved for this edge
+                            double fLeftStart(0.0);
+
+                            // now add all points targeted to be at this index
+                            while (nNewInd < nTempPointCount && rTempPoints[nNewInd].getIndex() == a && fLeftStart < 1.0)
+                            {
+                                const temporaryPoint& rTempPoint = rTempPoints[nNewInd++];
+
+                                // split curve segment. Splits need to come sorted and need to be < 1.0. Also,
+                                // since original segment is consumed from left to right, the cut values need
+                                // to be scaled to the remaining part
+                                B2DCubicBezier aLeftPart;
+                                const double fRelativeSplitPoint((rTempPoint.getCut() - fLeftStart) / (1.0 - fLeftStart));
+                                aEdge.split(fRelativeSplitPoint, &aLeftPart, &aEdge);
+                                fLeftStart = rTempPoint.getCut();
+
+                                // add left bow
+                                aRetval.appendBezierSegment(aLeftPart.getControlPointA(), aLeftPart.getControlPointB(), rTempPoint.getPoint());
+                            }
+
+                            // add remaining bow
+                            aRetval.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
+                        }
+                        else
+                        {
+                            // add all points targeted to be at this index
+                            while(nNewInd < nTempPointCount && rTempPoints[nNewInd].getIndex() == a)
+                            {
+                                const temporaryPoint& rTempPoint = rTempPoints[nNewInd++];
+                                const B2DPoint& aNewPoint(rTempPoint.getPoint());
+
+                                // do not add points double
+                                if(!aRetval.getB2DPoint(aRetval.count() - 1).equal(aNewPoint))
+                                {
+                                    aRetval.append(aNewPoint);
+                                }
+                            }
+
+                            // add edge end point
+                            aRetval.append(aEdge.getEndPoint());
+                        }
+                    }
+                }
+
+                if(rCandidate.isClosed())
+                {
+                    // set closed flag and correct last point (which is added double now).
+                    utils::closeWithGeometryChange(aRetval);
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        void adaptAndTransferCutsWithBezierSegment(
+            const temporaryPointVector& rPointVector, const B2DPolygon& rPolygon,
+            sal_uInt32 nInd, temporaryPointVector& rTempPoints)
+        {
+            // assuming that the subdivision to create rPolygon used equidistant pieces
+            // (as in adaptiveSubdivideByCount) it is now possible to calculate back the
+            // cut positions in the polygon to relative cut positions on the original bezier
+            // segment.
+            const sal_uInt32 nEdgeCount(rPolygon.count() ? rPolygon.count() - 1 : 0);
+
+            if(!rPointVector.empty() && nEdgeCount)
+            {
+                for( const auto& rTempPoint : rPointVector )
+                {
+                    const double fCutPosInPolygon(static_cast<double>(rTempPoint.getIndex()) + rTempPoint.getCut());
+                    const double fRelativeCutPos(fCutPosInPolygon / static_cast<double>(nEdgeCount));
+                    rTempPoints.emplace_back(rTempPoint.getPoint(), nInd, fRelativeCutPos);
+                }
+            }
+        }
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx
+{
+    namespace
+    {
+
+        // predefines for calls to this methods before method implementation
+
+        void findCuts(const B2DPolygon& rCandidate, temporaryPointVector& rTempPoints, size_t* pPointLimit = nullptr);
+        void findTouches(const B2DPolygon& rEdgePolygon, const B2DPolygon& rPointPolygon, temporaryPointVector& rTempPoints);
+        void findCuts(const B2DPolygon& rCandidateA, const B2DPolygon& rCandidateB, temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB);
+
+        void findEdgeCutsTwoEdges(
+            const B2DPoint& rCurrA, const B2DPoint& rNextA,
+            const B2DPoint& rCurrB, const B2DPoint& rNextB,
+            sal_uInt32 nIndA, sal_uInt32 nIndB,
+            temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB)
+        {
+            // no null length edges
+            if(rCurrA.equal(rNextA) || rCurrB.equal(rNextB))
+                return;
+
+            // no common start/end points, this can be no cuts
+            if(rCurrB.equal(rCurrA) || rCurrB.equal(rNextA) || rNextB.equal(rCurrA) || rNextB.equal(rNextA))
+                return;
+
+            const B2DVector aVecA(rNextA - rCurrA);
+            const B2DVector aVecB(rNextB - rCurrB);
+            double fCut(aVecA.cross(aVecB));
+
+            if(fTools::equalZero(fCut))
+                return;
+
+            const double fZero(0.0);
+            const double fOne(1.0);
+            fCut = (aVecB.getY() * (rCurrB.getX() - rCurrA.getX()) + aVecB.getX() * (rCurrA.getY() - rCurrB.getY())) / fCut;
+
+            if (!fTools::betweenOrEqualEither(fCut, fZero, fOne))
+                return;
+
+            // it's a candidate, but also need to test parameter value of cut on line 2
+            double fCut2;
+
+            // choose the more precise version
+            if(fabs(aVecB.getX()) > fabs(aVecB.getY()))
+            {
+                fCut2 = (rCurrA.getX() + (fCut * aVecA.getX()) - rCurrB.getX()) / aVecB.getX();
+            }
+            else
+            {
+                fCut2 = (rCurrA.getY() + (fCut * aVecA.getY()) - rCurrB.getY()) / aVecB.getY();
+            }
+
+            if (fTools::betweenOrEqualEither(fCut2, fZero, fOne))
+            {
+                // cut is in range, add point. Two edges can have only one cut, but
+                // add a cut point to each list. The lists may be the same for
+                // self intersections.
+                const B2DPoint aCutPoint(interpolate(rCurrA, rNextA, fCut));
+                rTempPointsA.emplace_back(aCutPoint, nIndA, fCut);
+                rTempPointsB.emplace_back(aCutPoint, nIndB, fCut2);
+            }
+        }
+
+        void findCutsAndTouchesAndCommonForBezier(const B2DPolygon& rCandidateA, const B2DPolygon& rCandidateB, temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB)
+        {
+            // #i76891#
+            // This new method is necessary since in findEdgeCutsBezierAndEdge and in findEdgeCutsTwoBeziers
+            // it is not sufficient to use findCuts() recursively. This will indeed find the cuts between the
+            // segments of the two temporarily adaptive subdivided bezier segments, but not the touches or
+            // equal points of them.
+            // It would be possible to find the touches using findTouches(), but at last with common points
+            // the adding of cut points (temporary points) would fail. But for these temporarily adaptive
+            // subdivided bezier segments, common points may be not very likely, but the bug shows that it
+            // happens.
+            // Touch points are a little bit more likely than common points. All in all it is best to use
+            // a specialized method here which can profit from knowing that it is working on a special
+            // family of B2DPolygons: no curve segments included and not closed.
+            OSL_ENSURE(!rCandidateA.areControlPointsUsed() && !rCandidateB.areControlPointsUsed(), "findCutsAndTouchesAndCommonForBezier only works with subdivided polygons (!)");
+            OSL_ENSURE(!rCandidateA.isClosed() && !rCandidateB.isClosed(), "findCutsAndTouchesAndCommonForBezier only works with opened polygons (!)");
+            const sal_uInt32 nPointCountA(rCandidateA.count());
+            const sal_uInt32 nPointCountB(rCandidateB.count());
+
+            if(nPointCountA <= 1 || nPointCountB <= 1)
+                return;
+
+            const sal_uInt32 nEdgeCountA(nPointCountA - 1);
+            const sal_uInt32 nEdgeCountB(nPointCountB - 1);
+            B2DPoint aCurrA(rCandidateA.getB2DPoint(0));
+
+            for(sal_uInt32 a(0); a < nEdgeCountA; a++)
+            {
+                const B2DPoint aNextA(rCandidateA.getB2DPoint(a + 1));
+                const B2DRange aRangeA(aCurrA, aNextA);
+                B2DPoint aCurrB(rCandidateB.getB2DPoint(0));
+
+                for(sal_uInt32 b(0); b < nEdgeCountB; b++)
+                {
+                    const B2DPoint aNextB(rCandidateB.getB2DPoint(b + 1));
+                    const B2DRange aRangeB(aCurrB, aNextB);
+
+                    if(aRangeA.overlaps(aRangeB))
+                    {
+                        // no null length edges
+                        if(!(aCurrA.equal(aNextA) || aCurrB.equal(aNextB)))
+                        {
+                            const B2DVector aVecA(aNextA - aCurrA);
+                            const B2DVector aVecB(aNextB - aCurrB);
+                            double fCutA(aVecA.cross(aVecB));
+
+                            if(!fTools::equalZero(fCutA))
+                            {
+                                const double fZero(0.0);
+                                const double fOne(1.0);
+                                fCutA = (aVecB.getY() * (aCurrB.getX() - aCurrA.getX()) + aVecB.getX() * (aCurrA.getY() - aCurrB.getY())) / fCutA;
+
+                                // use range [0.0 .. 1.0[, thus in the loop, all direct aCurrA cuts will be registered
+                                // as 0.0 cut. The 1.0 cut will be registered in the next loop step
+                                if(fTools::moreOrEqual(fCutA, fZero) && fTools::less(fCutA, fOne))
+                                {
+                                    // it's a candidate, but also need to test parameter value of cut on line 2
+                                    double fCutB;
+
+                                    // choose the more precise version
+                                    if(fabs(aVecB.getX()) > fabs(aVecB.getY()))
+                                    {
+                                        fCutB = (aCurrA.getX() + (fCutA * aVecA.getX()) - aCurrB.getX()) / aVecB.getX();
+                                    }
+                                    else
+                                    {
+                                        fCutB = (aCurrA.getY() + (fCutA * aVecA.getY()) - aCurrB.getY()) / aVecB.getY();
+                                    }
+
+                                    // use range [0.0 .. 1.0[, thus in the loop, all direct aCurrA cuts will be registered
+                                    // as 0.0 cut. The 1.0 cut will be registered in the next loop step
+                                    if(fTools::moreOrEqual(fCutB, fZero) && fTools::less(fCutB, fOne))
+                                    {
+                                        // cut is in both ranges. Add points for A and B
+                                        // #i111715# use fTools::equal instead of fTools::equalZero for better accuracy
+                                        if(fTools::equal(fCutA, fZero))
+                                        {
+                                            // ignore for start point in first edge; this is handled
+                                            // by outer methods and would just produce a double point
+                                            if(a)
+                                            {
+                                                rTempPointsA.emplace_back(aCurrA, a, 0.0);
+                                            }
+                                        }
+                                        else
+                                        {
+                                            const B2DPoint aCutPoint(interpolate(aCurrA, aNextA, fCutA));
+                                            rTempPointsA.emplace_back(aCutPoint, a, fCutA);
+                                        }
+
+                                        // #i111715# use fTools::equal instead of fTools::equalZero for better accuracy
+                                        if(fTools::equal(fCutB, fZero))
+                                        {
+                                            // ignore for start point in first edge; this is handled
+                                            // by outer methods and would just produce a double point
+                                            if(b)
+                                            {
+                                                rTempPointsB.emplace_back(aCurrB, b, 0.0);
+                                            }
+                                        }
+                                        else
+                                        {
+                                            const B2DPoint aCutPoint(interpolate(aCurrB, aNextB, fCutB));
+                                            rTempPointsB.emplace_back(aCutPoint, b, fCutB);
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+
+                    // prepare next step
+                    aCurrB = aNextB;
+                }
+
+                // prepare next step
+                aCurrA = aNextA;
+            }
+        }
+
+        void findEdgeCutsBezierAndEdge(
+            const B2DCubicBezier& rCubicA,
+            const B2DPoint& rCurrB, const B2DPoint& rNextB,
+            sal_uInt32 nIndA, sal_uInt32 nIndB,
+            temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB)
+        {
+            // find all cuts between given bezier segment and edge. Add an entry to the tempPoints
+            // for each common point with the cut value describing the relative position on given
+            // bezier segment and edge.
+            B2DPolygon aTempPolygonA;
+            B2DPolygon aTempPolygonEdge;
+            temporaryPointVector aTempPointVectorA;
+            temporaryPointVector aTempPointVectorEdge;
+
+            // create subdivided polygons and find cuts between them
+            // Keep adaptiveSubdivideByCount due to needed quality
+            aTempPolygonA.reserve(SUBDIVIDE_FOR_CUT_TEST_COUNT + 8);
+            aTempPolygonA.append(rCubicA.getStartPoint());
+            rCubicA.adaptiveSubdivideByCount(aTempPolygonA, SUBDIVIDE_FOR_CUT_TEST_COUNT);
+            aTempPolygonEdge.append(rCurrB);
+            aTempPolygonEdge.append(rNextB);
+
+            // #i76891# using findCuts recursively is not sufficient here
+            findCutsAndTouchesAndCommonForBezier(aTempPolygonA, aTempPolygonEdge, aTempPointVectorA, aTempPointVectorEdge);
+
+            if(!aTempPointVectorA.empty())
+            {
+                // adapt tempVector entries to segment
+                adaptAndTransferCutsWithBezierSegment(aTempPointVectorA, aTempPolygonA, nIndA, rTempPointsA);
+            }
+
+            // append remapped tempVector entries for edge to tempPoints for edge
+            for(const temporaryPoint & rTempPoint : aTempPointVectorEdge)
+            {
+                rTempPointsB.emplace_back(rTempPoint.getPoint(), nIndB, rTempPoint.getCut());
+            }
+        }
+
+        void findEdgeCutsTwoBeziers(
+            const B2DCubicBezier& rCubicA,
+            const B2DCubicBezier& rCubicB,
+            sal_uInt32 nIndA, sal_uInt32 nIndB,
+            temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB)
+        {
+            // find all cuts between the two given bezier segments. Add an entry to the tempPoints
+            // for each common point with the cut value describing the relative position on given
+            // bezier segments.
+            B2DPolygon aTempPolygonA;
+            B2DPolygon aTempPolygonB;
+            temporaryPointVector aTempPointVectorA;
+            temporaryPointVector aTempPointVectorB;
+
+            // create subdivided polygons and find cuts between them
+            // Keep adaptiveSubdivideByCount due to needed quality
+            aTempPolygonA.reserve(SUBDIVIDE_FOR_CUT_TEST_COUNT + 8);
+            aTempPolygonA.append(rCubicA.getStartPoint());
+            rCubicA.adaptiveSubdivideByCount(aTempPolygonA, SUBDIVIDE_FOR_CUT_TEST_COUNT);
+            aTempPolygonB.reserve(SUBDIVIDE_FOR_CUT_TEST_COUNT + 8);
+            aTempPolygonB.append(rCubicB.getStartPoint());
+            rCubicB.adaptiveSubdivideByCount(aTempPolygonB, SUBDIVIDE_FOR_CUT_TEST_COUNT);
+
+            // #i76891# using findCuts recursively is not sufficient here
+            findCutsAndTouchesAndCommonForBezier(aTempPolygonA, aTempPolygonB, aTempPointVectorA, aTempPointVectorB);
+
+            if(!aTempPointVectorA.empty())
+            {
+                // adapt tempVector entries to segment
+                adaptAndTransferCutsWithBezierSegment(aTempPointVectorA, aTempPolygonA, nIndA, rTempPointsA);
+            }
+
+            if(!aTempPointVectorB.empty())
+            {
+                // adapt tempVector entries to segment
+                adaptAndTransferCutsWithBezierSegment(aTempPointVectorB, aTempPolygonB, nIndB, rTempPointsB);
+            }
+        }
+
+        void findEdgeCutsOneBezier(
+            const B2DCubicBezier& rCubicA,
+            sal_uInt32 nInd, temporaryPointVector& rTempPoints)
+        {
+            // avoid expensive part of this method if possible
+            // TODO: use hasAnyExtremum() method instead when it becomes available
+            double fDummy;
+            const bool bHasAnyExtremum = rCubicA.getMinimumExtremumPosition( fDummy );
+            if( !bHasAnyExtremum )
+                return;
+
+            // find all self-intersections on the given bezier segment. Add an entry to the tempPoints
+            // for each self intersection point with the cut value describing the relative position on given
+            // bezier segment.
+            B2DPolygon aTempPolygon;
+            temporaryPointVector aTempPointVector;
+
+            // create subdivided polygon and find cuts on it
+            // Keep adaptiveSubdivideByCount due to needed quality
+            aTempPolygon.reserve(SUBDIVIDE_FOR_CUT_TEST_COUNT + 8);
+            aTempPolygon.append(rCubicA.getStartPoint());
+            rCubicA.adaptiveSubdivideByCount(aTempPolygon, SUBDIVIDE_FOR_CUT_TEST_COUNT);
+            findCuts(aTempPolygon, aTempPointVector);
+
+            if(!aTempPointVector.empty())
+            {
+                // adapt tempVector entries to segment
+                adaptAndTransferCutsWithBezierSegment(aTempPointVector, aTempPolygon, nInd, rTempPoints);
+            }
+        }
+
+        void findCuts(const B2DPolygon& rCandidate, temporaryPointVector& rTempPoints, size_t* pPointLimit)
+        {
+            // find out if there are edges with intersections (self-cuts). If yes, add
+            // entries to rTempPoints accordingly
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(!nPointCount)
+                return;
+
+            const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+
+            if(!nEdgeCount)
+                return;
+
+            const bool bCurvesInvolved(rCandidate.areControlPointsUsed());
+
+            if(bCurvesInvolved)
+            {
+                B2DCubicBezier aCubicA;
+                B2DCubicBezier aCubicB;
+
+                for(sal_uInt32 a(0); a < nEdgeCount - 1; a++)
+                {
+                    rCandidate.getBezierSegment(a, aCubicA);
+                    aCubicA.testAndSolveTrivialBezier();
+                    const bool bEdgeAIsCurve(aCubicA.isBezier());
+                    const B2DRange aRangeA(aCubicA.getRange());
+
+                    if(bEdgeAIsCurve)
+                    {
+                        // curved segments may have self-intersections, do not forget those (!)
+                        findEdgeCutsOneBezier(aCubicA, a, rTempPoints);
+                    }
+
+                    for(sal_uInt32 b(a + 1); b < nEdgeCount; b++)
+                    {
+                        rCandidate.getBezierSegment(b, aCubicB);
+                        aCubicB.testAndSolveTrivialBezier();
+                        const B2DRange aRangeB(aCubicB.getRange());
+
+                        // only overlapping segments need to be tested
+                        // consecutive segments touch of course
+                        bool bOverlap = false;
+                        if( b > a+1)
+                            bOverlap = aRangeA.overlaps(aRangeB);
+                        else
+                            bOverlap = aRangeA.overlapsMore(aRangeB);
+                        if( bOverlap)
+                        {
+                            const bool bEdgeBIsCurve(aCubicB.isBezier());
+                            if(bEdgeAIsCurve && bEdgeBIsCurve)
+                            {
+                                // test for bezier-bezier cuts
+                                findEdgeCutsTwoBeziers(aCubicA, aCubicB, a, b, rTempPoints, rTempPoints);
+                            }
+                            else if(bEdgeAIsCurve)
+                            {
+                                // test for bezier-edge cuts
+                                findEdgeCutsBezierAndEdge(aCubicA, aCubicB.getStartPoint(), aCubicB.getEndPoint(), a, b, rTempPoints, rTempPoints);
+                            }
+                            else if(bEdgeBIsCurve)
+                            {
+                                // test for bezier-edge cuts
+                                findEdgeCutsBezierAndEdge(aCubicB, aCubicA.getStartPoint(), aCubicA.getEndPoint(), b, a, rTempPoints, rTempPoints);
+                            }
+                            else
+                            {
+                                // test for simple edge-edge cuts
+                                findEdgeCutsTwoEdges(aCubicA.getStartPoint(), aCubicA.getEndPoint(), aCubicB.getStartPoint(), aCubicB.getEndPoint(),
+                                    a, b, rTempPoints, rTempPoints);
+                            }
+                        }
+                    }
+                }
+            }
+            else
+            {
+                B2DPoint aCurrA(rCandidate.getB2DPoint(0));
+
+                for(sal_uInt32 a(0); a < nEdgeCount - 1; a++)
+                {
+                    const B2DPoint aNextA(rCandidate.getB2DPoint(a + 1 == nPointCount ? 0 : a + 1));
+                    const B2DRange aRangeA(aCurrA, aNextA);
+                    B2DPoint aCurrB(rCandidate.getB2DPoint(a + 1));
+
+                    for(sal_uInt32 b(a + 1); b < nEdgeCount; b++)
+                    {
+                        const B2DPoint aNextB(rCandidate.getB2DPoint(b + 1 == nPointCount ? 0 : b + 1));
+                        const B2DRange aRangeB(aCurrB, aNextB);
+
+                        // consecutive segments touch of course
+                        bool bOverlap = false;
+                        if( b > a+1)
+                            bOverlap = aRangeA.overlaps(aRangeB);
+                        else
+                            bOverlap = aRangeA.overlapsMore(aRangeB);
+                        if( bOverlap)
+                        {
+                            findEdgeCutsTwoEdges(aCurrA, aNextA, aCurrB, aNextB, a, b, rTempPoints, rTempPoints);
+                        }
+
+                        if (pPointLimit && rTempPoints.size() > *pPointLimit)
+                            break;
+
+                        // prepare next step
+                        aCurrB = aNextB;
+                    }
+
+                    // prepare next step
+                    aCurrA = aNextA;
+                }
+            }
+
+            if (pPointLimit)
+            {
+                if (rTempPoints.size() > *pPointLimit)
+                    *pPointLimit = 0;
+                else
+                    *pPointLimit -= rTempPoints.size();
+            }
+        }
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx
+{
+    namespace
+    {
+
+        void findTouchesOnEdge(
+            const B2DPoint& rCurr, const B2DPoint& rNext, const B2DPolygon& rPointPolygon,
+            sal_uInt32 nInd, temporaryPointVector& rTempPoints)
+        {
+            // find out if points from rPointPolygon are positioned on given edge. If Yes, add
+            // points there to represent touches (which may be enter or leave nodes later).
+            const sal_uInt32 nPointCount(rPointPolygon.count());
+
+            if(!nPointCount)
+                return;
+
+            const B2DRange aRange(rCurr, rNext);
+            const B2DVector aEdgeVector(rNext - rCurr);
+            bool bTestUsingX(fabs(aEdgeVector.getX()) > fabs(aEdgeVector.getY()));
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const B2DPoint aTestPoint(rPointPolygon.getB2DPoint(a));
+
+                if(aRange.isInside(aTestPoint))
+                {
+                    if(!aTestPoint.equal(rCurr) && !aTestPoint.equal(rNext))
+                    {
+                        const B2DVector aTestVector(aTestPoint - rCurr);
+
+                        if(areParallel(aEdgeVector, aTestVector))
+                        {
+                            const double fCut(bTestUsingX
+                                ? aTestVector.getX() / aEdgeVector.getX()
+                                : aTestVector.getY() / aEdgeVector.getY());
+                            const double fZero(0.0);
+                            const double fOne(1.0);
+
+                            if(fTools::more(fCut, fZero) && fTools::less(fCut, fOne))
+                            {
+                                rTempPoints.emplace_back(aTestPoint, nInd, fCut);
+                            }
+                        }
+                    }
+                }
+            }
+        }
+
+        void findTouchesOnCurve(
+            const B2DCubicBezier& rCubicA, const B2DPolygon& rPointPolygon,
+            sal_uInt32 nInd, temporaryPointVector& rTempPoints)
+        {
+            // find all points from rPointPolygon which touch the given bezier segment. Add an entry
+            // for each touch to the given pointVector. The cut for that entry is the relative position on
+            // the given bezier segment.
+            B2DPolygon aTempPolygon;
+            temporaryPointVector aTempPointVector;
+
+            // create subdivided polygon and find cuts on it
+            // Keep adaptiveSubdivideByCount due to needed quality
+            aTempPolygon.reserve(SUBDIVIDE_FOR_CUT_TEST_COUNT + 8);
+            aTempPolygon.append(rCubicA.getStartPoint());
+            rCubicA.adaptiveSubdivideByCount(aTempPolygon, SUBDIVIDE_FOR_CUT_TEST_COUNT);
+            findTouches(aTempPolygon, rPointPolygon, aTempPointVector);
+
+            if(!aTempPointVector.empty())
+            {
+                // adapt tempVector entries to segment
+                adaptAndTransferCutsWithBezierSegment(aTempPointVector, aTempPolygon, nInd, rTempPoints);
+            }
+        }
+
+        void findTouches(const B2DPolygon& rEdgePolygon, const B2DPolygon& rPointPolygon, temporaryPointVector& rTempPoints)
+        {
+            // find out if points from rPointPolygon touch edges from rEdgePolygon. If yes,
+            // add entries to rTempPoints
+            const sal_uInt32 nPointCount(rPointPolygon.count());
+            const sal_uInt32 nEdgePointCount(rEdgePolygon.count());
+
+            if(!(nPointCount && nEdgePointCount))
+                return;
+
+            const sal_uInt32 nEdgeCount(rEdgePolygon.isClosed() ? nEdgePointCount : nEdgePointCount - 1);
+            B2DPoint aCurr(rEdgePolygon.getB2DPoint(0));
+
+            for(sal_uInt32 a(0); a < nEdgeCount; a++)
+            {
+                const sal_uInt32 nNextIndex((a + 1) % nEdgePointCount);
+                const B2DPoint aNext(rEdgePolygon.getB2DPoint(nNextIndex));
+
+                if(!aCurr.equal(aNext))
+                {
+                    bool bHandleAsSimpleEdge(true);
+
+                    if(rEdgePolygon.areControlPointsUsed())
+                    {
+                        const B2DPoint aNextControlPoint(rEdgePolygon.getNextControlPoint(a));
+                        const B2DPoint aPrevControlPoint(rEdgePolygon.getPrevControlPoint(nNextIndex));
+                        const bool bEdgeIsCurve(!aNextControlPoint.equal(aCurr) || !aPrevControlPoint.equal(aNext));
+
+                        if(bEdgeIsCurve)
+                        {
+                            bHandleAsSimpleEdge = false;
+                            const B2DCubicBezier aCubicA(aCurr, aNextControlPoint, aPrevControlPoint, aNext);
+                            findTouchesOnCurve(aCubicA, rPointPolygon, a, rTempPoints);
+                        }
+                    }
+
+                    if(bHandleAsSimpleEdge)
+                    {
+                        findTouchesOnEdge(aCurr, aNext, rPointPolygon, a, rTempPoints);
+                    }
+                }
+
+                // next step
+                aCurr = aNext;
+            }
+        }
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx
+{
+    namespace
+    {
+
+        void findCuts(const B2DPolygon& rCandidateA, const B2DPolygon& rCandidateB, temporaryPointVector& rTempPointsA, temporaryPointVector& rTempPointsB)
+        {
+            // find out if edges from both polygons cut. If so, add entries to rTempPoints which
+            // should be added to the polygons accordingly
+            const sal_uInt32 nPointCountA(rCandidateA.count());
+            const sal_uInt32 nPointCountB(rCandidateB.count());
+
+            if(!(nPointCountA && nPointCountB))
+                return;
+
+            const sal_uInt32 nEdgeCountA(rCandidateA.isClosed() ? nPointCountA : nPointCountA - 1);
+            const sal_uInt32 nEdgeCountB(rCandidateB.isClosed() ? nPointCountB : nPointCountB - 1);
+
+            if(!(nEdgeCountA && nEdgeCountB))
+                return;
+
+            const bool bCurvesInvolved(rCandidateA.areControlPointsUsed() || rCandidateB.areControlPointsUsed());
+
+            if(bCurvesInvolved)
+            {
+                B2DCubicBezier aCubicA;
+                B2DCubicBezier aCubicB;
+
+                for(sal_uInt32 a(0); a < nEdgeCountA; a++)
+                {
+                    rCandidateA.getBezierSegment(a, aCubicA);
+                    aCubicA.testAndSolveTrivialBezier();
+                    const bool bEdgeAIsCurve(aCubicA.isBezier());
+                    const B2DRange aRangeA(aCubicA.getRange());
+
+                    for(sal_uInt32 b(0); b < nEdgeCountB; b++)
+                    {
+                        rCandidateB.getBezierSegment(b, aCubicB);
+                        aCubicB.testAndSolveTrivialBezier();
+                        const B2DRange aRangeB(aCubicB.getRange());
+
+                        // consecutive segments touch of course
+                        bool bOverlap = false;
+                        if( b > a+1)
+                            bOverlap = aRangeA.overlaps(aRangeB);
+                        else
+                            bOverlap = aRangeA.overlapsMore(aRangeB);
+                        if( bOverlap)
+                        {
+                            const bool bEdgeBIsCurve(aCubicB.isBezier());
+                            if(bEdgeAIsCurve && bEdgeBIsCurve)
+                            {
+                                // test for bezier-bezier cuts
+                                findEdgeCutsTwoBeziers(aCubicA, aCubicB, a, b, rTempPointsA, rTempPointsB);
+                            }
+                            else if(bEdgeAIsCurve)
+                            {
+                                // test for bezier-edge cuts
+                                findEdgeCutsBezierAndEdge(aCubicA, aCubicB.getStartPoint(), aCubicB.getEndPoint(), a, b, rTempPointsA, rTempPointsB);
+                            }
+                            else if(bEdgeBIsCurve)
+                            {
+                                // test for bezier-edge cuts
+                                findEdgeCutsBezierAndEdge(aCubicB, aCubicA.getStartPoint(), aCubicA.getEndPoint(), b, a, rTempPointsB, rTempPointsA);
+                            }
+                            else
+                            {
+                                // test for simple edge-edge cuts
+                                findEdgeCutsTwoEdges(aCubicA.getStartPoint(), aCubicA.getEndPoint(), aCubicB.getStartPoint(), aCubicB.getEndPoint(),
+                                    a, b, rTempPointsA, rTempPointsB);
+                            }
+                        }
+                    }
+                }
+            }
+            else
+            {
+                B2DPoint aCurrA(rCandidateA.getB2DPoint(0));
+
+                for(sal_uInt32 a(0); a < nEdgeCountA; a++)
+                {
+                    const B2DPoint aNextA(rCandidateA.getB2DPoint(a + 1 == nPointCountA ? 0 : a + 1));
+                    const B2DRange aRangeA(aCurrA, aNextA);
+                    B2DPoint aCurrB(rCandidateB.getB2DPoint(0));
+
+                    for(sal_uInt32 b(0); b < nEdgeCountB; b++)
+                    {
+                        const B2DPoint aNextB(rCandidateB.getB2DPoint(b + 1 == nPointCountB ? 0 : b + 1));
+                        const B2DRange aRangeB(aCurrB, aNextB);
+
+                        // consecutive segments touch of course
+                        bool bOverlap = false;
+                        if( b > a+1)
+                            bOverlap = aRangeA.overlaps(aRangeB);
+                        else
+                            bOverlap = aRangeA.overlapsMore(aRangeB);
+                        if( bOverlap)
+                        {
+                            // test for simple edge-edge cuts
+                            findEdgeCutsTwoEdges(aCurrA, aNextA, aCurrB, aNextB, a, b, rTempPointsA, rTempPointsB);
+                        }
+
+                        // prepare next step
+                        aCurrB = aNextB;
+                    }
+
+                    // prepare next step
+                    aCurrA = aNextA;
+                }
+            }
+        }
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx::utils
+{
+
+        B2DPolygon addPointsAtCutsAndTouches(const B2DPolygon& rCandidate, size_t* pPointLimit)
+        {
+            if(rCandidate.count())
+            {
+                temporaryPointVector aTempPoints;
+
+                findTouches(rCandidate, rCandidate, aTempPoints);
+                findCuts(rCandidate, aTempPoints, pPointLimit);
+                if (pPointLimit && !*pPointLimit)
+                {
+                    SAL_WARN("basegfx", "addPointsAtCutsAndTouches hit point limit");
+                    return rCandidate;
+                }
+
+                return mergeTemporaryPointsAndPolygon(rCandidate, aTempPoints);
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolyPolygon addPointsAtCutsAndTouches(const B2DPolyPolygon& rCandidate, size_t* pPointLimit)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nCount)
+            {
+                B2DPolyPolygon aRetval;
+
+                if(nCount == 1)
+                {
+                    // remove self intersections
+                    aRetval.append(addPointsAtCutsAndTouches(rCandidate.getB2DPolygon(0), pPointLimit));
+                }
+                else
+                {
+                    // first solve self cuts and self touches for all contained single polygons
+                    std::unique_ptr<temporaryPolygonData[]> pTempData(new temporaryPolygonData[nCount]);
+                    sal_uInt32 a, b;
+
+                    for(a = 0; a < nCount; a++)
+                    {
+                        // use polygons with solved self intersections
+                        pTempData[a].setPolygon(addPointsAtCutsAndTouches(rCandidate.getB2DPolygon(a), pPointLimit));
+                    }
+
+                    if (pPointLimit && !*pPointLimit)
+                    {
+                        SAL_WARN("basegfx", "addPointsAtCutsAndTouches hit point limit");
+                        return rCandidate;
+                    }
+
+                    // now cuts and touches between the polygons
+                    for(a = 0; a < nCount; a++)
+                    {
+                        for(b = 0; b < nCount; b++)
+                        {
+                            if(a != b)
+                            {
+                                // look for touches, compare each edge polygon to all other points
+                                if(pTempData[a].getRange().overlaps(pTempData[b].getRange()))
+                                {
+                                    findTouches(pTempData[a].getPolygon(), pTempData[b].getPolygon(), pTempData[a].getTemporaryPointVector());
+                                }
+                            }
+
+                            if(a < b)
+                            {
+                                // look for cuts, compare each edge polygon to following ones
+                                if(pTempData[a].getRange().overlaps(pTempData[b].getRange()))
+                                {
+                                    findCuts(pTempData[a].getPolygon(), pTempData[b].getPolygon(), pTempData[a].getTemporaryPointVector(), pTempData[b].getTemporaryPointVector());
+                                }
+                            }
+                        }
+                    }
+
+                    // consolidate the result
+                    for(a = 0; a < nCount; a++)
+                    {
+                        aRetval.append(mergeTemporaryPointsAndPolygon(pTempData[a].getPolygon(), pTempData[a].getTemporaryPointVector()));
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolygon addPointsAtCuts(const B2DPolygon& rCandidate, const B2DPoint& rStart, const B2DPoint& rEnd)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nCount && !rStart.equal(rEnd))
+            {
+                const B2DRange aPolygonRange(rCandidate.getB2DRange());
+                const B2DRange aEdgeRange(rStart, rEnd);
+
+                if(aPolygonRange.overlaps(aEdgeRange))
+                {
+                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nCount : nCount - 1);
+                    temporaryPointVector aTempPoints;
+                    temporaryPointVector aUnusedTempPoints;
+                    B2DCubicBezier aCubic;
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        rCandidate.getBezierSegment(a, aCubic);
+                        B2DRange aCubicRange(aCubic.getStartPoint(), aCubic.getEndPoint());
+
+                        if(aCubic.isBezier())
+                        {
+                            aCubicRange.expand(aCubic.getControlPointA());
+                            aCubicRange.expand(aCubic.getControlPointB());
+
+                            if(aCubicRange.overlaps(aEdgeRange))
+                            {
+                                findEdgeCutsBezierAndEdge(aCubic, rStart, rEnd, a, 0, aTempPoints, aUnusedTempPoints);
+                            }
+                        }
+                        else
+                        {
+                            if(aCubicRange.overlaps(aEdgeRange))
+                            {
+                                findEdgeCutsTwoEdges(aCubic.getStartPoint(), aCubic.getEndPoint(), rStart, rEnd, a, 0, aTempPoints, aUnusedTempPoints);
+                            }
+                        }
+                    }
+
+                    return mergeTemporaryPointsAndPolygon(rCandidate, aTempPoints);
+                }
+            }
+
+            return rCandidate;
+        }
+
+        B2DPolygon addPointsAtCuts(const B2DPolygon& rCandidate, const B2DPolyPolygon& rPolyMask)
+        {
+            const sal_uInt32 nCountA(rCandidate.count());
+            const sal_uInt32 nCountM(rPolyMask.count());
+
+            if(nCountA && nCountM)
+            {
+                const B2DRange aRangeA(rCandidate.getB2DRange());
+                const B2DRange aRangeM(rPolyMask.getB2DRange());
+
+                if(aRangeA.overlaps(aRangeM))
+                {
+                    const sal_uInt32 nEdgeCountA(rCandidate.isClosed() ? nCountA : nCountA - 1);
+                    temporaryPointVector aTempPointsA;
+                    temporaryPointVector aUnusedTempPointsB;
+
+                    for(sal_uInt32 m(0); m < nCountM; m++)
+                    {
+                        const B2DPolygon& aMask(rPolyMask.getB2DPolygon(m));
+                        const sal_uInt32 nCountB(aMask.count());
+
+                        if(nCountB)
+                        {
+                            B2DCubicBezier aCubicA;
+                            B2DCubicBezier aCubicB;
+
+                            for(sal_uInt32 a(0); a < nEdgeCountA; a++)
+                            {
+                                rCandidate.getBezierSegment(a, aCubicA);
+                                const bool bCubicAIsCurve(aCubicA.isBezier());
+                                B2DRange aCubicRangeA(aCubicA.getStartPoint(), aCubicA.getEndPoint());
+
+                                if(bCubicAIsCurve)
+                                {
+                                    aCubicRangeA.expand(aCubicA.getControlPointA());
+                                    aCubicRangeA.expand(aCubicA.getControlPointB());
+                                }
+
+                                for(sal_uInt32 b(0); b < nCountB; b++)
+                                {
+                                    aMask.getBezierSegment(b, aCubicB);
+                                    const bool bCubicBIsCurve(aCubicB.isBezier());
+                                    B2DRange aCubicRangeB(aCubicB.getStartPoint(), aCubicB.getEndPoint());
+
+                                    if(bCubicBIsCurve)
+                                    {
+                                        aCubicRangeB.expand(aCubicB.getControlPointA());
+                                        aCubicRangeB.expand(aCubicB.getControlPointB());
+                                    }
+
+                                    if(aCubicRangeA.overlaps(aCubicRangeB))
+                                    {
+                                        if(bCubicAIsCurve && bCubicBIsCurve)
+                                        {
+                                            findEdgeCutsTwoBeziers(aCubicA, aCubicB, a, b, aTempPointsA, aUnusedTempPointsB);
+                                        }
+                                        else if(bCubicAIsCurve)
+                                        {
+                                            findEdgeCutsBezierAndEdge(aCubicA, aCubicB.getStartPoint(), aCubicB.getEndPoint(), a, b, aTempPointsA, aUnusedTempPointsB);
+                                        }
+                                        else if(bCubicBIsCurve)
+                                        {
+                                            findEdgeCutsBezierAndEdge(aCubicB, aCubicA.getStartPoint(), aCubicA.getEndPoint(), b, a, aUnusedTempPointsB, aTempPointsA);
+                                        }
+                                        else
+                                        {
+                                            findEdgeCutsTwoEdges(aCubicA.getStartPoint(), aCubicA.getEndPoint(), aCubicB.getStartPoint(), aCubicB.getEndPoint(), a, b, aTempPointsA, aUnusedTempPointsB);
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+
+                    return mergeTemporaryPointsAndPolygon(rCandidate, aTempPointsA);
+                }
+            }
+
+            return rCandidate;
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolygontools.cxx b/basegfx/source/polygon/b2dpolygontools.cxx
new file mode 100644
index 0000000000..b3f43669dd
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygontools.cxx
@@ -0,0 +1,3702 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+#include <numeric>
+#include <algorithm>
+#include <stack>
+
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <osl/diagnose.h>
+#include <rtl/math.hxx>
+#include <sal/log.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/point/b3dpoint.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/curve/b2dbeziertools.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+
+// #i37443#
+#define ANGLE_BOUND_START_VALUE     (2.25)
+#define ANGLE_BOUND_MINIMUM_VALUE   (0.1)
+#define STEPSPERQUARTER     (3)
+
+namespace basegfx::utils
+{
+        void openWithGeometryChange(B2DPolygon& rCandidate)
+        {
+            if(!rCandidate.isClosed())
+                return;
+
+            if(rCandidate.count())
+            {
+                rCandidate.append(rCandidate.getB2DPoint(0));
+
+                if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(0))
+                {
+                    rCandidate.setPrevControlPoint(rCandidate.count() - 1, rCandidate.getPrevControlPoint(0));
+                    rCandidate.resetPrevControlPoint(0);
+                }
+            }
+
+            rCandidate.setClosed(false);
+        }
+
+        void closeWithGeometryChange(B2DPolygon& rCandidate)
+        {
+            if(rCandidate.isClosed())
+                return;
+
+            while(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
+            {
+                if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(rCandidate.count() - 1))
+                {
+                    rCandidate.setPrevControlPoint(0, rCandidate.getPrevControlPoint(rCandidate.count() - 1));
+                }
+
+                rCandidate.remove(rCandidate.count() - 1);
+            }
+
+            rCandidate.setClosed(true);
+        }
+
+        void checkClosed(B2DPolygon& rCandidate)
+        {
+            // #i80172# Removed unnecessary assertion
+            // OSL_ENSURE(!rCandidate.isClosed(), "checkClosed: already closed (!)");
+
+            if(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
+            {
+                closeWithGeometryChange(rCandidate);
+            }
+        }
+
+        // Get successor and predecessor indices. Returning the same index means there
+        // is none. Same for successor.
+        sal_uInt32 getIndexOfPredecessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");
+
+            if(nIndex)
+            {
+                return nIndex - 1;
+            }
+            else if(rCandidate.count())
+            {
+                return rCandidate.count() - 1;
+            }
+            else
+            {
+                return nIndex;
+            }
+        }
+
+        sal_uInt32 getIndexOfSuccessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");
+
+            if(nIndex + 1 < rCandidate.count())
+            {
+                return nIndex + 1;
+            }
+            else if(nIndex + 1 == rCandidate.count())
+            {
+                return 0;
+            }
+            else
+            {
+                return nIndex;
+            }
+        }
+
+        B2VectorOrientation getOrientation(const B2DPolygon& rCandidate)
+        {
+            B2VectorOrientation eRetval(B2VectorOrientation::Neutral);
+
+            if(rCandidate.count() > 2 || rCandidate.areControlPointsUsed())
+            {
+                const double fSignedArea(getSignedArea(rCandidate));
+
+                if(fTools::equalZero(fSignedArea))
+                {
+                    // B2VectorOrientation::Neutral, already set
+                }
+                if(fSignedArea > 0.0)
+                {
+                    eRetval = B2VectorOrientation::Positive;
+                }
+                else if(fSignedArea < 0.0)
+                {
+                    eRetval = B2VectorOrientation::Negative;
+                }
+            }
+
+            return eRetval;
+        }
+
+        B2VectorContinuity getContinuityInPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            return rCandidate.getContinuityInPoint(nIndex);
+        }
+
+        B2DPolygon adaptiveSubdivideByDistance(const B2DPolygon& rCandidate, double fDistanceBound, int nRecurseLimit)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                const sal_uInt32 nPointCount(rCandidate.count());
+                B2DPolygon aRetval;
+
+                if(nPointCount)
+                {
+                    // prepare edge-oriented loop
+                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    B2DCubicBezier aBezier;
+                    aBezier.setStartPoint(rCandidate.getB2DPoint(0));
+
+                    // perf: try to avoid too many reallocations by guessing the result's pointcount
+                    aRetval.reserve(nPointCount*4);
+
+                    // add start point (always)
+                    aRetval.append(aBezier.getStartPoint());
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        // get next and control points
+                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                        aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+                        aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
+                        aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                        aBezier.testAndSolveTrivialBezier();
+
+                        if(aBezier.isBezier())
+                        {
+                            // add curved edge and generate DistanceBound
+                            double fBound(0.0);
+
+                            if(fDistanceBound == 0.0)
+                            {
+                                // If not set, use B2DCubicBezier functionality to guess a rough value
+                                const double fRoughLength((aBezier.getEdgeLength() + aBezier.getControlPolygonLength()) / 2.0);
+
+                                // take 1/100th of the rough curve length
+                                fBound = fRoughLength * 0.01;
+                            }
+                            else
+                            {
+                                // use given bound value
+                                fBound = fDistanceBound;
+                            }
+
+                            // make sure bound value is not too small. The base units are 1/100th mm, thus
+                            // just make sure it's not smaller then 1/100th of that
+                            if(fBound < 0.01)
+                            {
+                                fBound = 0.01;
+                            }
+
+                            // call adaptive subdivide which adds edges to aRetval accordingly
+                            aBezier.adaptiveSubdivideByDistance(aRetval, fBound, nRecurseLimit);
+                        }
+                        else
+                        {
+                            // add non-curved edge
+                            aRetval.append(aBezier.getEndPoint());
+                        }
+
+                        // prepare next step
+                        aBezier.setStartPoint(aBezier.getEndPoint());
+                    }
+
+                    if(rCandidate.isClosed())
+                    {
+                        // set closed flag and correct last point (which is added double now).
+                        closeWithGeometryChange(aRetval);
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolygon adaptiveSubdivideByAngle(const B2DPolygon& rCandidate, double fAngleBound)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                const sal_uInt32 nPointCount(rCandidate.count());
+                B2DPolygon aRetval;
+
+                if(nPointCount)
+                {
+                    // prepare edge-oriented loop
+                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    B2DCubicBezier aBezier;
+                    aBezier.setStartPoint(rCandidate.getB2DPoint(0));
+
+                    // perf: try to avoid too many reallocations by guessing the result's pointcount
+                    aRetval.reserve(nPointCount*4);
+
+                    // add start point (always)
+                    aRetval.append(aBezier.getStartPoint());
+
+                    // #i37443# prepare convenient AngleBound if none was given
+                    if(fAngleBound == 0.0)
+                    {
+                        fAngleBound = ANGLE_BOUND_START_VALUE;
+                    }
+                    else if(fTools::less(fAngleBound, ANGLE_BOUND_MINIMUM_VALUE))
+                    {
+                        fAngleBound = 0.1;
+                    }
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        // get next and control points
+                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                        aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+                        aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
+                        aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                        aBezier.testAndSolveTrivialBezier();
+
+                        if(aBezier.isBezier())
+                        {
+                            // call adaptive subdivide
+                            aBezier.adaptiveSubdivideByAngle(aRetval, fAngleBound);
+                        }
+                        else
+                        {
+                            // add non-curved edge
+                            aRetval.append(aBezier.getEndPoint());
+                        }
+
+                        // prepare next step
+                        aBezier.setStartPoint(aBezier.getEndPoint());
+                    }
+
+                    if(rCandidate.isClosed())
+                    {
+                        // set closed flag and correct last point (which is added double now).
+                        closeWithGeometryChange(aRetval);
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        bool isInside(const B2DPolygon& rCandidate, const B2DPoint& rPoint, bool bWithBorder)
+        {
+            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
+
+            if(bWithBorder && isPointOnPolygon(aCandidate, rPoint))
+            {
+                return true;
+            }
+            else
+            {
+                bool bRetval(false);
+                const sal_uInt32 nPointCount(aCandidate.count());
+
+                if(nPointCount)
+                {
+                    B2DPoint aCurrentPoint(aCandidate.getB2DPoint(nPointCount - 1));
+
+                    for(sal_uInt32 a(0); a < nPointCount; a++)
+                    {
+                        const B2DPoint aPreviousPoint(aCurrentPoint);
+                        aCurrentPoint = aCandidate.getB2DPoint(a);
+
+                        // cross-over in Y? tdf#130150 use full precision, no need for epsilon
+                        const bool bCompYA(aPreviousPoint.getY() > rPoint.getY());
+                        const bool bCompYB(aCurrentPoint.getY() > rPoint.getY());
+
+                        if(bCompYA != bCompYB)
+                        {
+                            // cross-over in X? tdf#130150 use full precision, no need for epsilon
+                            const bool bCompXA(aPreviousPoint.getX() > rPoint.getX());
+                            const bool bCompXB(aCurrentPoint.getX() > rPoint.getX());
+
+                            if(bCompXA == bCompXB)
+                            {
+                                if(bCompXA)
+                                {
+                                    bRetval = !bRetval;
+                                }
+                            }
+                            else
+                            {
+                                const double fCompare(
+                                    aCurrentPoint.getX() - (aCurrentPoint.getY() - rPoint.getY()) *
+                                    (aPreviousPoint.getX() - aCurrentPoint.getX()) /
+                                    (aPreviousPoint.getY() - aCurrentPoint.getY()));
+
+                                // tdf#130150 use full precision, no need for epsilon
+                                if(fCompare > rPoint.getX())
+                                {
+                                    bRetval = !bRetval;
+                                }
+                            }
+                        }
+                    }
+                }
+
+                return bRetval;
+            }
+        }
+
+        bool isInside(const B2DPolygon& rCandidate, const B2DPolygon& rPolygon, bool bWithBorder)
+        {
+            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
+            const B2DPolygon aPolygon(rPolygon.areControlPointsUsed() ? rPolygon.getDefaultAdaptiveSubdivision() : rPolygon);
+            const sal_uInt32 nPointCount(aPolygon.count());
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const B2DPoint aTestPoint(aPolygon.getB2DPoint(a));
+
+                if(!isInside(aCandidate, aTestPoint, bWithBorder))
+                {
+                    return false;
+                }
+            }
+
+            return true;
+        }
+
+        B2DRange getRange(const B2DPolygon& rCandidate)
+        {
+            // changed to use internally buffered version at B2DPolygon
+            return rCandidate.getB2DRange();
+        }
+
+        double getSignedArea(const B2DPolygon& rCandidate)
+        {
+            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
+            double fRetval(0.0);
+            const sal_uInt32 nPointCount(aCandidate.count());
+
+            if(nPointCount > 2)
+            {
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    const B2DPoint aPreviousPoint(aCandidate.getB2DPoint((!a) ? nPointCount - 1 : a - 1));
+                    const B2DPoint aCurrentPoint(aCandidate.getB2DPoint(a));
+
+                    fRetval += aPreviousPoint.getX() * aCurrentPoint.getY();
+                    fRetval -= aPreviousPoint.getY() * aCurrentPoint.getX();
+                }
+
+                // correct to zero if small enough. Also test the quadratic
+                // of the result since the precision is near quadratic due to
+                // the algorithm
+                if(fTools::equalZero(fRetval) || fTools::equalZero(fRetval * fRetval))
+                {
+                    fRetval = 0.0;
+                }
+            }
+
+            return fRetval;
+        }
+
+        double getArea(const B2DPolygon& rCandidate)
+        {
+            double fRetval(0.0);
+
+            if(rCandidate.count() > 2 || rCandidate.areControlPointsUsed())
+            {
+                fRetval = getSignedArea(rCandidate);
+                const double fZero(0.0);
+
+                if(fTools::less(fRetval, fZero))
+                {
+                    fRetval = -fRetval;
+                }
+            }
+
+            return fRetval;
+        }
+
+        double getEdgeLength(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+            OSL_ENSURE(nIndex < nPointCount, "getEdgeLength: Access to polygon out of range (!)");
+            double fRetval(0.0);
+
+            if(nPointCount)
+            {
+                const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+
+                if(rCandidate.areControlPointsUsed())
+                {
+                    B2DCubicBezier aEdge;
+
+                    aEdge.setStartPoint(rCandidate.getB2DPoint(nIndex));
+                    aEdge.setControlPointA(rCandidate.getNextControlPoint(nIndex));
+                    aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                    aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+
+                    fRetval = aEdge.getLength();
+                }
+                else
+                {
+                    const B2DPoint aCurrent(rCandidate.getB2DPoint(nIndex));
+                    const B2DPoint aNext(rCandidate.getB2DPoint(nNextIndex));
+
+                    fRetval = B2DVector(aNext - aCurrent).getLength();
+                }
+            }
+
+            return fRetval;
+        }
+
+        double getLength(const B2DPolygon& rCandidate, bool bApproximateBezierLength)
+        {
+            double fRetval(0.0);
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount)
+            {
+                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+
+                if(rCandidate.areControlPointsUsed())
+                {
+                    if (bApproximateBezierLength)
+                    {
+                        B2DPoint aStartPoint = rCandidate.getB2DPoint(0);
+
+                        for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                        {
+                            // An approximate length of a cubic Bezier curve is the average
+                            // of its chord length and the sum of the lengths of its control net sides.
+                            const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                            const B2DPoint& aControlPoint1 = rCandidate.getNextControlPoint(a);
+                            const B2DPoint& aControlPoint2 = rCandidate.getPrevControlPoint(nNextIndex);
+                            const B2DPoint& aEndPoint = rCandidate.getB2DPoint(nNextIndex);
+
+                            double chord_length = B2DVector(aEndPoint - aStartPoint).getLength();
+                            double control_net_length = B2DVector(aStartPoint - aControlPoint1).getLength()
+                                + B2DVector(aControlPoint2 - aControlPoint1).getLength()
+                                + B2DVector(aEndPoint - aControlPoint2).getLength();
+                            double approximate_arc_length = (control_net_length + chord_length) / 2;
+
+                            fRetval += approximate_arc_length;
+                            aStartPoint = aEndPoint;
+                        }
+
+                    }
+                    else
+                    {
+                        B2DCubicBezier aEdge;
+                        aEdge.setStartPoint(rCandidate.getB2DPoint(0));
+
+                        for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                        {
+                            const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                            aEdge.setControlPointA(rCandidate.getNextControlPoint(a));
+                            aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                            aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+
+                            fRetval += aEdge.getLength();
+                            aEdge.setStartPoint(aEdge.getEndPoint());
+                        }
+                    }
+                }
+                else
+                {
+                    B2DPoint aCurrent(rCandidate.getB2DPoint(0));
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                        const B2DPoint aNext(rCandidate.getB2DPoint(nNextIndex));
+
+                        fRetval += B2DVector(aNext - aCurrent).getLength();
+                        aCurrent = aNext;
+                    }
+                }
+            }
+
+            return fRetval;
+        }
+
+        B2DPoint getPositionAbsolute(const B2DPolygon& rCandidate, double fDistance, double fLength)
+        {
+            B2DPoint aRetval;
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if( nPointCount == 1 )
+            {
+                // only one point (i.e. no edge) - simply take that point
+                aRetval = rCandidate.getB2DPoint(0);
+            }
+            else if(nPointCount > 1)
+            {
+                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                sal_uInt32 nIndex(0);
+                bool bIndexDone(false);
+
+                // get length if not given
+                if(fTools::equalZero(fLength))
+                {
+                    fLength = getLength(rCandidate);
+                }
+
+                if(fTools::less(fDistance, 0.0))
+                {
+                    // handle fDistance < 0.0
+                    if(rCandidate.isClosed())
+                    {
+                        // if fDistance < 0.0 increment with multiple of fLength
+                        sal_uInt32 nCount(sal_uInt32(-fDistance / fLength));
+                        fDistance += double(nCount + 1) * fLength;
+                    }
+                    else
+                    {
+                        // crop to polygon start
+                        fDistance = 0.0;
+                        bIndexDone = true;
+                    }
+                }
+                else if(fTools::moreOrEqual(fDistance, fLength))
+                {
+                    // handle fDistance >= fLength
+                    if(rCandidate.isClosed())
+                    {
+                        // if fDistance >= fLength decrement with multiple of fLength
+                        sal_uInt32 nCount(sal_uInt32(fDistance / fLength));
+                        fDistance -= static_cast<double>(nCount) * fLength;
+                    }
+                    else
+                    {
+                        // crop to polygon end
+                        fDistance = 0.0;
+                        nIndex = nEdgeCount;
+                        bIndexDone = true;
+                    }
+                }
+
+                // look for correct index. fDistance is now [0.0 .. fLength[
+                double fEdgeLength(getEdgeLength(rCandidate, nIndex));
+
+                while(!bIndexDone)
+                {
+                    // edge found must be on the half-open range
+                    // [0,fEdgeLength).
+                    // Note that in theory, we cannot move beyond
+                    // the last polygon point, since fDistance>=fLength
+                    // is checked above. Unfortunately, with floating-
+                    // point calculations, this case might happen.
+                    // Handled by nIndex check below
+                    if (nIndex+1 < nEdgeCount && fTools::moreOrEqual(fDistance, fEdgeLength))
+                    {
+                        // go to next edge
+                        fDistance -= fEdgeLength;
+                        fEdgeLength = getEdgeLength(rCandidate, ++nIndex);
+                    }
+                    else
+                    {
+                        // it's on this edge, stop
+                        bIndexDone = true;
+                    }
+                }
+
+                // get the point using nIndex
+                aRetval = rCandidate.getB2DPoint(nIndex);
+
+                // if fDistance != 0.0, move that length on the edge. The edge
+                // length is in fEdgeLength.
+                if(!fTools::equalZero(fDistance))
+                {
+                    if(fTools::moreOrEqual(fDistance, fEdgeLength))
+                    {
+                        // end point of chosen edge
+                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                        aRetval = rCandidate.getB2DPoint(nNextIndex);
+                    }
+                    else if(fTools::equalZero(fDistance))
+                    {
+                        // start point of chosen edge
+                    }
+                    else
+                    {
+                        // inside edge
+                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                        const B2DPoint aNextPoint(rCandidate.getB2DPoint(nNextIndex));
+                        bool bDone(false);
+
+                        // add calculated average value to the return value
+                        if(rCandidate.areControlPointsUsed())
+                        {
+                            // get as bezier segment
+                            const B2DCubicBezier aBezierSegment(
+                                aRetval, rCandidate.getNextControlPoint(nIndex),
+                                rCandidate.getPrevControlPoint(nNextIndex), aNextPoint);
+
+                            if(aBezierSegment.isBezier())
+                            {
+                                // use B2DCubicBezierHelper to bridge the non-linear gap between
+                                // length and bezier distances
+                                const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
+                                const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fDistance));
+
+                                aRetval = aBezierSegment.interpolatePoint(fBezierDistance);
+                                bDone = true;
+                            }
+                        }
+
+                        if(!bDone)
+                        {
+                            const double fRelativeInEdge(fDistance / fEdgeLength);
+                            aRetval = interpolate(aRetval, aNextPoint, fRelativeInEdge);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPoint getPositionRelative(const B2DPolygon& rCandidate, double fDistance, double fLength)
+        {
+            // get length if not given
+            if(fTools::equalZero(fLength))
+            {
+                fLength = getLength(rCandidate);
+            }
+
+            // multiply fDistance with real length to get absolute position and
+            // use getPositionAbsolute
+            return getPositionAbsolute(rCandidate, fDistance * fLength, fLength);
+        }
+
+        B2DPolygon getSnippetAbsolute(const B2DPolygon& rCandidate, double fFrom, double fTo, double fLength)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount)
+            {
+                // get length if not given
+                if(fTools::equalZero(fLength))
+                {
+                    fLength = getLength(rCandidate);
+                }
+
+                // test and correct fFrom
+                if(fTools::less(fFrom, 0.0))
+                {
+                    fFrom = 0.0;
+                }
+
+                // test and correct fTo
+                if(fTools::more(fTo, fLength))
+                {
+                    fTo = fLength;
+                }
+
+                // test and correct relationship of fFrom, fTo
+                if(fTools::more(fFrom, fTo))
+                {
+                    fFrom = fTo = (fFrom + fTo) / 2.0;
+                }
+
+                if(fTools::equalZero(fFrom) && fTools::equal(fTo, fLength))
+                {
+                    // no change, result is the whole polygon
+                    return rCandidate;
+                }
+                else
+                {
+                    B2DPolygon aRetval;
+                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    double fPositionOfStart(0.0);
+                    bool bStartDone(false);
+                    bool bEndDone(false);
+
+                    for(sal_uInt32 a(0); !(bStartDone && bEndDone) && a < nEdgeCount; a++)
+                    {
+                        const double fEdgeLength(getEdgeLength(rCandidate, a));
+
+                        if(!bStartDone)
+                        {
+                            if(fTools::equalZero(fFrom))
+                            {
+                                aRetval.append(rCandidate.getB2DPoint(a));
+
+                                if(rCandidate.areControlPointsUsed())
+                                {
+                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
+                                }
+
+                                bStartDone = true;
+                            }
+                            else if(fTools::moreOrEqual(fFrom, fPositionOfStart) && fTools::less(fFrom, fPositionOfStart + fEdgeLength))
+                            {
+                                // calculate and add start point
+                                if(fTools::equalZero(fEdgeLength))
+                                {
+                                    aRetval.append(rCandidate.getB2DPoint(a));
+
+                                    if(rCandidate.areControlPointsUsed())
+                                    {
+                                        aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
+                                    }
+                                }
+                                else
+                                {
+                                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                                    const B2DPoint aStart(rCandidate.getB2DPoint(a));
+                                    const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
+                                    bool bDone(false);
+
+                                    if(rCandidate.areControlPointsUsed())
+                                    {
+                                        const B2DCubicBezier aBezierSegment(
+                                            aStart, rCandidate.getNextControlPoint(a),
+                                            rCandidate.getPrevControlPoint(nNextIndex), aEnd);
+
+                                        if(aBezierSegment.isBezier())
+                                        {
+                                            // use B2DCubicBezierHelper to bridge the non-linear gap between
+                                            // length and bezier distances
+                                            const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
+                                            const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fFrom - fPositionOfStart));
+                                            B2DCubicBezier aRight;
+
+                                            aBezierSegment.split(fBezierDistance, nullptr, &aRight);
+                                            aRetval.append(aRight.getStartPoint());
+                                            aRetval.setNextControlPoint(aRetval.count() - 1, aRight.getControlPointA());
+                                            bDone = true;
+                                        }
+                                    }
+
+                                    if(!bDone)
+                                    {
+                                        const double fRelValue((fFrom - fPositionOfStart) / fEdgeLength);
+                                        aRetval.append(interpolate(aStart, aEnd, fRelValue));
+                                    }
+                                }
+
+                                bStartDone = true;
+
+                                // if same point, end is done, too.
+                                if(rtl::math::approxEqual(fFrom, fTo))
+                                {
+                                    bEndDone = true;
+                                }
+                            }
+                        }
+
+                        if(!bEndDone && fTools::moreOrEqual(fTo, fPositionOfStart) && fTools::less(fTo, fPositionOfStart + fEdgeLength))
+                        {
+                            // calculate and add end point
+                            if(fTools::equalZero(fEdgeLength))
+                            {
+                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                                aRetval.append(rCandidate.getB2DPoint(nNextIndex));
+
+                                if(rCandidate.areControlPointsUsed())
+                                {
+                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
+                                }
+                            }
+                            else
+                            {
+                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                                const B2DPoint aStart(rCandidate.getB2DPoint(a));
+                                const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
+                                bool bDone(false);
+
+                                if(rCandidate.areControlPointsUsed())
+                                {
+                                    const B2DCubicBezier aBezierSegment(
+                                        aStart, rCandidate.getNextControlPoint(a),
+                                        rCandidate.getPrevControlPoint(nNextIndex), aEnd);
+
+                                    if(aBezierSegment.isBezier())
+                                    {
+                                        // use B2DCubicBezierHelper to bridge the non-linear gap between
+                                        // length and bezier distances
+                                        const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
+                                        const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fTo - fPositionOfStart));
+                                        B2DCubicBezier aLeft;
+
+                                        aBezierSegment.split(fBezierDistance, &aLeft, nullptr);
+                                        aRetval.append(aLeft.getEndPoint());
+                                        aRetval.setPrevControlPoint(aRetval.count() - 1, aLeft.getControlPointB());
+                                        bDone = true;
+                                    }
+                                }
+
+                                if(!bDone)
+                                {
+                                    const double fRelValue((fTo - fPositionOfStart) / fEdgeLength);
+                                    aRetval.append(interpolate(aStart, aEnd, fRelValue));
+                                }
+                            }
+
+                            bEndDone = true;
+                        }
+
+                        if(!bEndDone)
+                        {
+                            if(bStartDone)
+                            {
+                                // add segments end point
+                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                                aRetval.append(rCandidate.getB2DPoint(nNextIndex));
+
+                                if(rCandidate.areControlPointsUsed())
+                                {
+                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
+                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(nNextIndex));
+                                }
+                            }
+
+                            // increment fPositionOfStart
+                            fPositionOfStart += fEdgeLength;
+                        }
+                    }
+                    return aRetval;
+                }
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        CutFlagValue findCut(
+            const B2DPoint& rEdge1Start, const B2DVector& rEdge1Delta,
+            const B2DPoint& rEdge2Start, const B2DVector& rEdge2Delta,
+            CutFlagValue aCutFlags,
+            double* pCut1, double* pCut2)
+        {
+            CutFlagValue aRetval(CutFlagValue::NONE);
+            double fCut1(0.0);
+            double fCut2(0.0);
+            bool bFinished(!static_cast<bool>(aCutFlags & CutFlagValue::ALL));
+
+            // test for same points?
+            if(!bFinished
+                && (aCutFlags & (CutFlagValue::START1|CutFlagValue::END1))
+                && (aCutFlags & (CutFlagValue::START2|CutFlagValue::END2)))
+            {
+                // same startpoint?
+                if((aCutFlags & (CutFlagValue::START1|CutFlagValue::START2)) == (CutFlagValue::START1|CutFlagValue::START2))
+                {
+                    if(rEdge1Start.equal(rEdge2Start))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::START1|CutFlagValue::START2);
+                    }
+                }
+
+                // same endpoint?
+                if(!bFinished && (aCutFlags & (CutFlagValue::END1|CutFlagValue::END2)) == (CutFlagValue::END1|CutFlagValue::END2))
+                {
+                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
+                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);
+
+                    if(aEnd1.equal(aEnd2))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::END1|CutFlagValue::END2);
+                        fCut1 = fCut2 = 1.0;
+                    }
+                }
+
+                // startpoint1 == endpoint2?
+                if(!bFinished && (aCutFlags & (CutFlagValue::START1|CutFlagValue::END2)) == (CutFlagValue::START1|CutFlagValue::END2))
+                {
+                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);
+
+                    if(rEdge1Start.equal(aEnd2))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::START1|CutFlagValue::END2);
+                        fCut1 = 0.0;
+                        fCut2 = 1.0;
+                    }
+                }
+
+                // startpoint2 == endpoint1?
+                if(!bFinished&& (aCutFlags & (CutFlagValue::START2|CutFlagValue::END1)) == (CutFlagValue::START2|CutFlagValue::END1))
+                {
+                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
+
+                    if(rEdge2Start.equal(aEnd1))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::START2|CutFlagValue::END1);
+                        fCut1 = 1.0;
+                        fCut2 = 0.0;
+                    }
+                }
+            }
+
+            if(!bFinished && (aCutFlags & CutFlagValue::LINE))
+            {
+                if(aCutFlags & CutFlagValue::START1)
+                {
+                    // start1 on line 2 ?
+                    if(isPointOnEdge(rEdge1Start, rEdge2Start, rEdge2Delta, &fCut2))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::LINE|CutFlagValue::START1);
+                    }
+                }
+
+                if(!bFinished && (aCutFlags & CutFlagValue::START2))
+                {
+                    // start2 on line 1 ?
+                    if(isPointOnEdge(rEdge2Start, rEdge1Start, rEdge1Delta, &fCut1))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::LINE|CutFlagValue::START2);
+                    }
+                }
+
+                if(!bFinished && (aCutFlags & CutFlagValue::END1))
+                {
+                    // end1 on line 2 ?
+                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
+
+                    if(isPointOnEdge(aEnd1, rEdge2Start, rEdge2Delta, &fCut2))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::LINE|CutFlagValue::END1);
+                    }
+                }
+
+                if(!bFinished && (aCutFlags & CutFlagValue::END2))
+                {
+                    // end2 on line 1 ?
+                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);
+
+                    if(isPointOnEdge(aEnd2, rEdge1Start, rEdge1Delta, &fCut1))
+                    {
+                        bFinished = true;
+                        aRetval = (CutFlagValue::LINE|CutFlagValue::END2);
+                    }
+                }
+
+                if(!bFinished)
+                {
+                    // cut in line1, line2 ?
+                    fCut1 = (rEdge1Delta.getX() * rEdge2Delta.getY()) - (rEdge1Delta.getY() * rEdge2Delta.getX());
+
+                    if(!fTools::equalZero(fCut1))
+                    {
+                        fCut1 = (rEdge2Delta.getY() * (rEdge2Start.getX() - rEdge1Start.getX())
+                            + rEdge2Delta.getX() * (rEdge1Start.getY() - rEdge2Start.getY())) / fCut1;
+
+                        const double fZero(0.0);
+                        const double fOne(1.0);
+
+                        // inside parameter range edge1 AND fCut2 is calculable
+                        if(fTools::more(fCut1, fZero) && fTools::less(fCut1, fOne)
+                            && (!fTools::equalZero(rEdge2Delta.getX()) || !fTools::equalZero(rEdge2Delta.getY())))
+                        {
+                            // take the more precise calculation of the two possible
+                            if(fabs(rEdge2Delta.getX()) > fabs(rEdge2Delta.getY()))
+                            {
+                                fCut2 = (rEdge1Start.getX() + fCut1
+                                    * rEdge1Delta.getX() - rEdge2Start.getX()) / rEdge2Delta.getX();
+                            }
+                            else
+                            {
+                                fCut2 = (rEdge1Start.getY() + fCut1
+                                    * rEdge1Delta.getY() - rEdge2Start.getY()) / rEdge2Delta.getY();
+                            }
+
+                            // inside parameter range edge2, too
+                            if(fTools::more(fCut2, fZero) && fTools::less(fCut2, fOne))
+                            {
+                                aRetval = CutFlagValue::LINE;
+                            }
+                        }
+                    }
+                }
+            }
+
+            // copy values if wanted
+            if(pCut1)
+            {
+                *pCut1 = fCut1;
+            }
+
+            if(pCut2)
+            {
+                *pCut2 = fCut2;
+            }
+
+            return aRetval;
+        }
+
+        bool isPointOnEdge(
+            const B2DPoint& rPoint,
+            const B2DPoint& rEdgeStart,
+            const B2DVector& rEdgeDelta,
+            double* pCut)
+        {
+            bool bDeltaXIsZero(fTools::equalZero(rEdgeDelta.getX()));
+            bool bDeltaYIsZero(fTools::equalZero(rEdgeDelta.getY()));
+            const double fZero(0.0);
+            const double fOne(1.0);
+
+            if(bDeltaXIsZero && bDeltaYIsZero)
+            {
+                // no line, just a point
+                return false;
+            }
+            else if(bDeltaXIsZero)
+            {
+                // vertical line
+                if(fTools::equal(rPoint.getX(), rEdgeStart.getX()))
+                {
+                    double fValue = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();
+
+                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
+                    {
+                        if(pCut)
+                        {
+                            *pCut = fValue;
+                        }
+
+                        return true;
+                    }
+                }
+            }
+            else if(bDeltaYIsZero)
+            {
+                // horizontal line
+                if(fTools::equal(rPoint.getY(), rEdgeStart.getY()))
+                {
+                    double fValue = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();
+
+                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
+                    {
+                        if(pCut)
+                        {
+                            *pCut = fValue;
+                        }
+
+                        return true;
+                    }
+                }
+            }
+            else
+            {
+                // any angle line
+                double fTOne = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();
+                double fTTwo = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();
+
+                if(fTools::equal(fTOne, fTTwo))
+                {
+                    // same parameter representation, point is on line. Take
+                    // middle value for better results
+                    double fValue = (fTOne + fTTwo) / 2.0;
+
+                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
+                    {
+                        // point is inside line bounds, too
+                        if(pCut)
+                        {
+                            *pCut = fValue;
+                        }
+
+                        return true;
+                    }
+                }
+            }
+
+            return false;
+        }
+
+        void applyLineDashing(
+            const B2DPolygon& rCandidate,
+            const std::vector<double>& rDotDashArray,
+            B2DPolyPolygon* pLineTarget,
+            B2DPolyPolygon* pGapTarget,
+            double fDotDashLength)
+        {
+            // clear targets in any case
+            if(pLineTarget)
+            {
+                pLineTarget->clear();
+            }
+
+            if(pGapTarget)
+            {
+                pGapTarget->clear();
+            }
+
+            // provide callbacks as lambdas
+            auto aLineCallback(
+                nullptr == pLineTarget
+                ? std::function<void(const basegfx::B2DPolygon&)>()
+                : [&pLineTarget](const basegfx::B2DPolygon& rSnippet){ pLineTarget->append(rSnippet); });
+            auto aGapCallback(
+                nullptr == pGapTarget
+                ? std::function<void(const basegfx::B2DPolygon&)>()
+                : [&pGapTarget](const basegfx::B2DPolygon& rSnippet){ pGapTarget->append(rSnippet); });
+
+            // call version that uses callbacks
+            applyLineDashing(
+                rCandidate,
+                rDotDashArray,
+                aLineCallback,
+                aGapCallback,
+                fDotDashLength);
+        }
+
+        static void implHandleSnippet(
+            const B2DPolygon& rSnippet,
+            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rTargetCallback,
+            B2DPolygon& rFirst,
+            B2DPolygon& rLast)
+        {
+            if(rSnippet.isClosed())
+            {
+                if(!rFirst.count())
+                {
+                    rFirst = rSnippet;
+                }
+                else
+                {
+                    if(rLast.count())
+                    {
+                        rTargetCallback(rLast);
+                    }
+
+                    rLast = rSnippet;
+                }
+            }
+            else
+            {
+                rTargetCallback(rSnippet);
+            }
+        }
+
+        static void implHandleFirstLast(
+            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rTargetCallback,
+            B2DPolygon& rFirst,
+            B2DPolygon& rLast)
+        {
+            if(rFirst.count() && rLast.count()
+                && rFirst.getB2DPoint(0).equal(rLast.getB2DPoint(rLast.count() - 1)))
+            {
+                // start of first and end of last are the same -> merge them
+                rLast.append(rFirst);
+                rLast.removeDoublePoints();
+                rFirst.clear();
+            }
+
+            if(rLast.count())
+            {
+                rTargetCallback(rLast);
+            }
+
+            if(rFirst.count())
+            {
+                rTargetCallback(rFirst);
+            }
+        }
+
+        void applyLineDashing(
+            const B2DPolygon& rCandidate,
+            const std::vector<double>& rDotDashArray,
+            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rLineTargetCallback,
+            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rGapTargetCallback,
+            double fDotDashLength)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+            const sal_uInt32 nDotDashCount(rDotDashArray.size());
+
+            if(fTools::lessOrEqual(fDotDashLength, 0.0))
+            {
+                fDotDashLength = std::accumulate(rDotDashArray.begin(), rDotDashArray.end(), 0.0);
+            }
+
+            if(fTools::lessOrEqual(fDotDashLength, 0.0) || (!rLineTargetCallback && !rGapTargetCallback) || !nPointCount)
+            {
+                // parameters make no sense, just add source to targets
+                if (rLineTargetCallback)
+                    rLineTargetCallback(rCandidate);
+
+                if (rGapTargetCallback)
+                    rGapTargetCallback(rCandidate);
+
+                return;
+            }
+
+            // precalculate maximal acceptable length of candidate polygon assuming
+            // we want to create a maximum of fNumberOfAllowedSnippets. For
+            // fNumberOfAllowedSnippets use ca. 65536, double due to line & gap.
+            static const double fNumberOfAllowedSnippets(100.0 * 2.0);
+            const double fAllowedLength((fNumberOfAllowedSnippets * fDotDashLength) / double(rDotDashArray.size()));
+            const double fCandidateLength(basegfx::utils::getLength(rCandidate, /*bApproximateBezierLength*/true));
+            std::vector<double> aDotDashArray(rDotDashArray);
+
+            if(fCandidateLength > fAllowedLength)
+            {
+                // we would produce more than fNumberOfAllowedSnippets, so
+                // adapt aDotDashArray to exactly produce assumed number. Also
+                // assert this to let the caller know about it.
+                // If this asserts: Please think about checking your DotDashArray
+                // before calling this function or evtl. use the callback version
+                // to *not* produce that much of data. Even then, you may still
+                // think about producing too much runtime (!)
+                assert(true && "applyLineDashing: potentially too expensive to do the requested dismantle - please consider stretched LineDash pattern (!)");
+
+                // calculate correcting factor, apply to aDotDashArray and fDotDashLength
+                // to enlarge these as needed
+                const double fFactor(fCandidateLength / fAllowedLength);
+                std::for_each(aDotDashArray.begin(), aDotDashArray.end(), [&fFactor](double &f){ f *= fFactor; });
+            }
+
+            // prepare current edge's start
+            B2DCubicBezier aCurrentEdge;
+            const bool bIsClosed(rCandidate.isClosed());
+            const sal_uInt32 nEdgeCount(bIsClosed ? nPointCount : nPointCount - 1);
+            aCurrentEdge.setStartPoint(rCandidate.getB2DPoint(0));
+
+            // prepare DotDashArray iteration and the line/gap switching bool
+            sal_uInt32 nDotDashIndex(0);
+            bool bIsLine(true);
+            double fDotDashMovingLength(aDotDashArray[0]);
+            B2DPolygon aSnippet;
+
+            // remember 1st and last snippets to try to merge after execution
+            // is complete and hand to callback
+            B2DPolygon aFirstLine, aLastLine;
+            B2DPolygon aFirstGap, aLastGap;
+
+            // iterate over all edges
+            for(sal_uInt32 a(0); a < nEdgeCount; a++)
+            {
+                // update current edge (fill in C1, C2 and end point)
+                double fLastDotDashMovingLength(0.0);
+                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                aCurrentEdge.setControlPointA(rCandidate.getNextControlPoint(a));
+                aCurrentEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                aCurrentEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+
+                // check if we have a trivial bezier segment -> possible fallback to edge
+                aCurrentEdge.testAndSolveTrivialBezier();
+
+                if(aCurrentEdge.isBezier())
+                {
+                    // bezier segment
+                    const B2DCubicBezierHelper aCubicBezierHelper(aCurrentEdge);
+                    const double fEdgeLength(aCubicBezierHelper.getLength());
+
+                    if(!fTools::equalZero(fEdgeLength))
+                    {
+                        while(fTools::less(fDotDashMovingLength, fEdgeLength))
+                        {
+                            // new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
+                            const bool bHandleLine(bIsLine && rLineTargetCallback);
+                            const bool bHandleGap(!bIsLine && rGapTargetCallback);
+
+                            if(bHandleLine || bHandleGap)
+                            {
+                                const double fBezierSplitStart(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));
+                                const double fBezierSplitEnd(aCubicBezierHelper.distanceToRelative(fDotDashMovingLength));
+                                B2DCubicBezier aBezierSnippet(aCurrentEdge.snippet(fBezierSplitStart, fBezierSplitEnd));
+
+                                if(!aSnippet.count())
+                                {
+                                    aSnippet.append(aBezierSnippet.getStartPoint());
+                                }
+
+                                aSnippet.appendBezierSegment(aBezierSnippet.getControlPointA(), aBezierSnippet.getControlPointB(), aBezierSnippet.getEndPoint());
+
+                                if(bHandleLine)
+                                {
+                                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
+                                }
+
+                                if(bHandleGap)
+                                {
+                                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
+                                }
+
+                                aSnippet.clear();
+                            }
+
+                            // prepare next DotDashArray step and flip line/gap flag
+                            fLastDotDashMovingLength = fDotDashMovingLength;
+                            fDotDashMovingLength += aDotDashArray[(++nDotDashIndex) % nDotDashCount];
+                            bIsLine = !bIsLine;
+                        }
+
+                        // append closing snippet [fLastDotDashMovingLength, fEdgeLength]
+                        const bool bHandleLine(bIsLine && rLineTargetCallback);
+                        const bool bHandleGap(!bIsLine && rGapTargetCallback);
+
+                        if(bHandleLine || bHandleGap)
+                        {
+                            B2DCubicBezier aRight;
+                            const double fBezierSplit(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));
+
+                            aCurrentEdge.split(fBezierSplit, nullptr, &aRight);
+
+                            if(!aSnippet.count())
+                            {
+                                aSnippet.append(aRight.getStartPoint());
+                            }
+
+                            aSnippet.appendBezierSegment(aRight.getControlPointA(), aRight.getControlPointB(), aRight.getEndPoint());
+                        }
+
+                        // prepare move to next edge
+                        fDotDashMovingLength -= fEdgeLength;
+                    }
+                }
+                else
+                {
+                    // simple edge
+                    const double fEdgeLength(aCurrentEdge.getEdgeLength());
+
+                    if(!fTools::equalZero(fEdgeLength))
+                    {
+                        while(fTools::less(fDotDashMovingLength, fEdgeLength))
+                        {
+                            // new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
+                            const bool bHandleLine(bIsLine && rLineTargetCallback);
+                            const bool bHandleGap(!bIsLine && rGapTargetCallback);
+
+                            if(bHandleLine || bHandleGap)
+                            {
+                                if(!aSnippet.count())
+                                {
+                                    aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
+                                }
+
+                                aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fDotDashMovingLength / fEdgeLength));
+
+                                if(bHandleLine)
+                                {
+                                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
+                                }
+
+                                if(bHandleGap)
+                                {
+                                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
+                                }
+
+                                aSnippet.clear();
+                            }
+
+                            // prepare next DotDashArray step and flip line/gap flag
+                            fLastDotDashMovingLength = fDotDashMovingLength;
+                            fDotDashMovingLength += aDotDashArray[(++nDotDashIndex) % nDotDashCount];
+                            bIsLine = !bIsLine;
+                        }
+
+                        // append snippet [fLastDotDashMovingLength, fEdgeLength]
+                        const bool bHandleLine(bIsLine && rLineTargetCallback);
+                        const bool bHandleGap(!bIsLine && rGapTargetCallback);
+
+                        if(bHandleLine || bHandleGap)
+                        {
+                            if(!aSnippet.count())
+                            {
+                                aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
+                            }
+
+                            aSnippet.append(aCurrentEdge.getEndPoint());
+                        }
+
+                        // prepare move to next edge
+                        fDotDashMovingLength -= fEdgeLength;
+                    }
+                }
+
+                // prepare next edge step (end point gets new start point)
+                aCurrentEdge.setStartPoint(aCurrentEdge.getEndPoint());
+            }
+
+            // append last intermediate results (if exists)
+            if(aSnippet.count())
+            {
+                const bool bHandleLine(bIsLine && rLineTargetCallback);
+                const bool bHandleGap(!bIsLine && rGapTargetCallback);
+
+                if(bHandleLine)
+                {
+                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
+                }
+
+                if(bHandleGap)
+                {
+                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
+                }
+            }
+
+            if(bIsClosed && rLineTargetCallback)
+            {
+                implHandleFirstLast(rLineTargetCallback, aFirstLine, aLastLine);
+            }
+
+            if(bIsClosed && rGapTargetCallback)
+            {
+                implHandleFirstLast(rGapTargetCallback, aFirstGap, aLastGap);
+            }
+        }
+
+        // test if point is inside epsilon-range around an edge defined
+        // by the two given points. Can be used for HitTesting. The epsilon-range
+        // is defined to be the rectangle centered to the given edge, using height
+        // 2 x fDistance, and the circle around both points with radius fDistance.
+        bool isInEpsilonRange(const B2DPoint& rEdgeStart, const B2DPoint& rEdgeEnd, const B2DPoint& rTestPosition, double fDistance)
+        {
+            // build edge vector
+            const B2DVector aEdge(rEdgeEnd - rEdgeStart);
+            bool bDoDistanceTestStart(false);
+            bool bDoDistanceTestEnd(false);
+
+            if(aEdge.equalZero())
+            {
+                // no edge, just a point. Do one of the distance tests.
+                bDoDistanceTestStart = true;
+            }
+            else
+            {
+                // edge has a length. Create perpendicular vector.
+                const B2DVector aPerpend(getPerpendicular(aEdge));
+                double fCut(
+                    (aPerpend.getY() * (rTestPosition.getX() - rEdgeStart.getX())
+                    + aPerpend.getX() * (rEdgeStart.getY() - rTestPosition.getY())) /
+                    (aEdge.getX() * aEdge.getX() + aEdge.getY() * aEdge.getY()));
+                const double fZero(0.0);
+                const double fOne(1.0);
+
+                if(fTools::less(fCut, fZero))
+                {
+                    // left of rEdgeStart
+                    bDoDistanceTestStart = true;
+                }
+                else if(fTools::more(fCut, fOne))
+                {
+                    // right of rEdgeEnd
+                    bDoDistanceTestEnd = true;
+                }
+                else
+                {
+                    // inside line [0.0 .. 1.0]
+                    const B2DPoint aCutPoint(interpolate(rEdgeStart, rEdgeEnd, fCut));
+                    const B2DVector aDelta(rTestPosition - aCutPoint);
+                    const double fDistanceSquare(aDelta.scalar(aDelta));
+
+                    return fDistanceSquare <= fDistance * fDistance;
+                }
+            }
+
+            if(bDoDistanceTestStart)
+            {
+                const B2DVector aDelta(rTestPosition - rEdgeStart);
+                const double fDistanceSquare(aDelta.scalar(aDelta));
+
+                if(fDistanceSquare <= fDistance * fDistance)
+                {
+                    return true;
+                }
+            }
+            else if(bDoDistanceTestEnd)
+            {
+                const B2DVector aDelta(rTestPosition - rEdgeEnd);
+                const double fDistanceSquare(aDelta.scalar(aDelta));
+
+                if(fDistanceSquare <= fDistance * fDistance)
+                {
+                    return true;
+                }
+            }
+
+            return false;
+        }
+
+        // test if point is inside epsilon-range around the given Polygon. Can be used
+        // for HitTesting. The epsilon-range is defined to be the tube around the polygon
+        // with distance fDistance and rounded edges (start and end point).
+        bool isInEpsilonRange(const B2DPolygon& rCandidate, const B2DPoint& rTestPosition, double fDistance)
+        {
+            // force to non-bezier polygon
+            const B2DPolygon& aCandidate(rCandidate.getDefaultAdaptiveSubdivision());
+            const sal_uInt32 nPointCount(aCandidate.count());
+
+            if(!nPointCount)
+                return false;
+
+            const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+            B2DPoint aCurrent(aCandidate.getB2DPoint(0));
+
+            if(nEdgeCount)
+            {
+                // edges
+                for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                {
+                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                    const B2DPoint aNext(aCandidate.getB2DPoint(nNextIndex));
+
+                    if(isInEpsilonRange(aCurrent, aNext, rTestPosition, fDistance))
+                    {
+                        return true;
+                    }
+
+                    // prepare next step
+                    aCurrent = aNext;
+                }
+            }
+            else
+            {
+                // no edges, but points -> not closed. Check single point. Just
+                // use isInEpsilonRange with twice the same point, it handles those well
+                if(isInEpsilonRange(aCurrent, aCurrent, rTestPosition, fDistance))
+                {
+                    return true;
+                }
+            }
+
+            return false;
+        }
+
+        // Calculates distance of curve point to its control point for a Bézier curve, that
+        // approximates a unit circle arc. fAngle is the center angle of the circle arc. The
+        // constrain 0<=fAngle<=pi/2 must not be violated to give a useful accuracy. For details
+        // and alternatives read document "ApproxCircleInfo.odt", attachment of bug tdf#121425.
+        static double impDistanceBezierPointToControl(double fAngle)
+        {
+            SAL_WARN_IF(fAngle < 0 || fAngle > M_PI_2,"basegfx","angle not suitable for approximate circle");
+            if (0 <= fAngle && fAngle <= M_PI_2)
+            {
+                return 4.0/3.0 * ( tan(fAngle/4.0));
+            }
+            else
+                return 0;
+        }
+
+        B2DPolygon createPolygonFromRect( const B2DRectangle& rRect, double fRadiusX, double fRadiusY )
+        {
+            const double fZero(0.0);
+            const double fOne(1.0);
+
+            fRadiusX = std::clamp(fRadiusX, 0.0, 1.0);
+            fRadiusY = std::clamp(fRadiusY, 0.0, 1.0);
+
+            if(rtl::math::approxEqual(fZero, fRadiusX) || rtl::math::approxEqual(fZero, fRadiusY))
+            {
+                // at least in one direction no radius, use rectangle.
+                // Do not use createPolygonFromRect() here since original
+                // creator (historical reasons) still creates a start point at the
+                // bottom center, so do the same here to get the same line patterns.
+                // Due to this the order of points is different, too.
+                const B2DPoint aBottomCenter(rRect.getCenter().getX(), rRect.getMaxY());
+                B2DPolygon aPolygon {
+                    aBottomCenter,
+                    { rRect.getMinX(), rRect.getMaxY() },
+                    { rRect.getMinX(), rRect.getMinY() },
+                    { rRect.getMaxX(), rRect.getMinY() },
+                    { rRect.getMaxX(), rRect.getMaxY() }
+                };
+
+                // close
+                aPolygon.setClosed( true );
+
+                return aPolygon;
+            }
+            else if(rtl::math::approxEqual(fOne, fRadiusX) && rtl::math::approxEqual(fOne, fRadiusY))
+            {
+                // in both directions full radius, use ellipse
+                const B2DPoint aCenter(rRect.getCenter());
+                const double fRectRadiusX(rRect.getWidth() / 2.0);
+                const double fRectRadiusY(rRect.getHeight() / 2.0);
+
+                return createPolygonFromEllipse( aCenter, fRectRadiusX, fRectRadiusY );
+            }
+            else
+            {
+                B2DPolygon aRetval;
+                const double fBowX((rRect.getWidth() / 2.0) * fRadiusX);
+                const double fBowY((rRect.getHeight() / 2.0) * fRadiusY);
+                const double fKappa(impDistanceBezierPointToControl(M_PI_2));
+
+                // create start point at bottom center
+                if(!rtl::math::approxEqual(fOne, fRadiusX))
+                {
+                    const B2DPoint aBottomCenter(rRect.getCenter().getX(), rRect.getMaxY());
+                    aRetval.append(aBottomCenter);
+                }
+
+                // create first bow
+                {
+                    const B2DPoint aBottomRight(rRect.getMaxX(), rRect.getMaxY());
+                    const B2DPoint aStart(aBottomRight + B2DPoint(-fBowX, 0.0));
+                    const B2DPoint aStop(aBottomRight + B2DPoint(0.0, -fBowY));
+                    aRetval.append(aStart);
+                    aRetval.appendBezierSegment(interpolate(aStart, aBottomRight, fKappa), interpolate(aStop, aBottomRight, fKappa), aStop);
+                }
+
+                // create second bow
+                {
+                    const B2DPoint aTopRight(rRect.getMaxX(), rRect.getMinY());
+                    const B2DPoint aStart(aTopRight + B2DPoint(0.0, fBowY));
+                    const B2DPoint aStop(aTopRight + B2DPoint(-fBowX, 0.0));
+                    aRetval.append(aStart);
+                    aRetval.appendBezierSegment(interpolate(aStart, aTopRight, fKappa), interpolate(aStop, aTopRight, fKappa), aStop);
+                }
+
+                // create third bow
+                {
+                    const B2DPoint aTopLeft(rRect.getMinX(), rRect.getMinY());
+                    const B2DPoint aStart(aTopLeft + B2DPoint(fBowX, 0.0));
+                    const B2DPoint aStop(aTopLeft + B2DPoint(0.0, fBowY));
+                    aRetval.append(aStart);
+                    aRetval.appendBezierSegment(interpolate(aStart, aTopLeft, fKappa), interpolate(aStop, aTopLeft, fKappa), aStop);
+                }
+
+                // create forth bow
+                {
+                    const B2DPoint aBottomLeft(rRect.getMinX(), rRect.getMaxY());
+                    const B2DPoint aStart(aBottomLeft + B2DPoint(0.0, -fBowY));
+                    const B2DPoint aStop(aBottomLeft + B2DPoint(fBowX, 0.0));
+                    aRetval.append(aStart);
+                    aRetval.appendBezierSegment(interpolate(aStart, aBottomLeft, fKappa), interpolate(aStop, aBottomLeft, fKappa), aStop);
+                }
+
+                // close
+                aRetval.setClosed( true );
+
+                // remove double created points if there are extreme radii involved
+                if(rtl::math::approxEqual(fOne, fRadiusX) || rtl::math::approxEqual(fOne, fRadiusY))
+                {
+                    aRetval.removeDoublePoints();
+                }
+
+                return aRetval;
+            }
+        }
+
+        B2DPolygon createPolygonFromRect( const B2DRectangle& rRect )
+        {
+            B2DPolygon aPolygon {
+                { rRect.getMinX(), rRect.getMinY() },
+                { rRect.getMaxX(), rRect.getMinY() },
+                { rRect.getMaxX(), rRect.getMaxY() },
+                { rRect.getMinX(), rRect.getMaxY() }
+            };
+
+            // close
+            aPolygon.setClosed( true );
+
+            return aPolygon;
+        }
+
+        B2DPolygon const & createUnitPolygon()
+        {
+            static auto const singleton = [] {
+                    B2DPolygon aPolygon {
+                        { 0.0, 0.0 },
+                        { 1.0, 0.0 },
+                        { 1.0, 1.0 },
+                        { 0.0, 1.0 }
+                    };
+
+                    // close
+                    aPolygon.setClosed( true );
+
+                    return aPolygon;
+            }();
+            return singleton;
+        }
+
+        B2DPolygon createPolygonFromCircle( const B2DPoint& rCenter, double fRadius )
+        {
+            return createPolygonFromEllipse( rCenter, fRadius, fRadius );
+        }
+
+        static B2DPolygon impCreateUnitCircle(sal_uInt32 nStartQuadrant)
+        {
+            B2DPolygon aUnitCircle;
+            const double fSegmentKappa = impDistanceBezierPointToControl(M_PI_2 / STEPSPERQUARTER);
+            const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(M_PI_2 / STEPSPERQUARTER));
+
+            B2DPoint aPoint(1.0, 0.0);
+            B2DPoint aForward(1.0, fSegmentKappa);
+            B2DPoint aBackward(1.0, -fSegmentKappa);
+
+            if(nStartQuadrant != 0)
+            {
+                const B2DHomMatrix aQuadrantMatrix(createRotateB2DHomMatrix(M_PI_2 * (nStartQuadrant % 4)));
+                aPoint *= aQuadrantMatrix;
+                aBackward *= aQuadrantMatrix;
+                aForward *= aQuadrantMatrix;
+            }
+
+            aUnitCircle.append(aPoint);
+
+            for(sal_uInt32 a(0); a < STEPSPERQUARTER * 4; a++)
+            {
+                aPoint *= aRotateMatrix;
+                aBackward *= aRotateMatrix;
+                aUnitCircle.appendBezierSegment(aForward, aBackward, aPoint);
+                aForward *= aRotateMatrix;
+            }
+
+            aUnitCircle.setClosed(true);
+            aUnitCircle.removeDoublePoints();
+
+            return aUnitCircle;
+        }
+
+        B2DPolygon const & createHalfUnitCircle()
+        {
+            static auto const singleton = [] {
+                    B2DPolygon aUnitHalfCircle;
+                    const double fSegmentKappa(impDistanceBezierPointToControl(M_PI_2 / STEPSPERQUARTER));
+                    const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(M_PI_2 / STEPSPERQUARTER));
+                    B2DPoint aPoint(1.0, 0.0);
+                    B2DPoint aForward(1.0, fSegmentKappa);
+                    B2DPoint aBackward(1.0, -fSegmentKappa);
+
+                    aUnitHalfCircle.append(aPoint);
+
+                    for(sal_uInt32 a(0); a < STEPSPERQUARTER * 2; a++)
+                    {
+                        aPoint *= aRotateMatrix;
+                        aBackward *= aRotateMatrix;
+                        aUnitHalfCircle.appendBezierSegment(aForward, aBackward, aPoint);
+                        aForward *= aRotateMatrix;
+                    }
+                    return aUnitHalfCircle;
+                }();
+            return singleton;
+        }
+
+        B2DPolygon const & createPolygonFromUnitCircle(sal_uInt32 nStartQuadrant)
+        {
+            switch(nStartQuadrant % 4)
+            {
+                case 1 :
+                    {
+                        static auto const singleton = impCreateUnitCircle(1);
+                        return singleton;
+                    }
+
+                case 2 :
+                    {
+                        static auto const singleton = impCreateUnitCircle(2);
+                        return singleton;
+                    }
+
+                case 3 :
+                    {
+                        static auto const singleton = impCreateUnitCircle(3);
+                        return singleton;
+                    }
+
+                default : // case 0 :
+                    {
+                        static auto const singleton = impCreateUnitCircle(0);
+                        return singleton;
+                    }
+            }
+        }
+
+        B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY, sal_uInt32 nStartQuadrant)
+        {
+            B2DPolygon aRetval(createPolygonFromUnitCircle(nStartQuadrant));
+            const B2DHomMatrix aMatrix(createScaleTranslateB2DHomMatrix(fRadiusX, fRadiusY, rCenter.getX(), rCenter.getY()));
+
+            aRetval.transform(aMatrix);
+
+            return aRetval;
+        }
+
+        B2DPolygon createPolygonFromUnitEllipseSegment( double fStart, double fEnd )
+        {
+            B2DPolygon aRetval;
+
+            // truncate fStart, fEnd to a range of [0.0 .. 2PI[ where 2PI
+            // falls back to 0.0 to ensure a unique definition
+            if(fTools::less(fStart, 0.0))
+            {
+                fStart = 0.0;
+            }
+
+            if(fTools::moreOrEqual(fStart, 2 * M_PI))
+            {
+                fStart = 0.0;
+            }
+
+            if(fTools::less(fEnd, 0.0))
+            {
+                fEnd = 0.0;
+            }
+
+            if(fTools::moreOrEqual(fEnd, 2 * M_PI))
+            {
+                fEnd = 0.0;
+            }
+
+            if(fTools::equal(fStart, fEnd))
+            {
+                // same start and end angle, add single point
+                aRetval.append(B2DPoint(cos(fStart), sin(fStart)));
+            }
+            else
+            {
+                const sal_uInt32 nSegments(STEPSPERQUARTER * 4);
+                const double fAnglePerSegment(M_PI_2 / STEPSPERQUARTER);
+                const sal_uInt32 nStartSegment(sal_uInt32(fStart / fAnglePerSegment) % nSegments);
+                const sal_uInt32 nEndSegment(sal_uInt32(fEnd / fAnglePerSegment) % nSegments);
+                const double fSegmentKappa(impDistanceBezierPointToControl(fAnglePerSegment));
+
+                B2DPoint aSegStart(cos(fStart), sin(fStart));
+                aRetval.append(aSegStart);
+
+                if(nStartSegment == nEndSegment && fTools::more(fEnd, fStart))
+                {
+                    // start and end in one sector and in the right order, create in one segment
+                    const B2DPoint aSegEnd(cos(fEnd), sin(fEnd));
+                    const double fFactor(impDistanceBezierPointToControl(fEnd - fStart));
+
+                    aRetval.appendBezierSegment(
+                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
+                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
+                        aSegEnd);
+                }
+                else
+                {
+                    double fSegEndRad((nStartSegment + 1) * fAnglePerSegment);
+                    double fFactor(impDistanceBezierPointToControl(fSegEndRad - fStart));
+                    B2DPoint aSegEnd(cos(fSegEndRad), sin(fSegEndRad));
+
+                    aRetval.appendBezierSegment(
+                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
+                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
+                        aSegEnd);
+
+                    sal_uInt32 nSegment((nStartSegment + 1) % nSegments);
+                    aSegStart = aSegEnd;
+
+                    while(nSegment != nEndSegment)
+                    {
+                        // No end in this sector, add full sector.
+                        fSegEndRad = (nSegment + 1) * fAnglePerSegment;
+                        aSegEnd = B2DPoint(cos(fSegEndRad), sin(fSegEndRad));
+
+                        aRetval.appendBezierSegment(
+                            aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fSegmentKappa),
+                            aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fSegmentKappa),
+                            aSegEnd);
+
+                        nSegment = (nSegment + 1) % nSegments;
+                        aSegStart = aSegEnd;
+                    }
+
+                    // End in this sector
+                    const double fSegStartRad(nSegment * fAnglePerSegment);
+                    fFactor= impDistanceBezierPointToControl(fEnd - fSegStartRad);
+                    aSegEnd = B2DPoint(cos(fEnd), sin(fEnd));
+
+                    aRetval.appendBezierSegment(
+                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
+                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
+                        aSegEnd);
+                }
+            }
+
+            // remove double points between segments created by segmented creation
+            aRetval.removeDoublePoints();
+
+            return aRetval;
+        }
+
+        B2DPolygon createPolygonFromEllipseSegment( const B2DPoint& rCenter, double fRadiusX, double fRadiusY, double fStart, double fEnd )
+        {
+            B2DPolygon aRetval(createPolygonFromUnitEllipseSegment(fStart, fEnd));
+            const B2DHomMatrix aMatrix(createScaleTranslateB2DHomMatrix(fRadiusX, fRadiusY, rCenter.getX(), rCenter.getY()));
+
+            aRetval.transform(aMatrix);
+
+            return aRetval;
+        }
+
+        bool hasNeutralPoints(const B2DPolygon& rCandidate)
+        {
+            OSL_ENSURE(!rCandidate.areControlPointsUsed(), "hasNeutralPoints: ATM works not for curves (!)");
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount <= 2)
+                return false;
+
+            B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1));
+            B2DPoint aCurrPoint(rCandidate.getB2DPoint(0));
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
+                const B2DVector aPrevVec(aPrevPoint - aCurrPoint);
+                const B2DVector aNextVec(aNextPoint - aCurrPoint);
+                const B2VectorOrientation aOrientation(getOrientation(aNextVec, aPrevVec));
+
+                if(aOrientation == B2VectorOrientation::Neutral)
+                {
+                    // current has neutral orientation
+                    return true;
+                }
+                else
+                {
+                    // prepare next
+                    aPrevPoint = aCurrPoint;
+                    aCurrPoint = aNextPoint;
+                }
+            }
+
+            return false;
+        }
+
+        B2DPolygon removeNeutralPoints(const B2DPolygon& rCandidate)
+        {
+            if(hasNeutralPoints(rCandidate))
+            {
+                const sal_uInt32 nPointCount(rCandidate.count());
+                B2DPolygon aRetval;
+                B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1));
+                B2DPoint aCurrPoint(rCandidate.getB2DPoint(0));
+
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
+                    const B2DVector aPrevVec(aPrevPoint - aCurrPoint);
+                    const B2DVector aNextVec(aNextPoint - aCurrPoint);
+                    const B2VectorOrientation aOrientation(getOrientation(aNextVec, aPrevVec));
+
+                    if(aOrientation == B2VectorOrientation::Neutral)
+                    {
+                        // current has neutral orientation, leave it out and prepare next
+                        aCurrPoint = aNextPoint;
+                    }
+                    else
+                    {
+                        // add current point
+                        aRetval.append(aCurrPoint);
+
+                        // prepare next
+                        aPrevPoint = aCurrPoint;
+                        aCurrPoint = aNextPoint;
+                    }
+                }
+
+                while(aRetval.count() && getOrientationForIndex(aRetval, 0) == B2VectorOrientation::Neutral)
+                {
+                    aRetval.remove(0);
+                }
+
+                // copy closed state
+                aRetval.setClosed(rCandidate.isClosed());
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        bool isConvex(const B2DPolygon& rCandidate)
+        {
+            OSL_ENSURE(!rCandidate.areControlPointsUsed(), "isConvex: ATM works not for curves (!)");
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount <= 2)
+                return true;
+
+            const B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1));
+            B2DPoint aCurrPoint(rCandidate.getB2DPoint(0));
+            B2DVector aCurrVec(aPrevPoint - aCurrPoint);
+            B2VectorOrientation aOrientation(B2VectorOrientation::Neutral);
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
+                const B2DVector aNextVec(aNextPoint - aCurrPoint);
+                const B2VectorOrientation aCurrentOrientation(getOrientation(aNextVec, aCurrVec));
+
+                if(aOrientation == B2VectorOrientation::Neutral)
+                {
+                    // set start value, maybe neutral again
+                    aOrientation = aCurrentOrientation;
+                }
+                else
+                {
+                    if(aCurrentOrientation != B2VectorOrientation::Neutral && aCurrentOrientation != aOrientation)
+                    {
+                        // different orientations found, that's it
+                        return false;
+                    }
+                }
+
+                // prepare next
+                aCurrPoint = aNextPoint;
+                aCurrVec = -aNextVec;
+            }
+
+            return true;
+        }
+
+        B2VectorOrientation getOrientationForIndex(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "getOrientationForIndex: index out of range (!)");
+            const B2DPoint aPrev(rCandidate.getB2DPoint(getIndexOfPredecessor(nIndex, rCandidate)));
+            const B2DPoint aCurr(rCandidate.getB2DPoint(nIndex));
+            const B2DPoint aNext(rCandidate.getB2DPoint(getIndexOfSuccessor(nIndex, rCandidate)));
+            const B2DVector aBack(aPrev - aCurr);
+            const B2DVector aForw(aNext - aCurr);
+
+            return getOrientation(aForw, aBack);
+        }
+
+        bool isPointOnLine(const B2DPoint& rStart, const B2DPoint& rEnd, const B2DPoint& rCandidate, bool bWithPoints)
+        {
+            if(rCandidate.equal(rStart) || rCandidate.equal(rEnd))
+            {
+                // candidate is in epsilon around start or end -> inside
+                return bWithPoints;
+            }
+            else if(rStart.equal(rEnd))
+            {
+                // start and end are equal, but candidate is outside their epsilon -> outside
+                return false;
+            }
+            else
+            {
+                const B2DVector aEdgeVector(rEnd - rStart);
+                const B2DVector aTestVector(rCandidate - rStart);
+
+                if(areParallel(aEdgeVector, aTestVector))
+                {
+                    const double fZero(0.0);
+                    const double fOne(1.0);
+                    const double fParamTestOnCurr(fabs(aEdgeVector.getX()) > fabs(aEdgeVector.getY())
+                        ? aTestVector.getX() / aEdgeVector.getX()
+                        : aTestVector.getY() / aEdgeVector.getY());
+
+                    if(fTools::more(fParamTestOnCurr, fZero) && fTools::less(fParamTestOnCurr, fOne))
+                    {
+                        return true;
+                    }
+                }
+
+                return false;
+            }
+        }
+
+        bool isPointOnPolygon(const B2DPolygon& rCandidate, const B2DPoint& rPoint, bool bWithPoints)
+        {
+            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
+            const sal_uInt32 nPointCount(aCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                const sal_uInt32 nLoopCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                B2DPoint aCurrentPoint(aCandidate.getB2DPoint(0));
+
+                for(sal_uInt32 a(0); a < nLoopCount; a++)
+                {
+                    const B2DPoint aNextPoint(aCandidate.getB2DPoint((a + 1) % nPointCount));
+
+                    if(isPointOnLine(aCurrentPoint, aNextPoint, rPoint, bWithPoints))
+                    {
+                        return true;
+                    }
+
+                    aCurrentPoint = aNextPoint;
+                }
+            }
+            else if(nPointCount && bWithPoints)
+            {
+                return rPoint.equal(aCandidate.getB2DPoint(0));
+            }
+
+            return false;
+        }
+
+        bool isPointInTriangle(const B2DPoint& rA, const B2DPoint& rB, const B2DPoint& rC, const B2DPoint& rCandidate, bool bWithBorder)
+        {
+            if(arePointsOnSameSideOfLine(rA, rB, rC, rCandidate, bWithBorder))
+            {
+                if(arePointsOnSameSideOfLine(rB, rC, rA, rCandidate, bWithBorder))
+                {
+                    if(arePointsOnSameSideOfLine(rC, rA, rB, rCandidate, bWithBorder))
+                    {
+                        return true;
+                    }
+                }
+            }
+
+            return false;
+        }
+
+        bool arePointsOnSameSideOfLine(const B2DPoint& rStart, const B2DPoint& rEnd, const B2DPoint& rCandidateA, const B2DPoint& rCandidateB, bool bWithLine)
+        {
+            const B2DVector aLineVector(rEnd - rStart);
+            const B2DVector aVectorToA(rEnd - rCandidateA);
+            const double fCrossA(aLineVector.cross(aVectorToA));
+
+            // tdf#88352 increase numerical correctness and use rtl::math::approxEqual
+            // instead of fTools::equalZero which compares with a fixed small value
+            if(fCrossA == 0.0)
+            {
+                // one point on the line
+                return bWithLine;
+            }
+
+            const B2DVector aVectorToB(rEnd - rCandidateB);
+            const double fCrossB(aLineVector.cross(aVectorToB));
+
+            // increase numerical correctness
+            if(fCrossB == 0.0)
+            {
+                // one point on the line
+                return bWithLine;
+            }
+
+            // return true if they both have the same sign
+            return ((fCrossA > 0.0) == (fCrossB > 0.0));
+        }
+
+        void addTriangleFan(
+            const B2DPolygon& rCandidate,
+            triangulator::B2DTriangleVector& rTarget)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nCount <= 2)
+                return;
+
+            const B2DPoint aStart(rCandidate.getB2DPoint(0));
+            B2DPoint aLast(rCandidate.getB2DPoint(1));
+
+            for(sal_uInt32 a(2); a < nCount; a++)
+            {
+                const B2DPoint aCurrent(rCandidate.getB2DPoint(a));
+                rTarget.emplace_back(
+                    aStart,
+                    aLast,
+                    aCurrent);
+
+                // prepare next
+                aLast = aCurrent;
+            }
+        }
+
+        namespace
+        {
+            /// return 0 for input of 0, -1 for negative and 1 for positive input
+            int lcl_sgn( const double n )
+            {
+                return n == 0.0 ? 0 : 1 - 2*int(std::signbit(n));
+            }
+        }
+
+        bool isRectangle( const B2DPolygon& rPoly )
+        {
+            // polygon must be closed to resemble a rect, and contain
+            // at least four points.
+            if( !rPoly.isClosed() ||
+                rPoly.count() < 4 ||
+                rPoly.areControlPointsUsed() )
+            {
+                return false;
+            }
+
+            // number of 90 degree turns the polygon has taken
+            int nNumTurns(0);
+
+            int  nVerticalEdgeType=0;
+            int  nHorizontalEdgeType=0;
+            bool bNullVertex(true);
+            bool bCWPolygon(false);  // when true, polygon is CW
+                                     // oriented, when false, CCW
+            bool bOrientationSet(false); // when false, polygon
+                                         // orientation has not yet
+                                         // been determined.
+
+            // scan all _edges_ (which involves coming back to point 0
+            // for the last edge - thus the modulo operation below)
+            const sal_Int32 nCount( rPoly.count() );
+            for( sal_Int32 i=0; i<nCount; ++i )
+            {
+                const B2DPoint& rPoint0( rPoly.getB2DPoint(i % nCount) );
+                const B2DPoint& rPoint1( rPoly.getB2DPoint((i+1) % nCount) );
+
+                // is 0 for zero direction vector, 1 for south edge and -1
+                // for north edge (standard screen coordinate system)
+                int nCurrVerticalEdgeType( lcl_sgn( rPoint1.getY() - rPoint0.getY() ) );
+
+                // is 0 for zero direction vector, 1 for east edge and -1
+                // for west edge (standard screen coordinate system)
+                int nCurrHorizontalEdgeType( lcl_sgn(rPoint1.getX() - rPoint0.getX()) );
+
+                if( nCurrVerticalEdgeType && nCurrHorizontalEdgeType )
+                    return false; // oblique edge - for sure no rect
+
+                const bool bCurrNullVertex( !nCurrVerticalEdgeType && !nCurrHorizontalEdgeType );
+
+                // current vertex is equal to previous - just skip,
+                // until we have a real edge
+                if( bCurrNullVertex )
+                    continue;
+
+                // if previous edge has two identical points, because
+                // no previous edge direction was available, simply
+                // take this first non-null edge as the start
+                // direction. That's what will happen here, if
+                // bNullVertex is false
+                if( !bNullVertex )
+                {
+                    // 2D cross product - is 1 for CW and -1 for CCW turns
+                    const int nCrossProduct( nHorizontalEdgeType*nCurrVerticalEdgeType -
+                                             nVerticalEdgeType*nCurrHorizontalEdgeType );
+
+                    if( !nCrossProduct )
+                        continue; // no change in orientation -
+                                  // collinear edges - just go on
+
+                    // if polygon orientation is not set, we'll
+                    // determine it now
+                    if( !bOrientationSet )
+                    {
+                        bCWPolygon = nCrossProduct == 1;
+                        bOrientationSet = true;
+                    }
+                    else
+                    {
+                        // if current turn orientation is not equal
+                        // initial orientation, this is not a
+                        // rectangle (as rectangles have consistent
+                        // orientation).
+                        if( (nCrossProduct == 1) != bCWPolygon )
+                            return false;
+                    }
+
+                    ++nNumTurns;
+
+                    // More than four 90 degree turns are an
+                    // indication that this must not be a rectangle.
+                    if( nNumTurns > 4 )
+                        return false;
+                }
+
+                // store current state for the next turn
+                nVerticalEdgeType   = nCurrVerticalEdgeType;
+                nHorizontalEdgeType = nCurrHorizontalEdgeType;
+                bNullVertex         = false; // won't reach this line,
+                                             // if bCurrNullVertex is
+                                             // true - see above
+            }
+
+            return true;
+        }
+
+        B3DPolygon createB3DPolygonFromB2DPolygon(const B2DPolygon& rCandidate, double fZCoordinate)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                // call myself recursively with subdivided input
+                const B2DPolygon aCandidate(adaptiveSubdivideByAngle(rCandidate));
+                return createB3DPolygonFromB2DPolygon(aCandidate, fZCoordinate);
+            }
+            else
+            {
+                B3DPolygon aRetval;
+
+                for(sal_uInt32 a(0); a < rCandidate.count(); a++)
+                {
+                    B2DPoint aPoint(rCandidate.getB2DPoint(a));
+                    aRetval.append(B3DPoint(aPoint.getX(), aPoint.getY(), fZCoordinate));
+                }
+
+                // copy closed state
+                aRetval.setClosed(rCandidate.isClosed());
+
+                return aRetval;
+            }
+        }
+
+        B2DPolygon createB2DPolygonFromB3DPolygon(const B3DPolygon& rCandidate, const B3DHomMatrix& rMat)
+        {
+            B2DPolygon aRetval;
+            const sal_uInt32 nCount(rCandidate.count());
+            const bool bIsIdentity(rMat.isIdentity());
+
+            for(sal_uInt32 a(0); a < nCount; a++)
+            {
+                B3DPoint aCandidate(rCandidate.getB3DPoint(a));
+
+                if(!bIsIdentity)
+                {
+                    aCandidate *= rMat;
+                }
+
+                aRetval.append(B2DPoint(aCandidate.getX(), aCandidate.getY()));
+            }
+
+            // copy closed state
+            aRetval.setClosed(rCandidate.isClosed());
+
+            return aRetval;
+        }
+
+        double getSmallestDistancePointToEdge(const B2DPoint& rPointA, const B2DPoint& rPointB, const B2DPoint& rTestPoint, double& rCut)
+        {
+            if(rPointA.equal(rPointB))
+            {
+                rCut = 0.0;
+                const B2DVector aVector(rTestPoint - rPointA);
+                return aVector.getLength();
+            }
+            else
+            {
+                // get the relative cut value on line vector (Vector1) for cut with perpendicular through TestPoint
+                const B2DVector aVector1(rPointB - rPointA);
+                const B2DVector aVector2(rTestPoint - rPointA);
+                const double fDividend((aVector2.getX() * aVector1.getX()) + (aVector2.getY() * aVector1.getY()));
+                const double fDivisor((aVector1.getX() * aVector1.getX()) + (aVector1.getY() * aVector1.getY()));
+                const double fCut(fDividend / fDivisor);
+
+                if(fCut < 0.0)
+                {
+                    // not in line range, get distance to PointA
+                    rCut = 0.0;
+                    return aVector2.getLength();
+                }
+                else if(fCut > 1.0)
+                {
+                    // not in line range, get distance to PointB
+                    rCut = 1.0;
+                    const B2DVector aVector(rTestPoint - rPointB);
+                    return aVector.getLength();
+                }
+                else
+                {
+                    // in line range
+                    const B2DPoint aCutPoint(rPointA + fCut * aVector1);
+                    const B2DVector aVector(rTestPoint - aCutPoint);
+                    rCut = fCut;
+                    return aVector.getLength();
+                }
+            }
+        }
+
+        double getSmallestDistancePointToPolygon(const B2DPolygon& rCandidate, const B2DPoint& rTestPoint, sal_uInt32& rEdgeIndex, double& rCut)
+        {
+            double fRetval(DBL_MAX);
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                const double fZero(0.0);
+                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                B2DCubicBezier aBezier;
+                aBezier.setStartPoint(rCandidate.getB2DPoint(0));
+
+                for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                {
+                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                    aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+                    double fEdgeDist;
+                    double fNewCut(0.0);
+                    bool bEdgeIsCurve(false);
+
+                    if(rCandidate.areControlPointsUsed())
+                    {
+                        aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
+                        aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                        aBezier.testAndSolveTrivialBezier();
+                        bEdgeIsCurve = aBezier.isBezier();
+                    }
+
+                    if(bEdgeIsCurve)
+                    {
+                        fEdgeDist = aBezier.getSmallestDistancePointToBezierSegment(rTestPoint, fNewCut);
+                    }
+                    else
+                    {
+                        fEdgeDist = getSmallestDistancePointToEdge(aBezier.getStartPoint(), aBezier.getEndPoint(), rTestPoint, fNewCut);
+                    }
+
+                    if(fRetval == DBL_MAX || fEdgeDist < fRetval)
+                    {
+                        fRetval = fEdgeDist;
+                        rEdgeIndex = a;
+                        rCut = fNewCut;
+
+                        if(fTools::equal(fRetval, fZero))
+                        {
+                            // already found zero distance, cannot get better. Ensure numerical zero value and end loop.
+                            fRetval = 0.0;
+                            break;
+                        }
+                    }
+
+                    // prepare next step
+                    aBezier.setStartPoint(aBezier.getEndPoint());
+                }
+
+                if(rtl::math::approxEqual(1.0, rCut))
+                {
+                    // correct rEdgeIndex when not last point
+                    if(rCandidate.isClosed())
+                    {
+                        rEdgeIndex = getIndexOfSuccessor(rEdgeIndex, rCandidate);
+                        rCut = 0.0;
+                    }
+                    else
+                    {
+                        if(rEdgeIndex != nEdgeCount - 1)
+                        {
+                            rEdgeIndex++;
+                            rCut = 0.0;
+                        }
+                    }
+                }
+            }
+
+            return fRetval;
+        }
+
+        B2DPoint distort(const B2DPoint& rCandidate, const B2DRange& rOriginal, const B2DPoint& rTopLeft, const B2DPoint& rTopRight, const B2DPoint& rBottomLeft, const B2DPoint& rBottomRight)
+        {
+            if(fTools::equalZero(rOriginal.getWidth()) || fTools::equalZero(rOriginal.getHeight()))
+            {
+                return rCandidate;
+            }
+            else
+            {
+                const double fRelativeX((rCandidate.getX() - rOriginal.getMinX()) / rOriginal.getWidth());
+                const double fRelativeY((rCandidate.getY() - rOriginal.getMinY()) / rOriginal.getHeight());
+                const double fOneMinusRelativeX(1.0 - fRelativeX);
+                const double fOneMinusRelativeY(1.0 - fRelativeY);
+                const double fNewX(fOneMinusRelativeY * (fOneMinusRelativeX * rTopLeft.getX() + fRelativeX * rTopRight.getX()) +
+                    fRelativeY * (fOneMinusRelativeX * rBottomLeft.getX() + fRelativeX * rBottomRight.getX()));
+                const double fNewY(fOneMinusRelativeX * (fOneMinusRelativeY * rTopLeft.getY() + fRelativeY * rBottomLeft.getY()) +
+                    fRelativeX * (fOneMinusRelativeY * rTopRight.getY() + fRelativeY * rBottomRight.getY()));
+
+                return B2DPoint(fNewX, fNewY);
+            }
+        }
+
+        B2DPolygon distort(const B2DPolygon& rCandidate, const B2DRange& rOriginal, const B2DPoint& rTopLeft, const B2DPoint& rTopRight, const B2DPoint& rBottomLeft, const B2DPoint& rBottomRight)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount && rOriginal.getWidth() != 0.0 && rOriginal.getHeight() != 0.0)
+            {
+                B2DPolygon aRetval;
+
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    aRetval.append(distort(rCandidate.getB2DPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
+
+                    if(rCandidate.areControlPointsUsed())
+                    {
+                        if(!rCandidate.getPrevControlPoint(a).equalZero())
+                        {
+                            aRetval.setPrevControlPoint(a, distort(rCandidate.getPrevControlPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
+                        }
+
+                        if(!rCandidate.getNextControlPoint(a).equalZero())
+                        {
+                            aRetval.setNextControlPoint(a, distort(rCandidate.getNextControlPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
+                        }
+                    }
+                }
+
+                aRetval.setClosed(rCandidate.isClosed());
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolygon expandToCurve(const B2DPolygon& rCandidate)
+        {
+            B2DPolygon aRetval(rCandidate);
+
+            for(sal_uInt32 a(0); a < rCandidate.count(); a++)
+            {
+                expandToCurveInPoint(aRetval, a);
+            }
+
+            return aRetval;
+        }
+
+        bool expandToCurveInPoint(B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "expandToCurveInPoint: Access to polygon out of range (!)");
+            bool bRetval(false);
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount)
+            {
+                // predecessor
+                if(!rCandidate.isPrevControlPointUsed(nIndex))
+                {
+                    if(!rCandidate.isClosed() && nIndex == 0)
+                    {
+                        // do not create previous vector for start point of open polygon
+                    }
+                    else
+                    {
+                        const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
+                        rCandidate.setPrevControlPoint(nIndex, interpolate(rCandidate.getB2DPoint(nIndex), rCandidate.getB2DPoint(nPrevIndex), 1.0 / 3.0));
+                        bRetval = true;
+                    }
+                }
+
+                // successor
+                if(!rCandidate.isNextControlPointUsed(nIndex))
+                {
+                    if(!rCandidate.isClosed() && nIndex + 1 == nPointCount)
+                    {
+                        // do not create next vector for end point of open polygon
+                    }
+                    else
+                    {
+                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                        rCandidate.setNextControlPoint(nIndex, interpolate(rCandidate.getB2DPoint(nIndex), rCandidate.getB2DPoint(nNextIndex), 1.0 / 3.0));
+                        bRetval = true;
+                    }
+                }
+            }
+
+            return bRetval;
+        }
+
+        bool setContinuityInPoint(B2DPolygon& rCandidate, sal_uInt32 nIndex, B2VectorContinuity eContinuity)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "setContinuityInPoint: Access to polygon out of range (!)");
+            bool bRetval(false);
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount)
+            {
+                const B2DPoint aCurrentPoint(rCandidate.getB2DPoint(nIndex));
+
+                switch(eContinuity)
+                {
+                    case B2VectorContinuity::NONE :
+                    {
+                        if(rCandidate.isPrevControlPointUsed(nIndex))
+                        {
+                            if(!rCandidate.isClosed() && nIndex == 0)
+                            {
+                                // remove existing previous vector for start point of open polygon
+                                rCandidate.resetPrevControlPoint(nIndex);
+                            }
+                            else
+                            {
+                                const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
+                                rCandidate.setPrevControlPoint(nIndex, interpolate(aCurrentPoint, rCandidate.getB2DPoint(nPrevIndex), 1.0 / 3.0));
+                            }
+
+                            bRetval = true;
+                        }
+
+                        if(rCandidate.isNextControlPointUsed(nIndex))
+                        {
+                            if(!rCandidate.isClosed() && nIndex == nPointCount + 1)
+                            {
+                                // remove next vector for end point of open polygon
+                                rCandidate.resetNextControlPoint(nIndex);
+                            }
+                            else
+                            {
+                                const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                                rCandidate.setNextControlPoint(nIndex, interpolate(aCurrentPoint, rCandidate.getB2DPoint(nNextIndex), 1.0 / 3.0));
+                            }
+
+                            bRetval = true;
+                        }
+
+                        break;
+                    }
+                    case B2VectorContinuity::C1 :
+                    {
+                        if(rCandidate.isPrevControlPointUsed(nIndex) && rCandidate.isNextControlPointUsed(nIndex))
+                        {
+                            // lengths both exist since both are used
+                            B2DVector aVectorPrev(rCandidate.getPrevControlPoint(nIndex) - aCurrentPoint);
+                            B2DVector aVectorNext(rCandidate.getNextControlPoint(nIndex) - aCurrentPoint);
+                            const double fLenPrev(aVectorPrev.getLength());
+                            const double fLenNext(aVectorNext.getLength());
+                            aVectorPrev.normalize();
+                            aVectorNext.normalize();
+                            const B2VectorOrientation aOrientation(getOrientation(aVectorPrev, aVectorNext));
+
+                            if(aOrientation == B2VectorOrientation::Neutral && aVectorPrev.scalar(aVectorNext) < 0.0)
+                            {
+                                // parallel and opposite direction; check length
+                                if(fTools::equal(fLenPrev, fLenNext))
+                                {
+                                    // this would be even C2, but we want C1. Use the lengths of the corresponding edges.
+                                    const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
+                                    const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                                    const double fLenPrevEdge(B2DVector(rCandidate.getB2DPoint(nPrevIndex) - aCurrentPoint).getLength() * (1.0 / 3.0));
+                                    const double fLenNextEdge(B2DVector(rCandidate.getB2DPoint(nNextIndex) - aCurrentPoint).getLength() * (1.0 / 3.0));
+
+                                    rCandidate.setControlPoints(nIndex,
+                                        aCurrentPoint + (aVectorPrev * fLenPrevEdge),
+                                        aCurrentPoint + (aVectorNext * fLenNextEdge));
+                                    bRetval = true;
+                                }
+                            }
+                            else
+                            {
+                                // not parallel or same direction, set vectors and length
+                                const B2DVector aNormalizedPerpendicular(getNormalizedPerpendicular(aVectorPrev + aVectorNext));
+
+                                if(aOrientation == B2VectorOrientation::Positive)
+                                {
+                                    rCandidate.setControlPoints(nIndex,
+                                        aCurrentPoint - (aNormalizedPerpendicular * fLenPrev),
+                                        aCurrentPoint + (aNormalizedPerpendicular * fLenNext));
+                                }
+                                else
+                                {
+                                    rCandidate.setControlPoints(nIndex,
+                                        aCurrentPoint + (aNormalizedPerpendicular * fLenPrev),
+                                        aCurrentPoint - (aNormalizedPerpendicular * fLenNext));
+                                }
+
+                                bRetval = true;
+                            }
+                        }
+                        break;
+                    }
+                    case B2VectorContinuity::C2 :
+                    {
+                        if(rCandidate.isPrevControlPointUsed(nIndex) && rCandidate.isNextControlPointUsed(nIndex))
+                        {
+                            // lengths both exist since both are used
+                            B2DVector aVectorPrev(rCandidate.getPrevControlPoint(nIndex) - aCurrentPoint);
+                            B2DVector aVectorNext(rCandidate.getNextControlPoint(nIndex) - aCurrentPoint);
+                            const double fCommonLength((aVectorPrev.getLength() + aVectorNext.getLength()) / 2.0);
+                            aVectorPrev.normalize();
+                            aVectorNext.normalize();
+                            const B2VectorOrientation aOrientation(getOrientation(aVectorPrev, aVectorNext));
+
+                            if(aOrientation == B2VectorOrientation::Neutral && aVectorPrev.scalar(aVectorNext) < 0.0)
+                            {
+                                // parallel and opposite direction; set length. Use one direction for better numerical correctness
+                                const B2DVector aScaledDirection(aVectorPrev * fCommonLength);
+
+                                rCandidate.setControlPoints(nIndex,
+                                    aCurrentPoint + aScaledDirection,
+                                    aCurrentPoint - aScaledDirection);
+                            }
+                            else
+                            {
+                                // not parallel or same direction, set vectors and length
+                                const B2DVector aNormalizedPerpendicular(getNormalizedPerpendicular(aVectorPrev + aVectorNext));
+                                const B2DVector aPerpendicular(aNormalizedPerpendicular * fCommonLength);
+
+                                if(aOrientation == B2VectorOrientation::Positive)
+                                {
+                                    rCandidate.setControlPoints(nIndex,
+                                        aCurrentPoint - aPerpendicular,
+                                        aCurrentPoint + aPerpendicular);
+                                }
+                                else
+                                {
+                                    rCandidate.setControlPoints(nIndex,
+                                        aCurrentPoint + aPerpendicular,
+                                        aCurrentPoint - aPerpendicular);
+                                }
+                            }
+
+                            bRetval = true;
+                        }
+                        break;
+                    }
+                }
+            }
+
+            return bRetval;
+        }
+
+        B2DPolygon growInNormalDirection(const B2DPolygon& rCandidate, double fValue)
+        {
+            if(fValue != 0.0)
+            {
+                if(rCandidate.areControlPointsUsed())
+                {
+                    // call myself recursively with subdivided input
+                    const B2DPolygon aCandidate(adaptiveSubdivideByAngle(rCandidate));
+                    return growInNormalDirection(aCandidate, fValue);
+                }
+                else
+                {
+                    B2DPolygon aRetval;
+                    const sal_uInt32 nPointCount(rCandidate.count());
+
+                    if(nPointCount)
+                    {
+                        B2DPoint aPrev(rCandidate.getB2DPoint(nPointCount - 1));
+                        B2DPoint aCurrent(rCandidate.getB2DPoint(0));
+
+                        for(sal_uInt32 a(0); a < nPointCount; a++)
+                        {
+                            const B2DPoint aNext(rCandidate.getB2DPoint(a + 1 == nPointCount ? 0 : a + 1));
+                            const B2DVector aBack(aPrev - aCurrent);
+                            const B2DVector aForw(aNext - aCurrent);
+                            const B2DVector aPerpBack(getNormalizedPerpendicular(aBack));
+                            const B2DVector aPerpForw(getNormalizedPerpendicular(aForw));
+                            B2DVector aDirection(aPerpBack - aPerpForw);
+                            aDirection.normalize();
+                            aDirection *= fValue;
+                            aRetval.append(aCurrent + aDirection);
+
+                            // prepare next step
+                            aPrev = aCurrent;
+                            aCurrent = aNext;
+                        }
+                    }
+
+                    // copy closed state
+                    aRetval.setClosed(rCandidate.isClosed());
+
+                    return aRetval;
+                }
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolygon reSegmentPolygon(const B2DPolygon& rCandidate, sal_uInt32 nSegments)
+        {
+            B2DPolygon aRetval;
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount && nSegments)
+            {
+                // get current segment count
+                const sal_uInt32 nSegmentCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+
+                if(nSegmentCount == nSegments)
+                {
+                    aRetval = rCandidate;
+                }
+                else
+                {
+                    const double fLength(getLength(rCandidate));
+                    const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nSegments : nSegments + 1);
+
+                    for(sal_uInt32 a(0); a < nLoopCount; a++)
+                    {
+                        const double fRelativePos(static_cast<double>(a) / static_cast<double>(nSegments)); // 0.0 .. 1.0
+                        const B2DPoint aNewPoint(getPositionRelative(rCandidate, fRelativePos, fLength));
+                        aRetval.append(aNewPoint);
+                    }
+
+                    // copy closed flag
+                    aRetval.setClosed(rCandidate.isClosed());
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolygon interpolate(const B2DPolygon& rOld1, const B2DPolygon& rOld2, double t)
+        {
+            OSL_ENSURE(rOld1.count() == rOld2.count(), "B2DPolygon interpolate: Different geometry (!)");
+
+            if(fTools::lessOrEqual(t, 0.0) || rOld1 == rOld2)
+            {
+                return rOld1;
+            }
+            else if(fTools::moreOrEqual(t, 1.0))
+            {
+                return rOld2;
+            }
+            else
+            {
+                B2DPolygon aRetval;
+                const bool bInterpolateVectors(rOld1.areControlPointsUsed() || rOld2.areControlPointsUsed());
+                aRetval.setClosed(rOld1.isClosed() && rOld2.isClosed());
+
+                for(sal_uInt32 a(0); a < rOld1.count(); a++)
+                {
+                    aRetval.append(interpolate(rOld1.getB2DPoint(a), rOld2.getB2DPoint(a), t));
+
+                    if(bInterpolateVectors)
+                    {
+                        aRetval.setPrevControlPoint(a, interpolate(rOld1.getPrevControlPoint(a), rOld2.getPrevControlPoint(a), t));
+                        aRetval.setNextControlPoint(a, interpolate(rOld1.getNextControlPoint(a), rOld2.getNextControlPoint(a), t));
+                    }
+                }
+
+                return aRetval;
+            }
+        }
+
+        // #i76891#
+        B2DPolygon simplifyCurveSegments(const B2DPolygon& rCandidate)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount && rCandidate.areControlPointsUsed())
+            {
+                // prepare loop
+                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                B2DPolygon aRetval;
+                B2DCubicBezier aBezier;
+                aBezier.setStartPoint(rCandidate.getB2DPoint(0));
+
+                // try to avoid costly reallocations
+                aRetval.reserve( nEdgeCount+1);
+
+                // add start point
+                aRetval.append(aBezier.getStartPoint());
+
+                for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                {
+                    // get values for edge
+                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                    aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
+                    aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
+                    aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
+                    aBezier.testAndSolveTrivialBezier();
+
+                    // still bezier?
+                    if(aBezier.isBezier())
+                    {
+                        // add edge with control vectors
+                        aRetval.appendBezierSegment(aBezier.getControlPointA(), aBezier.getControlPointB(), aBezier.getEndPoint());
+                    }
+                    else
+                    {
+                        // add edge
+                        aRetval.append(aBezier.getEndPoint());
+                    }
+
+                    // next point
+                    aBezier.setStartPoint(aBezier.getEndPoint());
+                }
+
+                if(rCandidate.isClosed())
+                {
+                    // set closed flag, rescue control point and correct last double point
+                    closeWithGeometryChange(aRetval);
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        // makes the given indexed point the new polygon start point. To do that, the points in the
+        // polygon will be rotated. This is only valid for closed polygons, for non-closed ones
+        // an assertion will be triggered
+        B2DPolygon makeStartPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndexOfNewStatPoint)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 2 && nIndexOfNewStatPoint != 0 && nIndexOfNewStatPoint < nPointCount)
+            {
+                OSL_ENSURE(rCandidate.isClosed(), "makeStartPoint: only valid for closed polygons (!)");
+                B2DPolygon aRetval;
+
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    const sal_uInt32 nSourceIndex((a + nIndexOfNewStatPoint) % nPointCount);
+                    aRetval.append(rCandidate.getB2DPoint(nSourceIndex));
+
+                    if(rCandidate.areControlPointsUsed())
+                    {
+                        aRetval.setPrevControlPoint(a, rCandidate.getPrevControlPoint(nSourceIndex));
+                        aRetval.setNextControlPoint(a, rCandidate.getNextControlPoint(nSourceIndex));
+                    }
+                }
+
+                return aRetval;
+            }
+
+            return rCandidate;
+        }
+
+        B2DPolygon createEdgesOfGivenLength(const B2DPolygon& rCandidate, double fLength, double fStart, double fEnd)
+        {
+            B2DPolygon aRetval;
+
+            if(fLength < 0.0)
+            {
+                fLength = 0.0;
+            }
+
+            if(!fTools::equalZero(fLength))
+            {
+                if(fStart < 0.0)
+                {
+                    fStart = 0.0;
+                }
+
+                if(fEnd < 0.0)
+                {
+                    fEnd = 0.0;
+                }
+
+                if(fEnd < fStart)
+                {
+                    fEnd = fStart;
+                }
+
+                // iterate and consume pieces with fLength. First subdivide to reduce input to line segments
+                const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
+                const sal_uInt32 nPointCount(aCandidate.count());
+
+                if(nPointCount > 1)
+                {
+                    const bool bEndActive(!fTools::equalZero(fEnd));
+                    const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    B2DPoint aCurrent(aCandidate.getB2DPoint(0));
+                    double fPositionInEdge(fStart);
+                    double fAbsolutePosition(fStart);
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                        const B2DPoint aNext(aCandidate.getB2DPoint(nNextIndex));
+                        const B2DVector aEdge(aNext - aCurrent);
+                        double fEdgeLength(aEdge.getLength());
+
+                        if(!fTools::equalZero(fEdgeLength))
+                        {
+                            while(fTools::less(fPositionInEdge, fEdgeLength))
+                            {
+                                // move position on edge forward as long as on edge
+                                const double fScalar(fPositionInEdge / fEdgeLength);
+                                aRetval.append(aCurrent + (aEdge * fScalar));
+                                fPositionInEdge += fLength;
+
+                                if(bEndActive)
+                                {
+                                    fAbsolutePosition += fLength;
+
+                                    if(fTools::more(fAbsolutePosition, fEnd))
+                                    {
+                                        break;
+                                    }
+                                }
+                            }
+
+                            // subtract length of current edge
+                            fPositionInEdge -= fEdgeLength;
+                        }
+
+                        if(bEndActive && fTools::more(fAbsolutePosition, fEnd))
+                        {
+                            break;
+                        }
+
+                        // prepare next step
+                        aCurrent = aNext;
+                    }
+
+                    // keep closed state
+                    aRetval.setClosed(aCandidate.isClosed());
+                }
+                else
+                {
+                    // source polygon has only one point, return unchanged
+                    aRetval = aCandidate;
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolygon createWaveline(const B2DPolygon& rCandidate, double fWaveWidth, double fWaveHeight)
+        {
+            B2DPolygon aRetval;
+
+            if(fWaveWidth < 0.0)
+            {
+                fWaveWidth = 0.0;
+            }
+
+            if(fWaveHeight < 0.0)
+            {
+                fWaveHeight = 0.0;
+            }
+
+            const bool bHasWidth(!fTools::equalZero(fWaveWidth));
+
+            if(bHasWidth)
+            {
+                const bool bHasHeight(!fTools::equalZero(fWaveHeight));
+                if(bHasHeight)
+                {
+                    // width and height, create waveline. First subdivide to reduce input to line segments
+                    // of WaveWidth. Last segment may be missing. If this turns out to be a problem, it
+                    // may be added here again using the original last point from rCandidate. It may
+                    // also be the case that rCandidate was closed. To simplify things it is handled here
+                    // as if it was opened.
+                    // Result from createEdgesOfGivenLength contains no curved segments, handle as straight
+                    // edges.
+                    const B2DPolygon aEqualLenghEdges(createEdgesOfGivenLength(rCandidate, fWaveWidth));
+                    const sal_uInt32 nPointCount(aEqualLenghEdges.count());
+
+                    if(nPointCount > 1)
+                    {
+                        // iterate over straight edges, add start point
+                        B2DPoint aCurrent(aEqualLenghEdges.getB2DPoint(0));
+                        aRetval.append(aCurrent);
+
+                        for(sal_uInt32 a(0); a < nPointCount - 1; a++)
+                        {
+                            const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                            const B2DPoint aNext(aEqualLenghEdges.getB2DPoint(nNextIndex));
+                            const B2DVector aEdge(aNext - aCurrent);
+                            const B2DVector aPerpendicular(getNormalizedPerpendicular(aEdge));
+                            const B2DVector aControlOffset((aEdge * 0.467308) - (aPerpendicular * fWaveHeight));
+
+                            // add curve segment
+                            aRetval.appendBezierSegment(
+                                aCurrent + aControlOffset,
+                                aNext - aControlOffset,
+                                aNext);
+
+                            // prepare next step
+                            aCurrent = aNext;
+                        }
+                    }
+                }
+                else
+                {
+                    // width but no height -> return original polygon
+                    aRetval = rCandidate;
+                }
+            }
+            else
+            {
+                // no width -> no waveline, stay empty and return
+            }
+
+            return aRetval;
+        }
+
+        // snap points of horizontal or vertical edges to discrete values
+        B2DPolygon snapPointsOfHorizontalOrVerticalEdges(const B2DPolygon& rCandidate)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                // Start by copying the source polygon to get a writeable copy. The closed state is
+                // copied by aRetval's initialisation, too, so no need to copy it in this method
+                B2DPolygon aRetval(rCandidate);
+
+                // prepare geometry data. Get rounded from original
+                B2ITuple aPrevTuple(basegfx::fround(rCandidate.getB2DPoint(nPointCount - 1)));
+                B2DPoint aCurrPoint(rCandidate.getB2DPoint(0));
+                B2ITuple aCurrTuple(basegfx::fround(aCurrPoint));
+
+                // loop over all points. This will also snap the implicit closing edge
+                // even when not closed, but that's no problem here
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    // get next point. Get rounded from original
+                    const bool bLastRun(a + 1 == nPointCount);
+                    const sal_uInt32 nNextIndex(bLastRun ? 0 : a + 1);
+                    const B2DPoint aNextPoint(rCandidate.getB2DPoint(nNextIndex));
+                    const B2ITuple aNextTuple(basegfx::fround(aNextPoint));
+
+                    // get the states
+                    const bool bPrevVertical(aPrevTuple.getX() == aCurrTuple.getX());
+                    const bool bNextVertical(aNextTuple.getX() == aCurrTuple.getX());
+                    const bool bPrevHorizontal(aPrevTuple.getY() == aCurrTuple.getY());
+                    const bool bNextHorizontal(aNextTuple.getY() == aCurrTuple.getY());
+                    const bool bSnapX(bPrevVertical || bNextVertical);
+                    const bool bSnapY(bPrevHorizontal || bNextHorizontal);
+
+                    if(bSnapX || bSnapY)
+                    {
+                        const B2DPoint aSnappedPoint(
+                            bSnapX ? aCurrTuple.getX() : aCurrPoint.getX(),
+                            bSnapY ? aCurrTuple.getY() : aCurrPoint.getY());
+
+                        aRetval.setB2DPoint(a, aSnappedPoint);
+                    }
+
+                    // prepare next point
+                    if(!bLastRun)
+                    {
+                        aPrevTuple = aCurrTuple;
+                        aCurrPoint = aNextPoint;
+                        aCurrTuple = aNextTuple;
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DVector getTangentEnteringPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            B2DVector aRetval(0.0, 0.0);
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nIndex >= nCount)
+            {
+                // out of range
+                return aRetval;
+            }
+
+            // start immediately at prev point compared to nIndex
+            const bool bClosed(rCandidate.isClosed());
+            sal_uInt32 nPrev(bClosed ? (nIndex + nCount - 1) % nCount : nIndex ? nIndex - 1 : nIndex);
+
+            if(nPrev == nIndex)
+            {
+                // no previous, done
+                return aRetval;
+            }
+
+            B2DCubicBezier aSegment;
+
+            // go backward in the polygon; if closed, maximal back to start index (nIndex); if not closed,
+            // until zero. Use nIndex as stop criteria
+            while(nPrev != nIndex)
+            {
+                // get BezierSegment and tangent at the *end* of segment
+                rCandidate.getBezierSegment(nPrev, aSegment);
+                aRetval = aSegment.getTangent(1.0);
+
+                if(!aRetval.equalZero())
+                {
+                    // if we have a tangent, return it
+                    return aRetval;
+                }
+
+                // prepare index before checked one
+                nPrev = bClosed ? (nPrev + nCount - 1) % nCount : nPrev ? nPrev - 1 : nIndex;
+            }
+
+            return aRetval;
+        }
+
+        B2DVector getTangentLeavingPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
+        {
+            B2DVector aRetval(0.0, 0.0);
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nIndex >= nCount)
+            {
+                // out of range
+                return aRetval;
+            }
+
+            // start at nIndex
+            const bool bClosed(rCandidate.isClosed());
+            sal_uInt32 nCurrent(nIndex);
+            B2DCubicBezier aSegment;
+
+            // go forward; if closed, do this until once around and back at start index (nIndex); if not
+            // closed, until last point (nCount - 1). Use nIndex as stop criteria
+            do
+            {
+                // get BezierSegment and tangent at the *beginning* of segment
+                rCandidate.getBezierSegment(nCurrent, aSegment);
+                aRetval = aSegment.getTangent(0.0);
+
+                if(!aRetval.equalZero())
+                {
+                    // if we have a tangent, return it
+                    return aRetval;
+                }
+
+                // prepare next index
+                nCurrent = bClosed ? (nCurrent + 1) % nCount : nCurrent + 1 < nCount ? nCurrent + 1 : nIndex;
+            }
+            while(nCurrent != nIndex);
+
+            return aRetval;
+        }
+
+        // converters for css::drawing::PointSequence
+
+        B2DPolygon UnoPointSequenceToB2DPolygon(
+            const css::drawing::PointSequence& rPointSequenceSource)
+        {
+            B2DPolygon aRetval;
+            const sal_uInt32 nLength(rPointSequenceSource.getLength());
+
+            if(nLength)
+            {
+                aRetval.reserve(nLength);
+                const css::awt::Point* pArray = rPointSequenceSource.getConstArray();
+                const css::awt::Point* pArrayEnd = pArray + rPointSequenceSource.getLength();
+
+                for(;pArray != pArrayEnd; pArray++)
+                {
+                    aRetval.append(B2DPoint(pArray->X, pArray->Y));
+                }
+
+                // check for closed state flag
+                utils::checkClosed(aRetval);
+            }
+
+            return aRetval;
+        }
+
+        void B2DPolygonToUnoPointSequence(
+            const B2DPolygon& rPolygon,
+            css::drawing::PointSequence& rPointSequenceRetval)
+        {
+            B2DPolygon aPolygon(rPolygon);
+
+            if(aPolygon.areControlPointsUsed())
+            {
+                OSL_ENSURE(false, "B2DPolygonToUnoPointSequence: Source contains bezier segments, wrong UNO API data type may be used (!)");
+                aPolygon = aPolygon.getDefaultAdaptiveSubdivision();
+            }
+
+            const sal_uInt32 nPointCount(aPolygon.count());
+
+            if(nPointCount)
+            {
+                // Take closed state into account, the API polygon still uses the old closed definition
+                // with last/first point are identical (cannot hold information about open polygons with identical
+                // first and last point, though)
+                const bool bIsClosed(aPolygon.isClosed());
+
+                rPointSequenceRetval.realloc(bIsClosed ? nPointCount + 1 : nPointCount);
+                css::awt::Point* pSequence = rPointSequenceRetval.getArray();
+
+                for(sal_uInt32 b(0); b < nPointCount; b++)
+                {
+                    const B2DPoint aPoint(aPolygon.getB2DPoint(b));
+                    const css::awt::Point aAPIPoint(fround(aPoint.getX()), fround(aPoint.getY()));
+
+                    *pSequence = aAPIPoint;
+                    pSequence++;
+                }
+
+                // copy first point if closed
+                if(bIsClosed)
+                {
+                    *pSequence = *rPointSequenceRetval.getConstArray();
+                }
+            }
+            else
+            {
+                rPointSequenceRetval.realloc(0);
+            }
+        }
+
+        // converters for css::drawing::PointSequence and
+        // css::drawing::FlagSequence to B2DPolygon (curved polygons)
+
+        B2DPolygon UnoPolygonBezierCoordsToB2DPolygon(
+            const css::drawing::PointSequence& rPointSequenceSource,
+            const css::drawing::FlagSequence& rFlagSequenceSource)
+        {
+            const sal_uInt32 nCount(static_cast<sal_uInt32>(rPointSequenceSource.getLength()));
+            OSL_ENSURE(nCount == static_cast<sal_uInt32>(rFlagSequenceSource.getLength()),
+                "UnoPolygonBezierCoordsToB2DPolygon: Unequal count of Points and Flags (!)");
+
+            // prepare new polygon
+            B2DPolygon aRetval;
+
+            if(0 != nCount)
+            {
+                aRetval.reserve(nCount);
+
+                const css::awt::Point* pPointSequence = rPointSequenceSource.getConstArray();
+                const css::drawing::PolygonFlags* pFlagSequence = rFlagSequenceSource.getConstArray();
+
+                // get first point and flag
+                B2DPoint aNewCoordinatePair(pPointSequence->X, pPointSequence->Y); pPointSequence++;
+                css::drawing::PolygonFlags ePolygonFlag(*pFlagSequence); pFlagSequence++;
+                B2DPoint aControlA;
+                B2DPoint aControlB;
+
+                // first point is not allowed to be a control point
+                OSL_ENSURE(ePolygonFlag != css::drawing::PolygonFlags_CONTROL,
+                    "UnoPolygonBezierCoordsToB2DPolygon: Start point is a control point, illegal input polygon (!)");
+
+                // add first point as start point
+                aRetval.append(aNewCoordinatePair);
+
+                for(sal_uInt32 b(1); b < nCount;)
+                {
+                    // prepare loop
+                    bool bControlA(false);
+                    bool bControlB(false);
+
+                    // get next point and flag
+                    aNewCoordinatePair = B2DPoint(pPointSequence->X, pPointSequence->Y);
+                    ePolygonFlag = *pFlagSequence;
+                    pPointSequence++; pFlagSequence++; b++;
+
+                    if(b < nCount && ePolygonFlag == css::drawing::PolygonFlags_CONTROL)
+                    {
+                        aControlA = aNewCoordinatePair;
+                        bControlA = true;
+
+                        // get next point and flag
+                        aNewCoordinatePair = B2DPoint(pPointSequence->X, pPointSequence->Y);
+                        ePolygonFlag = *pFlagSequence;
+                        pPointSequence++; pFlagSequence++; b++;
+                    }
+
+                    if(b < nCount && ePolygonFlag == css::drawing::PolygonFlags_CONTROL)
+                    {
+                        aControlB = aNewCoordinatePair;
+                        bControlB = true;
+
+                        // get next point and flag
+                        aNewCoordinatePair = B2DPoint(pPointSequence->X, pPointSequence->Y);
+                        ePolygonFlag = *pFlagSequence;
+                        pPointSequence++; pFlagSequence++; b++;
+                    }
+
+                    // two or no control points are consumed, another one would be an error.
+                    // It's also an error if only one control point was read
+                    SAL_WARN_IF(ePolygonFlag == css::drawing::PolygonFlags_CONTROL || bControlA != bControlB,
+                        "basegfx", "UnoPolygonBezierCoordsToB2DPolygon: Illegal source polygon (!)");
+
+                    // the previous writes used the B2DPolyPolygon -> utils::PolyPolygon converter
+                    // which did not create minimal PolyPolygons, but created all control points
+                    // as null vectors (identical points). Because of the former P(CA)(CB)-norm of
+                    // B2DPolygon and it's unused sign of being the zero-vector and CA and CB being
+                    // relative to P, an empty edge was exported as P == CA == CB. Luckily, the new
+                    // export format can be read without errors by the old OOo-versions, so we need only
+                    // to correct here at read and do not need to export a wrong but compatible version
+                    // for the future.
+                    if(bControlA
+                        && aControlA.equal(aControlB)
+                        && aControlA.equal(aRetval.getB2DPoint(aRetval.count() - 1)))
+                    {
+                        bControlA = false;
+                    }
+
+                    if(bControlA)
+                    {
+                        // add bezier edge
+                        aRetval.appendBezierSegment(aControlA, aControlB, aNewCoordinatePair);
+                    }
+                    else
+                    {
+                        // add edge
+                        aRetval.append(aNewCoordinatePair);
+                    }
+                }
+
+                // #i72807# API import uses old line start/end-equal definition for closed,
+                // so we need to correct this to closed state here
+                checkClosed(aRetval);
+            }
+
+            return aRetval;
+        }
+
+        void B2DPolygonToUnoPolygonBezierCoords(
+            const B2DPolygon& rPolygon,
+            css::drawing::PointSequence& rPointSequenceRetval,
+            css::drawing::FlagSequence& rFlagSequenceRetval)
+        {
+            const sal_uInt32 nPointCount(rPolygon.count());
+
+            if(nPointCount)
+            {
+                const bool bCurve(rPolygon.areControlPointsUsed());
+                const bool bClosed(rPolygon.isClosed());
+
+                if(bCurve)
+                {
+                    // calculate target point count
+                    const sal_uInt32 nLoopCount(bClosed ? nPointCount : nPointCount - 1);
+
+                    if(nLoopCount)
+                    {
+                        // prepare target data. The real needed number of target points (and flags)
+                        // could only be calculated by using two loops, so use dynamic memory
+                        std::vector< css::awt::Point > aCollectPoints;
+                        std::vector< css::drawing::PolygonFlags > aCollectFlags;
+
+                        // reserve maximum creatable points
+                        const sal_uInt32 nMaxTargetCount((nLoopCount * 3) + 1);
+                        aCollectPoints.reserve(nMaxTargetCount);
+                        aCollectFlags.reserve(nMaxTargetCount);
+
+                        // prepare current bezier segment by setting start point
+                        B2DCubicBezier aBezierSegment;
+                        aBezierSegment.setStartPoint(rPolygon.getB2DPoint(0));
+
+                        for(sal_uInt32 a(0); a < nLoopCount; a++)
+                        {
+                            // add current point (always) and remember StartPointIndex for evtl. later corrections
+                            const sal_uInt32 nStartPointIndex(aCollectPoints.size());
+                            aCollectPoints.emplace_back(
+                                    fround(aBezierSegment.getStartPoint().getX()),
+                                    fround(aBezierSegment.getStartPoint().getY()));
+                            aCollectFlags.push_back(css::drawing::PolygonFlags_NORMAL);
+
+                            // prepare next segment
+                            const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                            aBezierSegment.setEndPoint(rPolygon.getB2DPoint(nNextIndex));
+                            aBezierSegment.setControlPointA(rPolygon.getNextControlPoint(a));
+                            aBezierSegment.setControlPointB(rPolygon.getPrevControlPoint(nNextIndex));
+
+                            if(aBezierSegment.isBezier())
+                            {
+                                // if bezier is used, add always two control points due to the old schema
+                                aCollectPoints.emplace_back(
+                                        fround(aBezierSegment.getControlPointA().getX()),
+                                        fround(aBezierSegment.getControlPointA().getY()));
+                                aCollectFlags.push_back(css::drawing::PolygonFlags_CONTROL);
+
+                                aCollectPoints.emplace_back(
+                                        fround(aBezierSegment.getControlPointB().getX()),
+                                        fround(aBezierSegment.getControlPointB().getY()));
+                                aCollectFlags.push_back(css::drawing::PolygonFlags_CONTROL);
+                            }
+
+                            // test continuity with previous control point to set flag value
+                            if(aBezierSegment.getControlPointA() != aBezierSegment.getStartPoint() && (bClosed || a))
+                            {
+                                const B2VectorContinuity eCont(rPolygon.getContinuityInPoint(a));
+
+                                if(eCont == B2VectorContinuity::C1)
+                                {
+                                    aCollectFlags[nStartPointIndex] = css::drawing::PolygonFlags_SMOOTH;
+                                }
+                                else if(eCont == B2VectorContinuity::C2)
+                                {
+                                    aCollectFlags[nStartPointIndex] = css::drawing::PolygonFlags_SYMMETRIC;
+                                }
+                            }
+
+                            // prepare next loop
+                            aBezierSegment.setStartPoint(aBezierSegment.getEndPoint());
+                        }
+
+                        if(bClosed)
+                        {
+                            // add first point again as closing point due to old definition
+                            aCollectPoints.push_back(aCollectPoints[0]);
+                            aCollectFlags.push_back(css::drawing::PolygonFlags_NORMAL);
+                        }
+                        else
+                        {
+                            // add last point as closing point
+                            const B2DPoint aClosingPoint(rPolygon.getB2DPoint(nPointCount - 1));
+                            aCollectPoints.emplace_back(
+                                    fround(aClosingPoint.getX()),
+                                    fround(aClosingPoint.getY()));
+                            aCollectFlags.push_back(css::drawing::PolygonFlags_NORMAL);
+                        }
+
+                        // copy collected data to target arrays
+                        const sal_uInt32 nTargetCount(aCollectPoints.size());
+                        OSL_ENSURE(nTargetCount == aCollectFlags.size(), "Unequal Point and Flag count (!)");
+
+                        rPointSequenceRetval.realloc(static_cast<sal_Int32>(nTargetCount));
+                        rFlagSequenceRetval.realloc(static_cast<sal_Int32>(nTargetCount));
+                        css::awt::Point* pPointSequence = rPointSequenceRetval.getArray();
+                        css::drawing::PolygonFlags* pFlagSequence = rFlagSequenceRetval.getArray();
+
+                        for(sal_uInt32 a(0); a < nTargetCount; a++)
+                        {
+                            *pPointSequence = aCollectPoints[a];
+                            *pFlagSequence = aCollectFlags[a];
+                            pPointSequence++;
+                            pFlagSequence++;
+                        }
+                    }
+                }
+                else
+                {
+                    // straightforward point list creation
+                    const sal_uInt32 nTargetCount(nPointCount + (bClosed ? 1 : 0));
+
+                    rPointSequenceRetval.realloc(static_cast<sal_Int32>(nTargetCount));
+                    rFlagSequenceRetval.realloc(static_cast<sal_Int32>(nTargetCount));
+
+                    css::awt::Point* pPointSequence = rPointSequenceRetval.getArray();
+                    css::drawing::PolygonFlags* pFlagSequence = rFlagSequenceRetval.getArray();
+
+                    for(sal_uInt32 a(0); a < nPointCount; a++)
+                    {
+                        const B2DPoint aB2DPoint(rPolygon.getB2DPoint(a));
+                        const css::awt::Point aAPIPoint(
+                            fround(aB2DPoint.getX()),
+                            fround(aB2DPoint.getY()));
+
+                        *pPointSequence = aAPIPoint;
+                        *pFlagSequence = css::drawing::PolygonFlags_NORMAL;
+                        pPointSequence++;
+                        pFlagSequence++;
+                    }
+
+                    if(bClosed)
+                    {
+                        // add first point as closing point
+                        *pPointSequence = *rPointSequenceRetval.getConstArray();
+                        *pFlagSequence = css::drawing::PolygonFlags_NORMAL;
+                    }
+                }
+            }
+            else
+            {
+                rPointSequenceRetval.realloc(0);
+                rFlagSequenceRetval.realloc(0);
+            }
+        }
+
+B2DPolygon createSimplifiedPolygon(const B2DPolygon& rCandidate, const double fTolerance)
+{
+    const sal_uInt32 nPointCount(rCandidate.count());
+    if (nPointCount < 3 || rCandidate.areControlPointsUsed())
+        return rCandidate;
+
+    // The solution does not use recursion directly, since this could lead to a stack overflow if
+    // nPointCount is very large. Instead, an own stack is used. This does not contain points, but
+    // pairs of low and high index of a range in rCandidate. A parallel boolean vector is used to note
+    // whether a point of rCandidate belongs to the output polygon or not.
+    std::vector<bool> bIsKeptVec(nPointCount, false);
+    bIsKeptVec[0] = true;
+    bIsKeptVec[nPointCount - 1] = true;
+    sal_uInt32 nKept = 2;
+    std::stack<std::pair<sal_uInt32, sal_uInt32>> aUnfinishedRangesStack;
+
+    // The RDP algorithm draws a straight line from the first point to the last point of a range.
+    // Then, from the inner points of the range, the point that has the largest distance to the line
+    // is determined. If the distance is greater than the tolerance, this point is kept and the lower
+    // and upper sub-segments of the range are treated in the same way. If the distance is smaller
+    // than the tolerance, none of the inner points will be kept.
+    sal_uInt32 nLowIndex = 0;
+    sal_uInt32 nHighIndex = nPointCount - 1;
+    bool bContinue = true;
+    do
+    {
+        bContinue = false;
+        if (nHighIndex - nLowIndex < 2) // maximal two points, range is finished.
+        {
+            // continue with sibling upper range if any
+            if (!aUnfinishedRangesStack.empty())
+            {
+                std::pair<sal_uInt32, sal_uInt32> aIndexPair = aUnfinishedRangesStack.top();
+                aUnfinishedRangesStack.pop();
+                nLowIndex = aIndexPair.first;
+                nHighIndex = aIndexPair.second;
+                bContinue = true;
+            }
+        }
+        else // the range needs examine the max distance
+        {
+            // Get maximal distance of inner points of the range to the straight line from start to
+            // end point of the range.
+            // For calculation of the distance we use the Hesse normal form of the straight line.
+            B2DPoint aLowPoint = rCandidate.getB2DPoint(nLowIndex);
+            B2DPoint aHighPoint = rCandidate.getB2DPoint(nHighIndex);
+            B2DVector aNormalVec
+                = basegfx::getNormalizedPerpendicular(B2DVector(aHighPoint) - B2DVector(aLowPoint));
+            double fLineOriginDistance = aNormalVec.scalar(B2DVector(aLowPoint));
+            double fMaxDist = 0;
+            sal_uInt32 nMaxPointIndex = nLowIndex;
+            for (sal_uInt32 i = nLowIndex + 1; i < nHighIndex; i++)
+            {
+                double fDistance
+                    = aNormalVec.scalar(B2DVector(rCandidate.getB2DPoint(i))) - fLineOriginDistance;
+                if (std::fabs(fDistance) > fMaxDist)
+                {
+                    fMaxDist = std::fabs(fDistance);
+                    nMaxPointIndex = i;
+                }
+            }
+
+            if (fMaxDist >= fTolerance)
+            {
+                // We need to divide the current range into two sub ranges.
+                bIsKeptVec[nMaxPointIndex] = true;
+                nKept++;
+                // continue with lower sub range and push upper sub range to stack
+                aUnfinishedRangesStack.push(std::make_pair(nMaxPointIndex, nHighIndex));
+                nHighIndex = nMaxPointIndex;
+                bContinue = true;
+            }
+            else
+            {
+                // We do not keep any of the inner points of the current range.
+                // continue with sibling upper range if any
+                if (!aUnfinishedRangesStack.empty())
+                {
+                    std::pair<sal_uInt32, sal_uInt32> aIndexPair = aUnfinishedRangesStack.top();
+                    aUnfinishedRangesStack.pop();
+                    nLowIndex = aIndexPair.first;
+                    nHighIndex = aIndexPair.second;
+                    bContinue = true;
+                }
+            }
+        }
+    } while (bContinue);
+
+    // Put all points which are marked as "keep" into the result polygon
+    B2DPolygon aResultPolygon;
+    aResultPolygon.reserve(nKept);
+    for (sal_uInt32 i = 0; i < nPointCount; i++)
+    {
+        if (bIsKeptVec[i])
+            aResultPolygon.append(rCandidate.getB2DPoint(i));
+    }
+    return aResultPolygon;
+}
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolygontriangulator.cxx b/basegfx/source/polygon/b2dpolygontriangulator.cxx
new file mode 100644
index 0000000000..8742ade70e
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygontriangulator.cxx
@@ -0,0 +1,434 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dpolygontriangulator.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+#include <algorithm>
+
+namespace basegfx
+{
+    namespace
+    {
+        class EdgeEntry
+        {
+            EdgeEntry*                              mpNext;
+            B2DPoint                                maStart;
+            B2DPoint                                maEnd;
+            double                                  mfAtan2;
+
+        public:
+            EdgeEntry(const B2DPoint& rStart, const B2DPoint& rEnd)
+            :   mpNext(nullptr),
+                maStart(rStart),
+                maEnd(rEnd),
+                mfAtan2(0.0)
+            {
+                // make sure edge goes down. If horizontal, let it go to the right (left-handed).
+                bool bSwap(false);
+
+                if(::basegfx::fTools::equal(maStart.getY(), maEnd.getY()))
+                {
+                    if(maStart.getX() > maEnd.getX())
+                    {
+                        bSwap = true;
+                    }
+                }
+                else if(maStart.getY() > maEnd.getY())
+                {
+                    bSwap = true;
+                }
+
+                if(bSwap)
+                {
+                    maStart = rEnd;
+                    maEnd = rStart;
+                }
+
+                mfAtan2 = atan2(maEnd.getY() - maStart.getY(), maEnd.getX() - maStart.getX());
+            }
+
+            bool operator<(const EdgeEntry& rComp) const
+            {
+                if(::basegfx::fTools::equal(maStart.getY(), rComp.maStart.getY()))
+                {
+                    if(::basegfx::fTools::equal(maStart.getX(), rComp.maStart.getX()))
+                    {
+                        // same in x and y -> same start point. Sort emitting vectors from left to right.
+                        return (mfAtan2 > rComp.mfAtan2);
+                    }
+
+                    return (maStart.getX() < rComp.maStart.getX());
+                }
+
+                return (maStart.getY() < rComp.maStart.getY());
+            }
+
+            bool operator==(const EdgeEntry& rComp) const
+            {
+                return (maStart.equal(rComp.maStart) && maEnd.equal(rComp.maEnd));
+            }
+
+            bool operator!=(const EdgeEntry& rComp) const
+            {
+                return !(*this == rComp);
+            }
+
+            const B2DPoint& getStart() const { return maStart; }
+            const B2DPoint& getEnd() const { return maEnd; }
+
+            EdgeEntry* getNext() const { return mpNext; }
+            void setNext(EdgeEntry* pNext) { mpNext = pNext; }
+        };
+
+        typedef std::vector< EdgeEntry > EdgeEntries;
+
+        class Triangulator
+        {
+            EdgeEntry*                                      mpList;
+            EdgeEntries                                     maStartEntries;
+            std::vector< std::unique_ptr<EdgeEntry> >       maNewEdgeEntries;
+            triangulator::B2DTriangleVector                 maResult;
+
+            void handleClosingEdge(const B2DPoint& rStart, const B2DPoint& rEnd);
+            bool CheckPointInTriangle(EdgeEntry* pEdgeA, EdgeEntry const * pEdgeB, const B2DPoint& rTestPoint);
+            void createTriangle(const B2DPoint& rA, const B2DPoint& rB, const B2DPoint& rC);
+
+        public:
+            explicit Triangulator(const B2DPolyPolygon& rCandidate);
+
+            const triangulator::B2DTriangleVector& getResult() const { return maResult; }
+        };
+
+        void Triangulator::handleClosingEdge(const B2DPoint& rStart, const B2DPoint& rEnd)
+        {
+            // create an entry, else the comparison might use the wrong edges
+            EdgeEntry aNew(rStart, rEnd);
+            EdgeEntry* pCurr = mpList;
+            EdgeEntry* pPrev = nullptr;
+
+            while(pCurr
+                && pCurr->getStart().getY() <= aNew.getStart().getY()
+                && *pCurr != aNew)
+            {
+                pPrev = pCurr;
+                pCurr = pCurr->getNext();
+            }
+
+            if(pCurr && *pCurr == aNew)
+            {
+                // found closing edge, remove
+                if(pPrev)
+                {
+                    pPrev->setNext(pCurr->getNext());
+                }
+                else
+                {
+                    mpList = pCurr->getNext();
+                }
+            }
+            else
+            {
+                // insert closing edge
+                EdgeEntry* pNew = new EdgeEntry(aNew);
+                maNewEdgeEntries.emplace_back(pNew);
+                pCurr = mpList;
+                pPrev = nullptr;
+
+                while(pCurr && *pCurr < *pNew)
+                {
+                    pPrev = pCurr;
+                    pCurr = pCurr->getNext();
+                }
+
+                if(pPrev)
+                {
+                    pNew->setNext(pPrev->getNext());
+                    pPrev->setNext(pNew);
+                }
+                else
+                {
+                    pNew->setNext(mpList);
+                    mpList = pNew;
+                }
+            }
+        }
+
+        bool Triangulator::CheckPointInTriangle(EdgeEntry* pEdgeA, EdgeEntry const * pEdgeB, const B2DPoint& rTestPoint)
+        {
+            // inside triangle or on edge?
+            if(!utils::isPointInTriangle(pEdgeA->getStart(), pEdgeA->getEnd(), pEdgeB->getEnd(), rTestPoint, true))
+                return true;
+
+            // but not on point
+            if(!rTestPoint.equal(pEdgeA->getEnd()) && !rTestPoint.equal(pEdgeB->getEnd()))
+            {
+                // found point in triangle -> split triangle inserting two edges
+                EdgeEntry* pStart = new EdgeEntry(pEdgeA->getStart(), rTestPoint);
+                EdgeEntry* pEnd = new EdgeEntry(*pStart);
+                maNewEdgeEntries.emplace_back(pStart);
+                maNewEdgeEntries.emplace_back(pEnd);
+
+                pStart->setNext(pEnd);
+                pEnd->setNext(pEdgeA->getNext());
+                pEdgeA->setNext(pStart);
+
+                return false;
+            }
+
+            return true;
+        }
+
+        void Triangulator::createTriangle(const B2DPoint& rA, const B2DPoint& rB, const B2DPoint& rC)
+        {
+            maResult.emplace_back(
+                rA,
+                rB,
+                rC);
+        }
+
+        // consume as long as there are edges
+        Triangulator::Triangulator(const B2DPolyPolygon& rCandidate)
+        :   mpList(nullptr)
+        {
+            // add all available edges to the single linked local list which will be sorted
+            // by Y,X,atan2 when adding nodes
+            if(rCandidate.count())
+            {
+                for(const auto& rPolygonCandidate : rCandidate)
+                {
+                    const sal_uInt32 nCount {rPolygonCandidate.count()};
+
+                    if(nCount > 2)
+                    {
+                        B2DPoint aPrevPnt(rPolygonCandidate.getB2DPoint(nCount - 1));
+
+                        for(sal_uInt32 b(0); b < nCount; b++)
+                        {
+                            B2DPoint aNextPnt(rPolygonCandidate.getB2DPoint(b));
+
+                            if( !aPrevPnt.equal(aNextPnt) )
+                            {
+                                maStartEntries.emplace_back(aPrevPnt, aNextPnt);
+                            }
+
+                            aPrevPnt = aNextPnt;
+                        }
+                    }
+                }
+
+                if(!maStartEntries.empty())
+                {
+                    // sort initial list
+                    std::sort(maStartEntries.begin(), maStartEntries.end());
+
+                    // insert to own simply linked list
+                    EdgeEntries::iterator aPos(maStartEntries.begin());
+                    mpList = &(*aPos++);
+                    EdgeEntry* pLast = mpList;
+
+                    while(aPos != maStartEntries.end())
+                    {
+                        EdgeEntry* pEntry = &(*aPos++);
+                        pLast->setNext(pEntry);
+                        pLast = pEntry;
+                    }
+                }
+            }
+
+            while(mpList)
+            {
+                if(mpList->getNext() && mpList->getNext()->getStart().equal(mpList->getStart()))
+                {
+                    // next candidate. There are two edges and start point is equal.
+                    // Length is not zero.
+                    EdgeEntry* pEdgeA = mpList;
+                    EdgeEntry* pEdgeB = pEdgeA->getNext();
+
+                    if( pEdgeA->getEnd().equal(pEdgeB->getEnd()) )
+                    {
+                        // start and end equal -> neutral triangle, delete both
+                        mpList = pEdgeB->getNext();
+                    }
+                    else
+                    {
+                        const B2DVector aLeft(pEdgeA->getEnd() - pEdgeA->getStart());
+                        const B2DVector aRight(pEdgeB->getEnd() - pEdgeA->getStart());
+
+                        if(getOrientation(aLeft, aRight) == B2VectorOrientation::Neutral)
+                        {
+                            // edges are parallel and have different length -> neutral triangle,
+                            // delete both edges and handle closing edge
+                            mpList = pEdgeB->getNext();
+                            handleClosingEdge(pEdgeA->getEnd(), pEdgeB->getEnd());
+                        }
+                        else
+                        {
+                            // not parallel, look for points inside
+                            B2DRange aRange(pEdgeA->getStart(), pEdgeA->getEnd());
+                            aRange.expand(pEdgeB->getEnd());
+                            EdgeEntry* pTestEdge = pEdgeB->getNext();
+                            bool bNoPointInTriangle(true);
+
+                            // look for start point in triangle
+                            while(bNoPointInTriangle && pTestEdge)
+                            {
+                                if(aRange.getMaxY() < pTestEdge->getStart().getY())
+                                {
+                                    // edge is below test range and edges are sorted -> stop looking
+                                    break;
+                                }
+                                else
+                                {
+                                    // do not look for edges with same start point, they are sorted and cannot end inside.
+                                    if(!pTestEdge->getStart().equal(pEdgeA->getStart()))
+                                    {
+                                        if(aRange.isInside(pTestEdge->getStart()))
+                                        {
+                                            bNoPointInTriangle = CheckPointInTriangle(pEdgeA, pEdgeB, pTestEdge->getStart());
+                                        }
+                                    }
+                                }
+
+                                // next candidate
+                                pTestEdge = pTestEdge->getNext();
+                            }
+
+                            if(bNoPointInTriangle)
+                            {
+                                // look for end point in triangle
+                                pTestEdge = pEdgeB->getNext();
+
+                                while(bNoPointInTriangle && pTestEdge)
+                                {
+                                    if(aRange.getMaxY() < pTestEdge->getStart().getY())
+                                    {
+                                        // edge is below test range and edges are sorted -> stop looking
+                                        break;
+                                    }
+                                    else
+                                    {
+                                        // do not look for edges with same end point, they are sorted and cannot end inside.
+                                        if(!pTestEdge->getEnd().equal(pEdgeA->getStart()))
+                                        {
+                                            if(aRange.isInside(pTestEdge->getEnd()))
+                                            {
+                                                bNoPointInTriangle = CheckPointInTriangle(pEdgeA, pEdgeB, pTestEdge->getEnd());
+                                            }
+                                        }
+                                    }
+
+                                    // next candidate
+                                    pTestEdge = pTestEdge->getNext();
+                                }
+                            }
+
+                            if(bNoPointInTriangle)
+                            {
+                                // create triangle, remove edges, handle closing edge
+                                mpList = pEdgeB->getNext();
+                                createTriangle(pEdgeA->getStart(), pEdgeB->getEnd(), pEdgeA->getEnd());
+                                handleClosingEdge(pEdgeA->getEnd(), pEdgeB->getEnd());
+                            }
+                        }
+                    }
+                }
+                else
+                {
+                    // only one entry at start point, delete it
+                    mpList = mpList->getNext();
+                }
+            }
+        }
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx::triangulator
+{
+        B2DTriangleVector triangulate(const B2DPolygon& rCandidate)
+        {
+            B2DTriangleVector aRetval;
+
+            // subdivide locally (triangulate does not work with beziers), remove double and neutral points
+            B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? utils::adaptiveSubdivideByAngle(rCandidate) : rCandidate);
+            aCandidate.removeDoublePoints();
+            aCandidate = utils::removeNeutralPoints(aCandidate);
+
+            if(aCandidate.count() == 2)
+            {
+                // candidate IS a triangle, just append
+                aRetval.emplace_back(
+                    aCandidate.getB2DPoint(0),
+                    aCandidate.getB2DPoint(1),
+                    aCandidate.getB2DPoint(2));
+            }
+            else if(aCandidate.count() > 2)
+            {
+                if(utils::isConvex(aCandidate))
+                {
+                    // polygon is convex, just use a triangle fan
+                    utils::addTriangleFan(aCandidate, aRetval);
+                }
+                else
+                {
+                    // polygon is concave.
+                    const B2DPolyPolygon aCandPolyPoly(aCandidate);
+                    Triangulator aTriangulator(aCandPolyPoly);
+
+                    aRetval = aTriangulator.getResult();
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DTriangleVector triangulate(const B2DPolyPolygon& rCandidate)
+        {
+            B2DTriangleVector aRetval;
+
+            // subdivide locally (triangulate does not work with beziers)
+            B2DPolyPolygon aCandidate(rCandidate.areControlPointsUsed() ? utils::adaptiveSubdivideByAngle(rCandidate) : rCandidate);
+
+            if(aCandidate.count() == 1)
+            {
+                // single polygon -> single polygon triangulation
+                const B2DPolygon& aSinglePolygon(aCandidate.getB2DPolygon(0));
+
+                aRetval = triangulate(aSinglePolygon);
+            }
+            else
+            {
+                Triangulator aTriangulator(aCandidate);
+
+                aRetval = aTriangulator.getResult();
+            }
+
+            return aRetval;
+        }
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolypolygon.cxx b/basegfx/source/polygon/b2dpolypolygon.cxx
new file mode 100644
index 0000000000..547634dc4d
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolypolygon.cxx
@@ -0,0 +1,432 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <sal/config.h>
+
+#include <cassert>
+#include <utility>
+
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/utils/systemdependentdata.hxx>
+
+namespace basegfx
+{
+
+class ImplB2DPolyPolygon
+{
+    basegfx::B2DPolygonVector                               maPolygons;
+    // we do not want to 'modify' the ImplB2DPolyPolygon,
+    // but add buffered data that is valid for all referencing instances
+    mutable std::unique_ptr<basegfx::SystemDependentDataHolder> mpSystemDependentDataHolder;
+
+public:
+    ImplB2DPolyPolygon()
+    {
+    }
+
+    explicit ImplB2DPolyPolygon(const ImplB2DPolyPolygon& rSource)
+    :   maPolygons(rSource.maPolygons)
+    {
+    }
+
+    explicit ImplB2DPolyPolygon(const basegfx::B2DPolygon& rToBeCopied)
+    :   maPolygons(1,rToBeCopied)
+    {
+    }
+
+    ImplB2DPolyPolygon& operator=(const ImplB2DPolyPolygon& rSource)
+    {
+        if (this != &rSource)
+        {
+            maPolygons = rSource.maPolygons;
+            mpSystemDependentDataHolder.reset();
+        }
+
+        return *this;
+    }
+
+    void addOrReplaceSystemDependentData(basegfx::SystemDependentData_SharedPtr& rData) const
+    {
+        if(!mpSystemDependentDataHolder)
+        {
+            mpSystemDependentDataHolder.reset(new basegfx::SystemDependentDataHolder());
+        }
+
+        mpSystemDependentDataHolder->addOrReplaceSystemDependentData(rData);
+    }
+
+    basegfx::SystemDependentData_SharedPtr getSystemDependentData(size_t hash_code) const
+    {
+        if(!mpSystemDependentDataHolder)
+        {
+            return basegfx::SystemDependentData_SharedPtr();
+        }
+
+        return mpSystemDependentDataHolder->getSystemDependentData(hash_code);
+    }
+
+    bool operator==(const ImplB2DPolyPolygon& rPolygonList) const
+    {
+        return maPolygons == rPolygonList.maPolygons;
+    }
+
+    const basegfx::B2DPolygon& getB2DPolygon(sal_uInt32 nIndex) const
+    {
+        assert(nIndex < maPolygons.size());
+        return maPolygons[nIndex];
+    }
+
+    void setB2DPolygon(sal_uInt32 nIndex, const basegfx::B2DPolygon& rPolygon)
+    {
+        assert(nIndex < maPolygons.size());
+        maPolygons[nIndex] = rPolygon;
+    }
+
+    void insert(sal_uInt32 nIndex, const basegfx::B2DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex <= maPolygons.size());
+        // add nCount copies of rPolygon
+        maPolygons.insert(maPolygons.begin() + nIndex, nCount, rPolygon);
+    }
+
+    void append(const basegfx::B2DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        insert(maPolygons.size(), rPolygon, nCount);
+    }
+
+    void reserve(sal_uInt32 nCount)
+    {
+        maPolygons.reserve(nCount);
+    }
+
+    void insert(sal_uInt32 nIndex, const basegfx::B2DPolyPolygon& rPolyPolygon)
+    {
+        assert(nIndex <= maPolygons.size());
+        // add nCount polygons from rPolyPolygon
+        maPolygons.insert(maPolygons.begin() + nIndex, rPolyPolygon.begin(), rPolyPolygon.end());
+    }
+
+    void append(const basegfx::B2DPolyPolygon& rPolyPolygon)
+    {
+        insert(maPolygons.size(), rPolyPolygon);
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        assert(nCount > 0);
+        assert(nIndex + nCount <= maPolygons.size());
+        // remove polygon data
+        auto aStart(maPolygons.begin() + nIndex);
+        auto aEnd(aStart + nCount);
+
+        maPolygons.erase(aStart, aEnd);
+    }
+
+    sal_uInt32 count() const
+    {
+        return maPolygons.size();
+    }
+
+    void setClosed(bool bNew)
+    {
+        for(basegfx::B2DPolygon & rPolygon : maPolygons)
+        {
+            rPolygon.setClosed(bNew);
+        }
+    }
+
+    void flip()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.flip();
+    }
+
+    void removeDoublePoints()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.removeDoublePoints();
+    }
+
+    void transform(const basegfx::B2DHomMatrix& rMatrix)
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.transform(rMatrix);
+    }
+
+    void makeUnique()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.makeUnique();
+    }
+
+    const basegfx::B2DPolygon* begin() const
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data();
+    }
+
+    const basegfx::B2DPolygon* end() const
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data() + maPolygons.size();
+    }
+
+    basegfx::B2DPolygon* begin()
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data();
+    }
+
+    basegfx::B2DPolygon* end()
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data() + maPolygons.size();
+    }
+};
+
+    B2DPolyPolygon::B2DPolyPolygon() = default;
+
+    B2DPolyPolygon::B2DPolyPolygon(const B2DPolyPolygon&) = default;
+
+    B2DPolyPolygon::B2DPolyPolygon(B2DPolyPolygon&&) = default;
+
+    B2DPolyPolygon::B2DPolyPolygon(const B2DPolygon& rPolygon) :
+        mpPolyPolygon( ImplB2DPolyPolygon(rPolygon) )
+    {
+    }
+
+    B2DPolyPolygon::~B2DPolyPolygon() = default;
+
+    B2DPolyPolygon& B2DPolyPolygon::operator=(const B2DPolyPolygon&) = default;
+
+    B2DPolyPolygon& B2DPolyPolygon::operator=(B2DPolyPolygon&&) = default;
+
+    void B2DPolyPolygon::makeUnique()
+    {
+        mpPolyPolygon->makeUnique(); // non-const cow_wrapper::operator-> calls make_unique
+    }
+
+    bool B2DPolyPolygon::operator==(const B2DPolyPolygon& rPolyPolygon) const
+    {
+        if(mpPolyPolygon.same_object(rPolyPolygon.mpPolyPolygon))
+            return true;
+
+        return ((*mpPolyPolygon) == (*rPolyPolygon.mpPolyPolygon));
+    }
+
+    bool B2DPolyPolygon::operator!=(const B2DPolyPolygon& rPolyPolygon) const
+    {
+        return !((*this) == rPolyPolygon);
+    }
+
+    sal_uInt32 B2DPolyPolygon::count() const
+    {
+        return mpPolyPolygon->count();
+    }
+
+    B2DPolygon const & B2DPolyPolygon::getB2DPolygon(sal_uInt32 nIndex) const
+    {
+        return mpPolyPolygon->getB2DPolygon(nIndex);
+    }
+
+    void B2DPolyPolygon::setB2DPolygon(sal_uInt32 nIndex, const B2DPolygon& rPolygon)
+    {
+        if(getB2DPolygon(nIndex) != rPolygon)
+            mpPolyPolygon->setB2DPolygon(nIndex, rPolygon);
+    }
+
+    bool B2DPolyPolygon::areControlPointsUsed() const
+    {
+        for(sal_uInt32 a(0); a < count(); a++)
+        {
+            if(getB2DPolygon(a).areControlPointsUsed())
+            {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    void B2DPolyPolygon::insert(sal_uInt32 nIndex, const B2DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolyPolygon->insert(nIndex, rPolygon, nCount);
+    }
+
+    void B2DPolyPolygon::append(const B2DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolyPolygon->append(rPolygon, nCount);
+    }
+
+    void B2DPolyPolygon::reserve(sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolyPolygon->reserve(nCount);
+    }
+
+    B2DPolyPolygon B2DPolyPolygon::getDefaultAdaptiveSubdivision() const
+    {
+        B2DPolyPolygon aRetval;
+        if (count())
+        {
+            ImplB2DPolyPolygon& dest = *aRetval.mpPolyPolygon;
+            dest.reserve(count());
+
+            for (sal_uInt32 a(0); a < count(); a++)
+            {
+                dest.append(getB2DPolygon(a).getDefaultAdaptiveSubdivision(), 1);
+            }
+        }
+
+        return aRetval;
+    }
+
+    B2DRange B2DPolyPolygon::getB2DRange() const
+    {
+        B2DRange aRetval;
+
+        for(sal_uInt32 a(0); a < count(); a++)
+        {
+            aRetval.expand(getB2DPolygon(a).getB2DRange());
+        }
+
+        return aRetval;
+    }
+
+    void B2DPolyPolygon::insert(sal_uInt32 nIndex, const B2DPolyPolygon& rPolyPolygon)
+    {
+        if(rPolyPolygon.count())
+            mpPolyPolygon->insert(nIndex, rPolyPolygon);
+    }
+
+    void B2DPolyPolygon::append(const B2DPolyPolygon& rPolyPolygon)
+    {
+        if(rPolyPolygon.count())
+            mpPolyPolygon->append(rPolyPolygon);
+    }
+
+    void B2DPolyPolygon::remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolyPolygon->remove(nIndex, nCount);
+    }
+
+    void B2DPolyPolygon::clear()
+    {
+        *mpPolyPolygon = ImplB2DPolyPolygon();
+    }
+
+    bool B2DPolyPolygon::isClosed() const
+    {
+        // PolyPOlygon is closed when all contained Polygons are closed or
+        // no Polygon exists.
+        for(sal_uInt32 a(0); a < count(); a++)
+        {
+            if(!getB2DPolygon(a).isClosed())
+                return false;
+        }
+
+        return true;
+    }
+
+    void B2DPolyPolygon::setClosed(bool bNew)
+    {
+        if(bNew != isClosed())
+            mpPolyPolygon->setClosed(bNew);
+    }
+
+    void B2DPolyPolygon::flip()
+    {
+        if(count())
+        {
+            mpPolyPolygon->flip();
+        }
+    }
+
+    bool B2DPolyPolygon::hasDoublePoints() const
+    {
+        for(sal_uInt32 a(0); a < count(); a++)
+        {
+            if(getB2DPolygon(a).hasDoublePoints())
+                return true;
+        }
+
+        return false;
+    }
+
+    void B2DPolyPolygon::removeDoublePoints()
+    {
+        if(hasDoublePoints())
+            mpPolyPolygon->removeDoublePoints();
+    }
+
+    void B2DPolyPolygon::transform(const B2DHomMatrix& rMatrix)
+    {
+        if(count() && !rMatrix.isIdentity())
+        {
+            mpPolyPolygon->transform(rMatrix);
+        }
+    }
+
+    const B2DPolygon* B2DPolyPolygon::begin() const
+    {
+        return mpPolyPolygon->begin();
+    }
+
+    const B2DPolygon* B2DPolyPolygon::end() const
+    {
+        return mpPolyPolygon->end();
+    }
+
+    B2DPolygon* B2DPolyPolygon::begin()
+    {
+        return mpPolyPolygon->begin();
+    }
+
+    B2DPolygon* B2DPolyPolygon::end()
+    {
+        return mpPolyPolygon->end();
+    }
+
+    void B2DPolyPolygon::addOrReplaceSystemDependentDataInternal(SystemDependentData_SharedPtr& rData) const
+    {
+        mpPolyPolygon->addOrReplaceSystemDependentData(rData);
+    }
+
+    SystemDependentData_SharedPtr B2DPolyPolygon::getSystemDependantDataInternal(size_t hash_code) const
+    {
+        return mpPolyPolygon->getSystemDependentData(hash_code);
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolypolygoncutter.cxx b/basegfx/source/polygon/b2dpolypolygoncutter.cxx
new file mode 100644
index 0000000000..42cfed615f
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolypolygoncutter.cxx
@@ -0,0 +1,1135 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <sal/log.hxx>
+#include <utility>
+#include <vector>
+#include <algorithm>
+#include <numeric>
+
+namespace basegfx
+{
+    namespace
+    {
+
+        struct StripHelper
+        {
+            B2DRange                                maRange;
+            sal_Int32                               mnDepth;
+            B2VectorOrientation                     meOrinetation;
+        };
+
+        struct PN
+        {
+        public:
+            B2DPoint                maPoint;
+            sal_uInt32              mnI;
+            sal_uInt32              mnIP;
+            sal_uInt32              mnIN;
+        };
+
+        struct VN
+        {
+        public:
+            B2DVector               maPrev;
+            B2DVector               maNext;
+
+            // to have the correct curve segments in the crossover checks,
+            // it is necessary to keep the original next vectors, too. Else,
+            // it may happen to use an already switched next vector which
+            // would interpolate the wrong comparison point
+            B2DVector               maOriginalNext;
+        };
+
+        struct SN
+        {
+        public:
+            PN*                     mpPN;
+
+            bool operator<(const SN& rComp) const
+            {
+                if(fTools::equal(mpPN->maPoint.getX(), rComp.mpPN->maPoint.getX()))
+                {
+                    if(fTools::equal(mpPN->maPoint.getY(), rComp.mpPN->maPoint.getY()))
+                    {
+                        return (mpPN->mnI < rComp.mpPN->mnI);
+                    }
+                    else
+                    {
+                        return fTools::less(mpPN->maPoint.getY(), rComp.mpPN->maPoint.getY());
+                    }
+                }
+                else
+                {
+                    return fTools::less(mpPN->maPoint.getX(), rComp.mpPN->maPoint.getX());
+                }
+            }
+        };
+
+        typedef std::vector< PN > PNV;
+        typedef std::vector< VN > VNV;
+        typedef std::vector< SN > SNV;
+        typedef std::pair< basegfx::B2DPoint /*orig*/, basegfx::B2DPoint /*repl*/ > CorrectionPair;
+
+        class solver
+        {
+        private:
+            const B2DPolyPolygon    maOriginal;
+            PNV                     maPNV;
+            VNV                     maVNV;
+            SNV                     maSNV;
+            std::vector< CorrectionPair >
+                                    maCorrectionTable;
+
+            bool                    mbIsCurve : 1;
+            bool                    mbChanged : 1;
+
+            void impAddPolygon(const sal_uInt32 aPos, const B2DPolygon& rGeometry)
+            {
+                const sal_uInt32 nCount(rGeometry.count());
+                PN aNewPN;
+                VN aNewVN;
+                SN aNewSN;
+
+                for(sal_uInt32 a(0); a < nCount; a++)
+                {
+                    const B2DPoint aPoint(rGeometry.getB2DPoint(a));
+                    aNewPN.maPoint = aPoint;
+                    aNewPN.mnI = aPos + a;
+                    aNewPN.mnIP = aPos + ((a != 0) ? a - 1 : nCount - 1);
+                    aNewPN.mnIN = aPos + ((a + 1 == nCount) ? 0 : a + 1);
+                    maPNV.push_back(aNewPN);
+
+                    if(mbIsCurve)
+                    {
+                        aNewVN.maPrev = rGeometry.getPrevControlPoint(a) - aPoint;
+                        aNewVN.maNext = rGeometry.getNextControlPoint(a) - aPoint;
+                        aNewVN.maOriginalNext = aNewVN.maNext;
+                        maVNV.push_back(aNewVN);
+                    }
+
+                    aNewSN.mpPN = &maPNV[maPNV.size() - 1];
+                    maSNV.push_back(aNewSN);
+                }
+            }
+
+            static bool impLeftOfEdges(const B2DVector& rVecA, const B2DVector& rVecB, const B2DVector& rTest)
+            {
+                // tests if rTest is left of both directed line segments along the line -rVecA, rVecB. Test is
+                // with border.
+                if(rVecA.cross(rVecB) > 0.0)
+                {
+                    // b is left turn seen from a, test if Test is left of both and so inside (left is seen as inside)
+                    const bool bBoolA(fTools::moreOrEqual(rVecA.cross(rTest), 0.0));
+                    const bool bBoolB(fTools::lessOrEqual(rVecB.cross(rTest), 0.0));
+
+                    return (bBoolA && bBoolB);
+                }
+                else
+                {
+                    // b is right turn seen from a, test if Test is right of both and so outside (left is seen as inside)
+                    const bool bBoolA(fTools::lessOrEqual(rVecA.cross(rTest), 0.0));
+                    const bool bBoolB(fTools::moreOrEqual(rVecB.cross(rTest), 0.0));
+
+                    return (!(bBoolA && bBoolB));
+                }
+            }
+
+            void impSwitchNext(PN& rPNa, PN& rPNb)
+            {
+                std::swap(rPNa.mnIN, rPNb.mnIN);
+
+                if(mbIsCurve)
+                {
+                    VN& rVNa = maVNV[rPNa.mnI];
+                    VN& rVNb = maVNV[rPNb.mnI];
+
+                    std::swap(rVNa.maNext, rVNb.maNext);
+                }
+
+                if(!mbChanged)
+                {
+                    mbChanged = true;
+                }
+            }
+
+            B2DCubicBezier createSegment(const PN& rPN, bool bPrev) const
+            {
+                const B2DPoint& rStart(rPN.maPoint);
+                const B2DPoint& rEnd(maPNV[bPrev ? rPN.mnIP : rPN.mnIN].maPoint);
+                const B2DVector& rCPA(bPrev ? maVNV[rPN.mnI].maPrev : maVNV[rPN.mnI].maNext);
+                // Use maOriginalNext, not maNext to create the original (yet unchanged)
+                // curve segment. Otherwise, this segment would NOT ne correct.
+                const B2DVector& rCPB(bPrev ? maVNV[maPNV[rPN.mnIP].mnI].maOriginalNext : maVNV[maPNV[rPN.mnIN].mnI].maPrev);
+
+                return B2DCubicBezier(rStart, rStart + rCPA, rEnd + rCPB, rEnd);
+            }
+
+            void impHandleCommon(PN& rPNa, PN& rPNb)
+            {
+                if(mbIsCurve)
+                {
+                    const B2DCubicBezier aNextA(createSegment(rPNa, false));
+                    const B2DCubicBezier aPrevA(createSegment(rPNa, true));
+
+                    if(aNextA.equal(aPrevA))
+                    {
+                        // deadend on A (identical edge)
+                        return;
+                    }
+
+                    const B2DCubicBezier aNextB(createSegment(rPNb, false));
+                    const B2DCubicBezier aPrevB(createSegment(rPNb, true));
+
+                    if(aNextB.equal(aPrevB))
+                    {
+                        // deadend on B (identical edge)
+                        return;
+                    }
+
+                    if(aPrevA.equal(aPrevB))
+                    {
+                        // common edge in same direction
+                        return;
+                    }
+                    else if(aPrevA.equal(aNextB))
+                    {
+                        // common edge in opposite direction
+                        if(aNextA.equal(aPrevB))
+                        {
+                            // common edge in opposite direction continues
+                            return;
+                        }
+                        else
+                        {
+                            // common edge in opposite direction leave
+                            impSwitchNext(rPNa, rPNb);
+                        }
+                    }
+                    else if(aNextA.equal(aNextB))
+                    {
+                        // common edge in same direction enter
+                        // search leave edge
+                        PN* pPNa2 = &maPNV[rPNa.mnIN];
+                        PN* pPNb2 = &maPNV[rPNb.mnIN];
+                        bool bOnEdge(true);
+
+                        do
+                        {
+                            const B2DCubicBezier aNextA2(createSegment(*pPNa2, false));
+                            const B2DCubicBezier aNextB2(createSegment(*pPNb2, false));
+
+                            if(aNextA2.equal(aNextB2))
+                            {
+                                pPNa2 = &maPNV[pPNa2->mnIN];
+                                pPNb2 = &maPNV[pPNb2->mnIN];
+                            }
+                            else
+                            {
+                                bOnEdge = false;
+                            }
+                        }
+                        while(bOnEdge && pPNa2 != &rPNa && pPNb2 != &rPNb);
+
+                        if(bOnEdge)
+                        {
+                            // loop over two identical polygon paths
+                            return;
+                        }
+                        else
+                        {
+                            // enter at rPNa, rPNb; leave at pPNa2, pPNb2. No common edges
+                            // at enter/leave. Check for crossover.
+                            const B2DVector aPrevCA(aPrevA.interpolatePoint(0.5) - aPrevA.getStartPoint());
+                            const B2DVector aNextCA(aNextA.interpolatePoint(0.5) - aNextA.getStartPoint());
+                            const B2DVector aPrevCB(aPrevB.interpolatePoint(0.5) - aPrevB.getStartPoint());
+                            const bool bEnter(impLeftOfEdges(aPrevCA, aNextCA, aPrevCB));
+
+                            const B2DCubicBezier aNextA2(createSegment(*pPNa2, false));
+                            const B2DCubicBezier aPrevA2(createSegment(*pPNa2, true));
+                            const B2DCubicBezier aNextB2(createSegment(*pPNb2, false));
+                            const B2DVector aPrevCA2(aPrevA2.interpolatePoint(0.5) - aPrevA2.getStartPoint());
+                            const B2DVector aNextCA2(aNextA2.interpolatePoint(0.5) - aNextA2.getStartPoint());
+                            const B2DVector aNextCB2(aNextB2.interpolatePoint(0.5) - aNextB2.getStartPoint());
+                            const bool bLeave(impLeftOfEdges(aPrevCA2, aNextCA2, aNextCB2));
+
+                            if(bEnter != bLeave)
+                            {
+                                // crossover
+                                impSwitchNext(rPNa, rPNb);
+                            }
+                        }
+                    }
+                    else if(aNextA.equal(aPrevB))
+                    {
+                        // common edge in opposite direction enter
+                        impSwitchNext(rPNa, rPNb);
+                    }
+                    else
+                    {
+                        // no common edges, check for crossover
+                        const B2DVector aPrevCA(aPrevA.interpolatePoint(0.5) - aPrevA.getStartPoint());
+                        const B2DVector aNextCA(aNextA.interpolatePoint(0.5) - aNextA.getStartPoint());
+                        const B2DVector aPrevCB(aPrevB.interpolatePoint(0.5) - aPrevB.getStartPoint());
+                        const B2DVector aNextCB(aNextB.interpolatePoint(0.5) - aNextB.getStartPoint());
+
+                        const bool bEnter(impLeftOfEdges(aPrevCA, aNextCA, aPrevCB));
+                        const bool bLeave(impLeftOfEdges(aPrevCA, aNextCA, aNextCB));
+
+                        if(bEnter != bLeave)
+                        {
+                            // crossover
+                            impSwitchNext(rPNa, rPNb);
+                        }
+                    }
+                }
+                else
+                {
+                    const B2DPoint& rNextA(maPNV[rPNa.mnIN].maPoint);
+                    const B2DPoint& rPrevA(maPNV[rPNa.mnIP].maPoint);
+
+                    if(rNextA.equal(rPrevA))
+                    {
+                        // deadend on A
+                        return;
+                    }
+
+                    const B2DPoint& rNextB(maPNV[rPNb.mnIN].maPoint);
+                    const B2DPoint& rPrevB(maPNV[rPNb.mnIP].maPoint);
+
+                    if(rNextB.equal(rPrevB))
+                    {
+                        // deadend on B
+                        return;
+                    }
+
+                    if(rPrevA.equal(rPrevB))
+                    {
+                        // common edge in same direction
+                        return;
+                    }
+                    else if(rPrevA.equal(rNextB))
+                    {
+                        // common edge in opposite direction
+                        if(rNextA.equal(rPrevB))
+                        {
+                            // common edge in opposite direction continues
+                            return;
+                        }
+                        else
+                        {
+                            // common edge in opposite direction leave
+                            impSwitchNext(rPNa, rPNb);
+                        }
+                    }
+                    else if(rNextA.equal(rNextB))
+                    {
+                        // common edge in same direction enter
+                        // search leave edge
+                        PN* pPNa2 = &maPNV[rPNa.mnIN];
+                        PN* pPNb2 = &maPNV[rPNb.mnIN];
+                        bool bOnEdge(true);
+
+                        do
+                        {
+                            const B2DPoint& rNextA2(maPNV[pPNa2->mnIN].maPoint);
+                            const B2DPoint& rNextB2(maPNV[pPNb2->mnIN].maPoint);
+
+                            if(rNextA2.equal(rNextB2))
+                            {
+                                pPNa2 = &maPNV[pPNa2->mnIN];
+                                pPNb2 = &maPNV[pPNb2->mnIN];
+                            }
+                            else
+                            {
+                                bOnEdge = false;
+                            }
+                        }
+                        while(bOnEdge && pPNa2 != &rPNa && pPNb2 != &rPNb);
+
+                        if(bOnEdge)
+                        {
+                            // loop over two identical polygon paths
+                            return;
+                        }
+                        else
+                        {
+                            // enter at rPNa, rPNb; leave at pPNa2, pPNb2. No common edges
+                            // at enter/leave. Check for crossover.
+                            const B2DPoint& aPointE(rPNa.maPoint);
+                            const B2DVector aPrevAE(rPrevA - aPointE);
+                            const B2DVector aNextAE(rNextA - aPointE);
+                            const B2DVector aPrevBE(rPrevB - aPointE);
+
+                            const B2DPoint& aPointL(pPNa2->maPoint);
+                            const B2DVector aPrevAL(maPNV[pPNa2->mnIP].maPoint - aPointL);
+                            const B2DVector aNextAL(maPNV[pPNa2->mnIN].maPoint - aPointL);
+                            const B2DVector aNextBL(maPNV[pPNb2->mnIN].maPoint - aPointL);
+
+                            const bool bEnter(impLeftOfEdges(aPrevAE, aNextAE, aPrevBE));
+                            const bool bLeave(impLeftOfEdges(aPrevAL, aNextAL, aNextBL));
+
+                            if(bEnter != bLeave)
+                            {
+                                // crossover; switch start or end
+                                impSwitchNext(rPNa, rPNb);
+                            }
+                        }
+                    }
+                    else if(rNextA.equal(rPrevB))
+                    {
+                        // common edge in opposite direction enter
+                        impSwitchNext(rPNa, rPNb);
+                    }
+                    else
+                    {
+                        // no common edges, check for crossover
+                        const B2DPoint& aPoint(rPNa.maPoint);
+                        const B2DVector aPrevA(rPrevA - aPoint);
+                        const B2DVector aNextA(rNextA - aPoint);
+                        const B2DVector aPrevB(rPrevB - aPoint);
+                        const B2DVector aNextB(rNextB - aPoint);
+
+                        const bool bEnter(impLeftOfEdges(aPrevA, aNextA, aPrevB));
+                        const bool bLeave(impLeftOfEdges(aPrevA, aNextA, aNextB));
+
+                        if(bEnter != bLeave)
+                        {
+                            // crossover
+                            impSwitchNext(rPNa, rPNb);
+                        }
+                    }
+                }
+            }
+
+            void impSolve()
+            {
+                // sort by point to identify common nodes easier
+                std::sort(maSNV.begin(), maSNV.end());
+
+                // handle common nodes
+                const sal_uInt32 nNodeCount(maSNV.size());
+                sal_uInt32 a(0);
+
+                // snap unsharp-equal points
+                if(nNodeCount)
+                {
+                    basegfx::B2DPoint* pLast(&maSNV[0].mpPN->maPoint);
+
+                    for(const auto& rSN : maSNV)
+                    {
+                        basegfx::B2DPoint* pCurrent(&rSN.mpPN->maPoint);
+
+                        if(pLast->equal(*pCurrent) && (pLast->getX() != pCurrent->getX() || pLast->getY() != pCurrent->getY()))
+                        {
+                            const basegfx::B2DPoint aMiddle((*pLast + *pCurrent) * 0.5);
+
+                            if(pLast->getX() != aMiddle.getX() || pLast->getY() != aMiddle.getY())
+                            {
+                                maCorrectionTable.emplace_back(*pLast, aMiddle);
+                                *pLast = aMiddle;
+                            }
+
+                            if(pCurrent->getX() != aMiddle.getX() || pCurrent->getY() != aMiddle.getY())
+                            {
+                                maCorrectionTable.emplace_back(*pCurrent, aMiddle);
+                                *pCurrent = aMiddle;
+                            }
+                        }
+
+                        pLast = pCurrent;
+                    }
+                }
+
+                for(a = 0; a < nNodeCount - 1; a++)
+                {
+                    // test a before using it, not after. Also use nPointCount instead of aSortNodes.size()
+                    PN& rPNb = *(maSNV[a].mpPN);
+
+                    for(sal_uInt32 b(a + 1); b < nNodeCount && rPNb.maPoint.equal(maSNV[b].mpPN->maPoint); b++)
+                    {
+                        impHandleCommon(rPNb, *maSNV[b].mpPN);
+                    }
+                }
+            }
+
+        public:
+            explicit solver(const B2DPolygon& rOriginal)
+            :   maOriginal(B2DPolyPolygon(rOriginal)),
+                mbIsCurve(false),
+                mbChanged(false)
+            {
+                const sal_uInt32 nOriginalCount(rOriginal.count());
+
+                if(!nOriginalCount)
+                    return;
+
+                B2DPolygon aGeometry(utils::addPointsAtCutsAndTouches(rOriginal));
+                aGeometry.removeDoublePoints();
+                aGeometry = utils::simplifyCurveSegments(aGeometry);
+                mbIsCurve = aGeometry.areControlPointsUsed();
+
+                const sal_uInt32 nPointCount(aGeometry.count());
+
+                // If it's not a bezier polygon, at least four points are needed to create
+                // a self-intersection. If it's a bezier polygon, the minimum point number
+                // is two, since with a single point You get a curve, but no self-intersection
+                if(!(nPointCount > 3 || (nPointCount > 1 && mbIsCurve)))
+                    return;
+
+                // reserve space in point, control and sort vector.
+                maSNV.reserve(nPointCount);
+                maPNV.reserve(nPointCount);
+                maVNV.reserve(mbIsCurve ? nPointCount : 0);
+
+                // fill data
+                impAddPolygon(0, aGeometry);
+
+                // solve common nodes
+                impSolve();
+            }
+
+            explicit solver(B2DPolyPolygon aOriginal, size_t* pPointLimit = nullptr)
+            :   maOriginal(std::move(aOriginal)),
+                mbIsCurve(false),
+                mbChanged(false)
+            {
+                sal_uInt32 nOriginalCount(maOriginal.count());
+
+                if(!nOriginalCount)
+                    return;
+
+                B2DPolyPolygon aGeometry(utils::addPointsAtCutsAndTouches(maOriginal, pPointLimit));
+                aGeometry.removeDoublePoints();
+                aGeometry = utils::simplifyCurveSegments(aGeometry);
+                mbIsCurve = aGeometry.areControlPointsUsed();
+                nOriginalCount = aGeometry.count();
+
+                if(!nOriginalCount)
+                    return;
+
+                // If it's not a bezier curve, at least three points would be needed to have a
+                // topological relevant (not empty) polygon. Since it's not known here if trivial
+                // edges (dead ends) will be kept or sorted out, add non-bezier polygons with
+                // more than one point.
+                // For bezier curves, the minimum for defining an area is also one.
+                sal_uInt32 nPointCount = std::accumulate( aGeometry.begin(), aGeometry.end(), sal_uInt32(0),
+                    [](sal_uInt32 a, const basegfx::B2DPolygon& b){return a + b.count();});
+
+                if(!nPointCount)
+                    return;
+
+                // reserve space in point, control and sort vector.
+                maSNV.reserve(nPointCount);
+                maPNV.reserve(nPointCount);
+                maVNV.reserve(mbIsCurve ? nPointCount : 0);
+
+                // fill data
+                sal_uInt32 nInsertIndex(0);
+
+                for(const auto& rCandidate : aGeometry )
+                {
+                    const sal_uInt32 nCandCount(rCandidate.count());
+
+                    // use same condition as above, the data vector is
+                    // pre-allocated
+                    if(nCandCount)
+                    {
+                        impAddPolygon(nInsertIndex, rCandidate);
+                        nInsertIndex += nCandCount;
+                    }
+                }
+
+                // solve common nodes
+                impSolve();
+            }
+
+            B2DPolyPolygon getB2DPolyPolygon()
+            {
+                if(mbChanged)
+                {
+                    B2DPolyPolygon aRetval;
+                    const sal_uInt32 nCount(maPNV.size());
+                    sal_uInt32 nCountdown(nCount);
+
+                    for(sal_uInt32 a(0); nCountdown && a < nCount; a++)
+                    {
+                        PN& rPN = maPNV[a];
+
+                        if(rPN.mnI != SAL_MAX_UINT32)
+                        {
+                            // unused node, start new part polygon
+                            B2DPolygon aNewPart;
+                            PN* pPNCurr = &rPN;
+
+                            do
+                            {
+                                const B2DPoint& rPoint = pPNCurr->maPoint;
+                                aNewPart.append(rPoint);
+
+                                if(mbIsCurve)
+                                {
+                                    const VN& rVNCurr = maVNV[pPNCurr->mnI];
+
+                                    if(!rVNCurr.maPrev.equalZero())
+                                    {
+                                        aNewPart.setPrevControlPoint(aNewPart.count() - 1, rPoint + rVNCurr.maPrev);
+                                    }
+
+                                    if(!rVNCurr.maNext.equalZero())
+                                    {
+                                        aNewPart.setNextControlPoint(aNewPart.count() - 1, rPoint + rVNCurr.maNext);
+                                    }
+                                }
+
+                                pPNCurr->mnI = SAL_MAX_UINT32;
+                                nCountdown--;
+                                pPNCurr = &(maPNV[pPNCurr->mnIN]);
+                            }
+                            while(pPNCurr != &rPN && pPNCurr->mnI != SAL_MAX_UINT32);
+
+                            // close and add
+                            aNewPart.setClosed(true);
+                            aRetval.append(aNewPart);
+                        }
+                    }
+
+                    return aRetval;
+                }
+                else
+                {
+                    const sal_uInt32 nCorrectionSize(maCorrectionTable.size());
+
+                    // no change, return original
+                    if(!nCorrectionSize)
+                    {
+                        return maOriginal;
+                    }
+
+                    // apply coordinate corrections to ensure inside/outside correctness after solving
+                    const sal_uInt32 nPolygonCount(maOriginal.count());
+                    basegfx::B2DPolyPolygon aRetval(maOriginal);
+
+                    for(sal_uInt32 a(0); a < nPolygonCount; a++)
+                    {
+                        basegfx::B2DPolygon aTemp(aRetval.getB2DPolygon(a));
+                        const sal_uInt32 nPointCount(aTemp.count());
+                        bool bChanged(false);
+
+                        for(sal_uInt32 b(0); b < nPointCount; b++)
+                        {
+                            const basegfx::B2DPoint aCandidate(aTemp.getB2DPoint(b));
+
+                            for(sal_uInt32 c(0); c < nCorrectionSize; c++)
+                            {
+                                if(maCorrectionTable[c].first.getX() == aCandidate.getX() && maCorrectionTable[c].first.getY() == aCandidate.getY())
+                                {
+                                    aTemp.setB2DPoint(b, maCorrectionTable[c].second);
+                                    bChanged = true;
+                                }
+                            }
+                        }
+
+                        if(bChanged)
+                        {
+                            aRetval.setB2DPolygon(a, aTemp);
+                        }
+                    }
+
+                    return aRetval;
+                }
+            }
+        };
+
+    } // end of anonymous namespace
+} // end of namespace basegfx
+
+namespace basegfx::utils
+{
+
+        B2DPolyPolygon solveCrossovers(const B2DPolyPolygon& rCandidate, size_t* pPointLimit)
+        {
+            if(rCandidate.count() > 0)
+            {
+                solver aSolver(rCandidate, pPointLimit);
+                return aSolver.getB2DPolyPolygon();
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolyPolygon solveCrossovers(const B2DPolygon& rCandidate)
+        {
+            solver aSolver(rCandidate);
+            return aSolver.getB2DPolyPolygon();
+        }
+
+        B2DPolyPolygon stripNeutralPolygons(const B2DPolyPolygon& rCandidate)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(const auto& rPolygon : rCandidate)
+            {
+                if(utils::getOrientation(rPolygon) != B2VectorOrientation::Neutral)
+                {
+                    aRetval.append(rPolygon);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon createNonzeroConform(const B2DPolyPolygon& rCandidate)
+        {
+            if (rCandidate.count() > 1000)
+            {
+                SAL_WARN("basegfx", "this poly is too large, " << rCandidate.count() << " elements, to be able to process timeously, falling back to ignoring the winding rule, which is likely to cause rendering artifacts");
+                return rCandidate;
+            }
+
+            B2DPolyPolygon aCandidate;
+
+            // remove all self-intersections and intersections
+            if(rCandidate.count() == 1)
+            {
+                aCandidate = basegfx::utils::solveCrossovers(rCandidate.getB2DPolygon(0));
+            }
+            else
+            {
+                aCandidate = basegfx::utils::solveCrossovers(rCandidate);
+            }
+
+            // cleanup evtl. neutral polygons
+            aCandidate = basegfx::utils::stripNeutralPolygons(aCandidate);
+
+            // remove all polygons which have the same orientation as the polygon they are directly contained in
+            const sal_uInt32 nCount(aCandidate.count());
+
+            if(nCount > 1)
+            {
+                sal_uInt32 a, b;
+                std::vector< StripHelper > aHelpers;
+                aHelpers.resize(nCount);
+
+                for(a = 0; a < nCount; a++)
+                {
+                    const B2DPolygon& aCand(aCandidate.getB2DPolygon(a));
+                    StripHelper* pNewHelper = &(aHelpers[a]);
+                    pNewHelper->maRange = utils::getRange(aCand);
+                    pNewHelper->meOrinetation = utils::getOrientation(aCand);
+
+                    // initialize with own orientation
+                    pNewHelper->mnDepth = (pNewHelper->meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
+                }
+
+                for(a = 0; a < nCount - 1; a++)
+                {
+                    const B2DPolygon& aCandA(aCandidate.getB2DPolygon(a));
+                    StripHelper& rHelperA = aHelpers[a];
+
+                    for(b = a + 1; b < nCount; b++)
+                    {
+                        const B2DPolygon& aCandB(aCandidate.getB2DPolygon(b));
+                        StripHelper& rHelperB = aHelpers[b];
+                        const bool bAInB(rHelperB.maRange.isInside(rHelperA.maRange) && utils::isInside(aCandB, aCandA, true));
+
+                        if(bAInB)
+                        {
+                            // A is inside B, add orientation of B to A
+                            rHelperA.mnDepth += (rHelperB.meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
+                        }
+
+                        const bool bBInA(rHelperA.maRange.isInside(rHelperB.maRange) && utils::isInside(aCandA, aCandB, true));
+
+                        if(bBInA)
+                        {
+                            // B is inside A, add orientation of A to B
+                            rHelperB.mnDepth += (rHelperA.meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
+                        }
+                    }
+                }
+
+                const B2DPolyPolygon aSource(aCandidate);
+                aCandidate.clear();
+
+                for(a = 0; a < nCount; a++)
+                {
+                    const StripHelper& rHelper = aHelpers[a];
+                    // for contained unequal oriented polygons sum will be 0
+                    // for contained equal it will be >=2 or <=-2
+                    // for free polygons (not contained) it will be 1 or -1
+                    // -> accept all which are >=-1 && <= 1
+                    bool bAcceptEntry(rHelper.mnDepth >= -1 && rHelper.mnDepth <= 1);
+
+                    if(bAcceptEntry)
+                    {
+                        aCandidate.append(aSource.getB2DPolygon(a));
+                    }
+                }
+            }
+
+            return aCandidate;
+        }
+
+        B2DPolyPolygon stripDispensablePolygons(const B2DPolyPolygon& rCandidate, bool bKeepAboveZero)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+            B2DPolyPolygon aRetval;
+
+            if(nCount)
+            {
+                if(nCount == 1)
+                {
+                    if(!bKeepAboveZero && utils::getOrientation(rCandidate.getB2DPolygon(0)) == B2VectorOrientation::Positive)
+                    {
+                        aRetval = rCandidate;
+                    }
+                }
+                else
+                {
+                    sal_uInt32 a, b;
+                    std::vector< StripHelper > aHelpers;
+                    aHelpers.resize(nCount);
+
+                    for(a = 0; a < nCount; a++)
+                    {
+                        const B2DPolygon& aCandidate(rCandidate.getB2DPolygon(a));
+                        StripHelper* pNewHelper = &(aHelpers[a]);
+                        pNewHelper->maRange = utils::getRange(aCandidate);
+                        pNewHelper->meOrinetation = utils::getOrientation(aCandidate);
+                        pNewHelper->mnDepth = (pNewHelper->meOrinetation == B2VectorOrientation::Negative ? -1 : 0);
+                    }
+
+                    for(a = 0; a < nCount - 1; a++)
+                    {
+                        const B2DPolygon& aCandA(rCandidate.getB2DPolygon(a));
+                        StripHelper& rHelperA = aHelpers[a];
+
+                        for(b = a + 1; b < nCount; b++)
+                        {
+                            const B2DPolygon& aCandB(rCandidate.getB2DPolygon(b));
+                            StripHelper& rHelperB = aHelpers[b];
+                            const bool bAInB(rHelperB.maRange.isInside(rHelperA.maRange) && utils::isInside(aCandB, aCandA, true));
+                            const bool bBInA(rHelperA.maRange.isInside(rHelperB.maRange) && utils::isInside(aCandA, aCandB, true));
+
+                            if(bAInB && bBInA)
+                            {
+                                // congruent
+                                if(rHelperA.meOrinetation == rHelperB.meOrinetation)
+                                {
+                                    // two polys or two holes. Lower one of them to get one of them out of the way.
+                                    // Since each will be contained in the other one, both will be increased, too.
+                                    // So, for lowering, increase only one of them
+                                    rHelperA.mnDepth++;
+                                }
+                                else
+                                {
+                                    // poly and hole. They neutralize, so get rid of both. Move securely below zero.
+                                    rHelperA.mnDepth = - static_cast<sal_Int32>(nCount);
+                                    rHelperB.mnDepth = - static_cast<sal_Int32>(nCount);
+                                }
+                            }
+                            else
+                            {
+                                if(bAInB)
+                                {
+                                    if(rHelperB.meOrinetation == B2VectorOrientation::Negative)
+                                    {
+                                        rHelperA.mnDepth--;
+                                    }
+                                    else
+                                    {
+                                        rHelperA.mnDepth++;
+                                    }
+                                }
+                                else if(bBInA)
+                                {
+                                    if(rHelperA.meOrinetation == B2VectorOrientation::Negative)
+                                    {
+                                        rHelperB.mnDepth--;
+                                    }
+                                    else
+                                    {
+                                        rHelperB.mnDepth++;
+                                    }
+                                }
+                            }
+                        }
+                    }
+
+                    for(a = 0; a < nCount; a++)
+                    {
+                        const StripHelper& rHelper = aHelpers[a];
+                        bool bAcceptEntry(bKeepAboveZero ? 1 <= rHelper.mnDepth : rHelper.mnDepth == 0);
+
+                        if(bAcceptEntry)
+                        {
+                            aRetval.append(rCandidate.getB2DPolygon(a));
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon prepareForPolygonOperation(const B2DPolygon& rCandidate)
+        {
+            solver aSolver(rCandidate);
+            B2DPolyPolygon aRetval(stripNeutralPolygons(aSolver.getB2DPolyPolygon()));
+
+            return correctOrientations(aRetval);
+        }
+
+        B2DPolyPolygon prepareForPolygonOperation(const B2DPolyPolygon& rCandidate)
+        {
+            solver aSolver(rCandidate);
+            B2DPolyPolygon aRetval(stripNeutralPolygons(aSolver.getB2DPolyPolygon()));
+
+            return correctOrientations(aRetval);
+        }
+
+        B2DPolyPolygon solvePolygonOperationOr(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
+        {
+            if(!rCandidateA.count())
+            {
+                return rCandidateB;
+            }
+            else if(!rCandidateB.count())
+            {
+                return rCandidateA;
+            }
+            else
+            {
+                // concatenate polygons, solve crossovers and throw away all sub-polygons
+                // which have a depth other than 0.
+                B2DPolyPolygon aRetval(rCandidateA);
+
+                aRetval.append(rCandidateB);
+                aRetval = solveCrossovers(aRetval);
+                aRetval = stripNeutralPolygons(aRetval);
+
+                return stripDispensablePolygons(aRetval);
+            }
+        }
+
+        B2DPolyPolygon solvePolygonOperationXor(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
+        {
+            if(!rCandidateA.count())
+            {
+                return rCandidateB;
+            }
+            else if(!rCandidateB.count())
+            {
+                return rCandidateA;
+            }
+            else
+            {
+                // XOR is pretty simple: By definition it is the simple concatenation of
+                // the single polygons since we imply XOR fill rule. Make it intersection-free
+                // and correct orientations
+                B2DPolyPolygon aRetval(rCandidateA);
+
+                aRetval.append(rCandidateB);
+                aRetval = solveCrossovers(aRetval);
+                aRetval = stripNeutralPolygons(aRetval);
+
+                return correctOrientations(aRetval);
+            }
+        }
+
+        B2DPolyPolygon solvePolygonOperationAnd(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
+        {
+            if(!rCandidateA.count())
+            {
+                return B2DPolyPolygon();
+            }
+            else if(!rCandidateB.count())
+            {
+                return B2DPolyPolygon();
+            }
+            else
+            {
+                // tdf#130150 shortcut & precision: If both are simple ranges,
+                // solve based on ranges
+                if(basegfx::utils::isRectangle(rCandidateA) && basegfx::utils::isRectangle(rCandidateB))
+                {
+                    // *if* both are ranges, AND always can be solved
+                    const basegfx::B2DRange aRangeA(rCandidateA.getB2DRange());
+                    const basegfx::B2DRange aRangeB(rCandidateB.getB2DRange());
+
+                    if(aRangeA.isInside(aRangeB))
+                    {
+                        // 2nd completely inside 1st -> 2nd is result of AND
+                        return rCandidateB;
+                    }
+
+                    if(aRangeB.isInside(aRangeA))
+                    {
+                        // 2nd completely inside 1st -> 2nd is result of AND
+                        return rCandidateA;
+                    }
+
+                    // solve by intersection
+                    basegfx::B2DRange aIntersect(aRangeA);
+                    aIntersect.intersect(aRangeB);
+
+                    if(aIntersect.isEmpty())
+                    {
+                        // no overlap -> empty polygon as result of AND
+                        return B2DPolyPolygon();
+                    }
+
+                    // create polygon result
+                    return B2DPolyPolygon(
+                        basegfx::utils::createPolygonFromRect(
+                            aIntersect));
+                }
+
+                // concatenate polygons, solve crossovers and throw away all sub-polygons
+                // with a depth of < 1. This means to keep all polygons where at least two
+                // polygons do overlap.
+                B2DPolyPolygon aRetval(rCandidateA);
+
+                aRetval.append(rCandidateB);
+                aRetval = solveCrossovers(aRetval);
+                aRetval = stripNeutralPolygons(aRetval);
+
+                return stripDispensablePolygons(aRetval, true);
+            }
+        }
+
+        B2DPolyPolygon solvePolygonOperationDiff(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
+        {
+            if(!rCandidateA.count())
+            {
+                return B2DPolyPolygon();
+            }
+            else if(!rCandidateB.count())
+            {
+                return rCandidateA;
+            }
+            else
+            {
+                // Make B topologically to holes and append to A
+                B2DPolyPolygon aRetval(rCandidateB);
+
+                aRetval.flip();
+                aRetval.append(rCandidateA);
+
+                // solve crossovers and throw away all sub-polygons which have a
+                // depth other than 0.
+                aRetval = basegfx::utils::solveCrossovers(aRetval);
+                aRetval = basegfx::utils::stripNeutralPolygons(aRetval);
+
+                return basegfx::utils::stripDispensablePolygons(aRetval);
+            }
+        }
+
+        B2DPolyPolygon mergeToSinglePolyPolygon(const B2DPolyPolygonVector& rInput)
+        {
+            if(rInput.empty())
+                return B2DPolyPolygon();
+
+            // first step: prepareForPolygonOperation and simple merge of non-overlapping
+            // PolyPolygons for speedup; this is possible for the wanted OR-operation
+            B2DPolyPolygonVector aResult;
+            aResult.reserve(rInput.size());
+
+            for(const basegfx::B2DPolyPolygon & a : rInput)
+            {
+                const basegfx::B2DPolyPolygon aCandidate(prepareForPolygonOperation(a));
+
+                if(!aResult.empty())
+                {
+                    const B2DRange aCandidateRange(aCandidate.getB2DRange());
+                    bool bCouldMergeSimple(false);
+
+                    for(auto & b: aResult)
+                    {
+                        basegfx::B2DPolyPolygon aTarget(b);
+                        const B2DRange aTargetRange(aTarget.getB2DRange());
+
+                        if(!aCandidateRange.overlaps(aTargetRange))
+                        {
+                            aTarget.append(aCandidate);
+                            b = aTarget;
+                            bCouldMergeSimple = true;
+                            break;
+                        }
+                    }
+
+                    if(!bCouldMergeSimple)
+                    {
+                        aResult.push_back(aCandidate);
+                    }
+                }
+                else
+                {
+                    aResult.push_back(aCandidate);
+                }
+            }
+
+            // second step: melt pairwise to a single PolyPolygon
+            while(aResult.size() > 1)
+            {
+                B2DPolyPolygonVector aResult2;
+                aResult2.reserve((aResult.size() / 2) + 1);
+
+                for(size_t a(0); a < aResult.size(); a += 2)
+                {
+                    if(a + 1 < aResult.size())
+                    {
+                        // a pair for processing
+                        aResult2.push_back(solvePolygonOperationOr(aResult[a], aResult[a + 1]));
+                    }
+                    else
+                    {
+                        // last single PolyPolygon; copy to target to not lose it
+                        aResult2.push_back(aResult[a]);
+                    }
+                }
+
+                aResult = aResult2;
+            }
+
+            // third step: get result
+            if(aResult.size() == 1)
+            {
+                return aResult[0];
+            }
+
+            return B2DPolyPolygon();
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dpolypolygontools.cxx b/basegfx/source/polygon/b2dpolypolygontools.cxx
new file mode 100644
index 0000000000..faf734f6e7
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolypolygontools.cxx
@@ -0,0 +1,657 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <osl/diagnose.h>
+#include <com/sun/star/drawing/PolyPolygonBezierCoords.hpp>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <rtl/math.hxx>
+
+#include <algorithm>
+#include <numeric>
+
+namespace basegfx::utils
+{
+        B2DPolyPolygon correctOrientations(const B2DPolyPolygon& rCandidate)
+        {
+            B2DPolyPolygon aRetval(rCandidate);
+            const sal_uInt32 nCount(aRetval.count());
+
+            for(sal_uInt32 a(0); a < nCount; a++)
+            {
+                const B2DPolygon& aCandidate(rCandidate.getB2DPolygon(a));
+                const B2VectorOrientation aOrientation(utils::getOrientation(aCandidate));
+                sal_uInt32 nDepth(0);
+
+                for(sal_uInt32 b(0); b < nCount; b++)
+                {
+                    if(b != a)
+                    {
+                        const B2DPolygon& aCompare(rCandidate.getB2DPolygon(b));
+
+                        if(utils::isInside(aCompare, aCandidate, true))
+                        {
+                            nDepth++;
+                        }
+                    }
+                }
+
+                const bool bShallBeHole((nDepth & 0x00000001) == 1);
+                const bool bIsHole(aOrientation == B2VectorOrientation::Negative);
+
+                if(bShallBeHole != bIsHole && aOrientation != B2VectorOrientation::Neutral)
+                {
+                    B2DPolygon aFlipped(aCandidate);
+                    aFlipped.flip();
+                    aRetval.setB2DPolygon(a, aFlipped);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon correctOutmostPolygon(const B2DPolyPolygon& rCandidate)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+
+            if(nCount > 1)
+            {
+                for(sal_uInt32 a(0); a < nCount; a++)
+                {
+                    const B2DPolygon& aCandidate(rCandidate.getB2DPolygon(a));
+                    sal_uInt32 nDepth(0);
+
+                    for(sal_uInt32 b(0); b < nCount; b++)
+                    {
+                        if(b != a)
+                        {
+                            const B2DPolygon& aCompare(rCandidate.getB2DPolygon(b));
+
+                            if(utils::isInside(aCompare, aCandidate, true))
+                            {
+                                nDepth++;
+                            }
+                        }
+                    }
+
+                    if(!nDepth)
+                    {
+                        B2DPolyPolygon aRetval(rCandidate);
+
+                        if(a != 0)
+                        {
+                            // exchange polygon a and polygon 0
+                            aRetval.setB2DPolygon(0, aCandidate);
+                            aRetval.setB2DPolygon(a, rCandidate.getB2DPolygon(0));
+                        }
+
+                        // exit
+                        return aRetval;
+                    }
+                }
+            }
+
+            return rCandidate;
+        }
+
+        B2DPolyPolygon adaptiveSubdivideByDistance(const B2DPolyPolygon& rCandidate, double fDistanceBound, int nRecurseLimit)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                B2DPolyPolygon aRetval;
+
+                for(auto const& rPolygon : rCandidate)
+                {
+                    if(rPolygon.areControlPointsUsed())
+                    {
+                        aRetval.append(utils::adaptiveSubdivideByDistance(rPolygon, fDistanceBound, nRecurseLimit));
+                    }
+                    else
+                    {
+                        aRetval.append(rPolygon);
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolyPolygon adaptiveSubdivideByAngle(const B2DPolyPolygon& rCandidate, double fAngleBound)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                B2DPolyPolygon aRetval;
+
+                for(auto const& rPolygon : rCandidate)
+                {
+                    if(rPolygon.areControlPointsUsed())
+                    {
+                        aRetval.append(utils::adaptiveSubdivideByAngle(rPolygon, fAngleBound));
+                    }
+                    else
+                    {
+                        aRetval.append(rPolygon);
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        bool isInside(const B2DPolyPolygon& rCandidate, const B2DPoint& rPoint, bool bWithBorder)
+        {
+            if(rCandidate.count() == 1)
+            {
+                return isInside(rCandidate.getB2DPolygon(0), rPoint, bWithBorder);
+            }
+            else
+            {
+                sal_Int32 nInsideCount = std::count_if(rCandidate.begin(), rCandidate.end(), [rPoint, bWithBorder](B2DPolygon polygon){ return isInside(polygon, rPoint, bWithBorder); });
+
+                return (nInsideCount % 2);
+            }
+        }
+
+        B2DRange getRange(const B2DPolyPolygon& rCandidate)
+        {
+            B2DRange aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.expand(utils::getRange(rPolygon));
+            }
+
+            return aRetval;
+        }
+
+        double getSignedArea(const B2DPolyPolygon& rCandidate)
+        {
+            double fRetval(0.0);
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                fRetval += utils::getSignedArea(rPolygon);
+            }
+
+            return fRetval;
+        }
+
+        double getArea(const B2DPolyPolygon& rCandidate)
+        {
+            return fabs(getSignedArea(rCandidate));
+        }
+
+        void applyLineDashing(const B2DPolyPolygon& rCandidate, const std::vector<double>& rDotDashArray, B2DPolyPolygon* pLineTarget, double fFullDashDotLen)
+        {
+            if(fFullDashDotLen == 0.0 && !rDotDashArray.empty())
+            {
+                // calculate fFullDashDotLen from rDotDashArray
+                fFullDashDotLen = std::accumulate(rDotDashArray.begin(), rDotDashArray.end(), 0.0);
+            }
+
+            if(!(rCandidate.count() && fFullDashDotLen > 0.0))
+                return;
+
+            B2DPolyPolygon aLineTarget;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                applyLineDashing(
+                    rPolygon,
+                    rDotDashArray,
+                    pLineTarget ? &aLineTarget : nullptr,
+                    nullptr,
+                    fFullDashDotLen);
+
+                if(pLineTarget)
+                {
+                    pLineTarget->append(aLineTarget);
+                }
+            }
+        }
+
+        bool isInEpsilonRange(const B2DPolyPolygon& rCandidate, const B2DPoint& rTestPosition, double fDistance)
+        {
+            for(auto const& rPolygon : rCandidate)
+            {
+                if(isInEpsilonRange(rPolygon, rTestPosition, fDistance))
+                {
+                    return true;
+                }
+            }
+
+            return false;
+        }
+
+        B3DPolyPolygon createB3DPolyPolygonFromB2DPolyPolygon(const B2DPolyPolygon& rCandidate, double fZCoordinate)
+        {
+            B3DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(createB3DPolygonFromB2DPolygon(rPolygon, fZCoordinate));
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon createB2DPolyPolygonFromB3DPolyPolygon(const B3DPolyPolygon& rCandidate, const B3DHomMatrix& rMat)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(createB2DPolygonFromB3DPolygon(rPolygon, rMat));
+            }
+
+            return aRetval;
+        }
+
+        double getSmallestDistancePointToPolyPolygon(const B2DPolyPolygon& rCandidate, const B2DPoint& rTestPoint, sal_uInt32& rPolygonIndex, sal_uInt32& rEdgeIndex, double& rCut)
+        {
+            double fRetval(DBL_MAX);
+            const double fZero(0.0);
+            const sal_uInt32 nPolygonCount(rCandidate.count());
+
+            for(sal_uInt32 a(0); a < nPolygonCount; a++)
+            {
+                const B2DPolygon& aCandidate(rCandidate.getB2DPolygon(a));
+                sal_uInt32 nNewEdgeIndex;
+                double fNewCut(0.0);
+                const double fNewDistance(getSmallestDistancePointToPolygon(aCandidate, rTestPoint, nNewEdgeIndex, fNewCut));
+
+                if(fRetval == DBL_MAX || fNewDistance < fRetval)
+                {
+                    fRetval = fNewDistance;
+                    rPolygonIndex = a;
+                    rEdgeIndex = nNewEdgeIndex;
+                    rCut = fNewCut;
+
+                    if(fTools::equal(fRetval, fZero))
+                    {
+                        // already found zero distance, cannot get better. Ensure numerical zero value and end loop.
+                        fRetval = 0.0;
+                        break;
+                    }
+                }
+            }
+
+            return fRetval;
+        }
+
+        B2DPolyPolygon distort(const B2DPolyPolygon& rCandidate, const B2DRange& rOriginal, const B2DPoint& rTopLeft, const B2DPoint& rTopRight, const B2DPoint& rBottomLeft, const B2DPoint& rBottomRight)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(distort(rPolygon, rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon expandToCurve(const B2DPolyPolygon& rCandidate)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(expandToCurve(rPolygon));
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon growInNormalDirection(const B2DPolyPolygon& rCandidate, double fValue)
+        {
+            if(fValue != 0.0)
+            {
+                B2DPolyPolygon aRetval;
+
+                for(auto const& rPolygon : rCandidate)
+                {
+                    aRetval.append(growInNormalDirection(rPolygon, fValue));
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolyPolygon reSegmentPolyPolygon(const B2DPolyPolygon& rCandidate, sal_uInt32 nSegments)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(reSegmentPolygon(rPolygon, nSegments));
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon interpolate(const B2DPolyPolygon& rOld1, const B2DPolyPolygon& rOld2, double t)
+        {
+            OSL_ENSURE(rOld1.count() == rOld2.count(), "B2DPolyPolygon interpolate: Different geometry (!)");
+            B2DPolyPolygon aRetval;
+
+            for(sal_uInt32 a(0); a < rOld1.count(); a++)
+            {
+                aRetval.append(interpolate(rOld1.getB2DPolygon(a), rOld2.getB2DPolygon(a), t));
+            }
+
+            return aRetval;
+        }
+
+        bool isRectangle( const B2DPolyPolygon& rPoly )
+        {
+            // exclude some cheap cases first
+            if( rPoly.count() != 1 )
+                return false;
+
+            return isRectangle( rPoly.getB2DPolygon(0) );
+        }
+
+        // #i76891#
+        B2DPolyPolygon simplifyCurveSegments(const B2DPolyPolygon& rCandidate)
+        {
+            if(rCandidate.areControlPointsUsed())
+            {
+                B2DPolyPolygon aRetval;
+
+                for(auto const& rPolygon : rCandidate)
+                {
+                    aRetval.append(simplifyCurveSegments(rPolygon));
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+        B2DPolyPolygon snapPointsOfHorizontalOrVerticalEdges(const B2DPolyPolygon& rCandidate)
+        {
+            B2DPolyPolygon aRetval;
+
+            for(auto const& rPolygon : rCandidate)
+            {
+                aRetval.append(snapPointsOfHorizontalOrVerticalEdges(rPolygon));
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon createSevenSegmentPolyPolygon(char nNumber, bool bLitSegments)
+        {
+            // config here
+            // {
+            const double fTotalSize=1.0;
+            const double fPosMiddleSegment=0.6;
+            const double fSegmentEndChopHoriz=0.08;
+            const double fSegmentEndChopVert =0.04;
+            // }
+            // config here
+
+            const double fLeft=0.0;
+            const double fRight=fTotalSize;
+            const double fTop=0.0;
+            const double fMiddle=fPosMiddleSegment;
+            const double fBottom=fTotalSize;
+
+            // from 0 to 5: pair of segment corner coordinates
+
+            // segment corner indices are these:
+
+            //   0 - 1
+            //   |   |
+            //   2 - 3
+            //   |   |
+            //   4 - 5
+
+            static const double corners[] =
+            {
+                fLeft,  fTop,
+                fRight, fTop,
+                fLeft,  fMiddle,
+                fRight, fMiddle,
+                fLeft,  fBottom,
+                fRight, fBottom
+            };
+
+            // from 0 to 9: which segments are 'lit' for this number?
+
+            // array denotes graph edges to traverse, with -1 means
+            // stop (the vertices are the corner indices from above):
+            //     0
+            //     -
+            // 1 |   | 2
+            //     - 3
+            // 4 |   | 5
+            //     -
+            //     6
+
+            static const int numbers[] =
+            {
+                1, 1, 1, 0, 1, 1, 1, // 0
+                0, 0, 1, 0, 0, 1, 0, // 1
+                1, 0, 1, 1, 1, 0, 1, // 2
+                1, 0, 1, 1, 0, 1, 1, // 3
+                0, 1, 1, 1, 0, 1, 0, // 4
+                1, 1, 0, 1, 0, 1, 1, // 5
+                1, 1, 0, 1, 1, 1, 1, // 6
+                1, 0, 1, 0, 0, 1, 0, // 1
+                1, 1, 1, 1, 1, 1, 1, // 8
+                1, 1, 1, 1, 0, 1, 1, // 9
+                0, 0, 0, 1, 0, 0, 0, // '-'
+                1, 1, 0, 1, 1, 0, 1, // 'E'
+            };
+
+            // maps segment index to two corner ids:
+            static const int index2corner[] =
+            {
+                0, 2,  // 0
+                0, 4,  // 1
+                2, 6,  // 2
+                4, 6,  // 3
+                4, 8,  // 4
+                6, 10, // 5
+                8, 10, // 6
+            };
+
+            B2DPolyPolygon aRes;
+            if( nNumber == '-' )
+            {
+                nNumber = 10;
+            }
+            else if( nNumber == 'E' )
+            {
+                nNumber = 11;
+            }
+            else if( nNumber == '.' )
+            {
+                if( bLitSegments )
+                    aRes.append(createPolygonFromCircle(B2DPoint(fTotalSize/2, fTotalSize),
+                                                        fSegmentEndChopHoriz));
+                return aRes;
+            }
+            else
+            {
+                nNumber=std::clamp<sal_uInt32>(nNumber,'0','9') - '0';
+            }
+
+            B2DPolygon aCurrSegment;
+            const size_t sliceSize=std::size(numbers)/12;
+            const int* pCurrSegment=numbers + nNumber*sliceSize;
+            for( size_t i=0; i<sliceSize; i++, pCurrSegment++)
+            {
+                if( !(*pCurrSegment ^ int(bLitSegments)) )
+                {
+                    const size_t j=2*i;
+                    aCurrSegment.clear();
+                    B2DPoint start(corners[index2corner[j]],
+                                   corners[index2corner[j]+1]  );
+                    B2DPoint end  (corners[index2corner[j+1]],
+                                   corners[index2corner[j+1]+1]);
+
+                    if( rtl::math::approxEqual(start.getX(), end.getX()) )
+                    {
+                        start.setY(start.getY()+fSegmentEndChopVert);
+                        end.setY(end.getY()-fSegmentEndChopVert);
+                    }
+                    else
+                    {
+                        start.setX(start.getX()+fSegmentEndChopHoriz);
+                        end.setX(end.getX()-fSegmentEndChopHoriz);
+                    }
+
+                    aCurrSegment.append(start);
+                    aCurrSegment.append(end);
+                }
+                aRes.append(aCurrSegment);
+            }
+
+            return aRes;
+        }
+
+        // converters for css::drawing::PointSequence
+
+        B2DPolyPolygon UnoPointSequenceSequenceToB2DPolyPolygon(
+            const css::drawing::PointSequenceSequence& rPointSequenceSequenceSource)
+        {
+            B2DPolyPolygon aRetval;
+            aRetval.reserve(rPointSequenceSequenceSource.getLength());
+            const css::drawing::PointSequence* pPointSequence = rPointSequenceSequenceSource.getConstArray();
+            const css::drawing::PointSequence* pPointSeqEnd = pPointSequence + rPointSequenceSequenceSource.getLength();
+
+            for(;pPointSequence != pPointSeqEnd; pPointSequence++)
+            {
+                const B2DPolygon aNewPolygon = UnoPointSequenceToB2DPolygon(*pPointSequence);
+                aRetval.append(aNewPolygon);
+            }
+
+            return aRetval;
+        }
+
+        void B2DPolyPolygonToUnoPointSequenceSequence(
+            const B2DPolyPolygon& rPolyPolygon,
+            css::drawing::PointSequenceSequence& rPointSequenceSequenceRetval)
+        {
+            const sal_uInt32 nCount(rPolyPolygon.count());
+
+            if(nCount)
+            {
+                rPointSequenceSequenceRetval.realloc(nCount);
+                css::drawing::PointSequence* pPointSequence = rPointSequenceSequenceRetval.getArray();
+
+                for(auto const& rPolygon : rPolyPolygon)
+                {
+                    B2DPolygonToUnoPointSequence(rPolygon, *pPointSequence);
+                    pPointSequence++;
+                }
+            }
+            else
+            {
+                rPointSequenceSequenceRetval.realloc(0);
+            }
+        }
+
+        // converters for css::drawing::PolyPolygonBezierCoords (curved polygons)
+
+        B2DPolyPolygon UnoPolyPolygonBezierCoordsToB2DPolyPolygon(
+            const css::drawing::PolyPolygonBezierCoords& rPolyPolygonBezierCoordsSource)
+        {
+            B2DPolyPolygon aRetval;
+            const sal_uInt32 nSequenceCount(static_cast<sal_uInt32>(rPolyPolygonBezierCoordsSource.Coordinates.getLength()));
+
+            if(nSequenceCount)
+            {
+                OSL_ENSURE(nSequenceCount == static_cast<sal_uInt32>(rPolyPolygonBezierCoordsSource.Flags.getLength()),
+                    "UnoPolyPolygonBezierCoordsToB2DPolyPolygon: unequal number of Points and Flags (!)");
+                const css::drawing::PointSequence* pPointSequence = rPolyPolygonBezierCoordsSource.Coordinates.getConstArray();
+                const css::drawing::FlagSequence* pFlagSequence = rPolyPolygonBezierCoordsSource.Flags.getConstArray();
+
+                for(sal_uInt32 a(0); a < nSequenceCount; a++)
+                {
+                    const B2DPolygon aNewPolygon(UnoPolygonBezierCoordsToB2DPolygon(
+                        *pPointSequence,
+                        *pFlagSequence));
+
+                    pPointSequence++;
+                    pFlagSequence++;
+                    aRetval.append(aNewPolygon);
+                }
+            }
+
+            return aRetval;
+        }
+
+        void B2DPolyPolygonToUnoPolyPolygonBezierCoords(
+            const B2DPolyPolygon& rPolyPolygon,
+            css::drawing::PolyPolygonBezierCoords& rPolyPolygonBezierCoordsRetval)
+        {
+            const sal_uInt32 nCount(rPolyPolygon.count());
+
+            if(nCount)
+            {
+                // prepare return value memory
+                rPolyPolygonBezierCoordsRetval.Coordinates.realloc(static_cast<sal_Int32>(nCount));
+                rPolyPolygonBezierCoordsRetval.Flags.realloc(static_cast<sal_Int32>(nCount));
+
+                // get pointers to arrays
+                css::drawing::PointSequence* pPointSequence = rPolyPolygonBezierCoordsRetval.Coordinates.getArray();
+                css::drawing::FlagSequence*  pFlagSequence = rPolyPolygonBezierCoordsRetval.Flags.getArray();
+
+                for(auto const& rSource : rPolyPolygon)
+                {
+                    B2DPolygonToUnoPolygonBezierCoords(
+                        rSource,
+                        *pPointSequence,
+                        *pFlagSequence);
+                    pPointSequence++;
+                    pFlagSequence++;
+                }
+            }
+            else
+            {
+                rPolyPolygonBezierCoordsRetval.Coordinates.realloc(0);
+                rPolyPolygonBezierCoordsRetval.Flags.realloc(0);
+            }
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dsvgpolypolygon.cxx b/basegfx/source/polygon/b2dsvgpolypolygon.cxx
new file mode 100644
index 0000000000..fe4f646eb3
--- /dev/null
+++ b/basegfx/source/polygon/b2dsvgpolypolygon.cxx
@@ -0,0 +1,931 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+
+#include <rtl/ustring.hxx>
+#include <sal/log.hxx>
+#include <rtl/math.hxx>
+#include <rtl/character.hxx>
+#include <stringconversiontools.hxx>
+
+namespace
+{
+
+void putCommandChar(OUStringBuffer& rBuffer,sal_Unicode& rLastSVGCommand, sal_Unicode aChar, bool bToLower,bool bVerbose)
+{
+    const sal_Unicode aCommand = bToLower ? rtl::toAsciiLowerCase(aChar) : aChar;
+
+    if (bVerbose && rBuffer.getLength())
+        rBuffer.append(' ');
+
+    if (bVerbose || rLastSVGCommand != aCommand)
+    {
+        rBuffer.append(aCommand);
+        rLastSVGCommand = aCommand;
+    }
+}
+
+void putNumberChar(OUStringBuffer& rStr,double fValue, double fOldValue, bool bUseRelativeCoordinates,bool bVerbose)
+{
+    if (bUseRelativeCoordinates)
+        fValue -= fOldValue;
+
+    const sal_Int32 aLen(rStr.getLength());
+    if (bVerbose || (aLen && basegfx::internal::isOnNumberChar(rStr[aLen - 1], false) && fValue >= 0.0))
+        rStr.append(' ');
+
+    rStr.append(fValue);
+}
+
+}
+
+namespace basegfx::utils
+{
+        bool PointIndex::operator<(const PointIndex& rComp) const
+        {
+            if(rComp.getPolygonIndex() == getPolygonIndex())
+            {
+                return rComp.getPointIndex() < getPointIndex();
+            }
+
+            return rComp.getPolygonIndex() < getPolygonIndex();
+        }
+
+        bool importFromSvgD(
+            B2DPolyPolygon& o_rPolyPolygon,
+            std::u16string_view rSvgDStatement,
+            bool bHandleRelativeNextPointCompatible,
+            PointIndexSet* pHelpPointIndexSet)
+        {
+            o_rPolyPolygon.clear();
+            const sal_Int32 nLen(rSvgDStatement.size());
+            sal_Int32 nPos(0);
+            double nLastX( 0.0 );
+            double nLastY( 0.0 );
+            B2DPolygon aCurrPoly;
+
+            // skip initial whitespace
+            basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+            while(nPos < nLen)
+            {
+                bool bRelative(false);
+                const sal_Unicode aCurrChar(rSvgDStatement[nPos]);
+
+                if(o_rPolyPolygon.count() && !aCurrPoly.count() && aCurrChar != 'm' && aCurrChar != 'M')
+                {
+                    // we have a new sub-polygon starting, but without a 'moveto' command.
+                    // this requires to add the current point as start point to the polygon
+                    // (see SVG1.1 8.3.3 The "closepath" command)
+                    aCurrPoly.append(B2DPoint(nLastX, nLastY));
+                }
+
+                switch(aCurrChar)
+                {
+                    case 'z' :
+                    case 'Z' :
+                    {
+                        // consume CurrChar and whitespace
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        // create closed polygon and reset import values
+                        if(aCurrPoly.count())
+                        {
+                            if(!bHandleRelativeNextPointCompatible)
+                            {
+                                // SVG defines that "the next subpath starts at the
+                                // same initial point as the current subpath", so set the
+                                // current point if we do not need to be compatible
+                                nLastX = aCurrPoly.getB2DPoint(0).getX();
+                                nLastY = aCurrPoly.getB2DPoint(0).getY();
+                            }
+
+                            aCurrPoly.setClosed(true);
+                            o_rPolyPolygon.append(aCurrPoly);
+                            aCurrPoly.clear();
+                        }
+
+                        break;
+                    }
+
+                    case 'm' :
+                    case 'M' :
+                    {
+                        // create non-closed polygon and reset import values
+                        if(aCurrPoly.count())
+                        {
+                            o_rPolyPolygon.append(aCurrPoly);
+                            aCurrPoly.clear();
+                        }
+                        [[fallthrough]]; // to add coordinate data as 1st point of new polygon
+                    }
+                    case 'l' :
+                    case 'L' :
+                    {
+                        if(aCurrChar == 'm' || aCurrChar == 'l')
+                        {
+                            bRelative = true;
+                        }
+
+                        // consume CurrChar and whitespace
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+
+                            // add point
+                            aCurrPoly.append(B2DPoint(nX, nY));
+                        }
+                        break;
+                    }
+
+                    case 'h' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'H' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY(nLastY);
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX += nLastX;
+                            }
+
+                            // set last position
+                            nLastX = nX;
+
+                            // add point
+                            aCurrPoly.append(B2DPoint(nX, nY));
+                        }
+                        break;
+                    }
+
+                    case 'v' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'V' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX(nLastX), nY;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nY += nLastY;
+                            }
+
+                            // set last position
+                            nLastY = nY;
+
+                            // add point
+                            aCurrPoly.append(B2DPoint(nX, nY));
+                        }
+                        break;
+                    }
+
+                    case 's' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'S' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+                            double nX2, nY2;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX2, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY2, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX2 += nLastX;
+                                nY2 += nLastY;
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            // ensure existence of start point
+                            if(!aCurrPoly.count())
+                            {
+                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
+                            }
+
+                            // get first control point. It's the reflection of the PrevControlPoint
+                            // of the last point. If not existent, use current point (see SVG)
+                            B2DPoint aPrevControl(nLastX, nLastY);
+                            const sal_uInt32 nIndex(aCurrPoly.count() - 1);
+
+                            if(aCurrPoly.areControlPointsUsed() && aCurrPoly.isPrevControlPointUsed(nIndex))
+                            {
+                                const B2DPoint aPrevPoint(aCurrPoly.getB2DPoint(nIndex));
+                                const B2DPoint aPrevControlPoint(aCurrPoly.getPrevControlPoint(nIndex));
+
+                                // use mirrored previous control point
+                                aPrevControl.setX((2.0 * aPrevPoint.getX()) - aPrevControlPoint.getX());
+                                aPrevControl.setY((2.0 * aPrevPoint.getY()) - aPrevControlPoint.getY());
+                            }
+
+                            // append curved edge
+                            aCurrPoly.appendBezierSegment(aPrevControl, B2DPoint(nX2, nY2), B2DPoint(nX, nY));
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+                        }
+                        break;
+                    }
+
+                    case 'c' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'C' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+                            double nX1, nY1;
+                            double nX2, nY2;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX1, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY1, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nX2, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY2, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX1 += nLastX;
+                                nY1 += nLastY;
+                                nX2 += nLastX;
+                                nY2 += nLastY;
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            // ensure existence of start point
+                            if(!aCurrPoly.count())
+                            {
+                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
+                            }
+
+                            // append curved edge
+                            aCurrPoly.appendBezierSegment(B2DPoint(nX1, nY1), B2DPoint(nX2, nY2), B2DPoint(nX, nY));
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+                        }
+                        break;
+                    }
+
+                    // #100617# quadratic beziers are imported as cubic ones
+                    case 'q' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'Q' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+                            double nX1, nY1;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX1, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY1, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX1 += nLastX;
+                                nY1 += nLastY;
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            // ensure existence of start point
+                            if(!aCurrPoly.count())
+                            {
+                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
+                            }
+
+                            // append curved edge
+                            aCurrPoly.appendQuadraticBezierSegment(B2DPoint(nX1, nY1), B2DPoint(nX, nY));
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+                        }
+                        break;
+                    }
+
+                    // #100617# relative quadratic beziers are imported as cubic
+                    case 't' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'T' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            // ensure existence of start point
+                            if(!aCurrPoly.count())
+                            {
+                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
+                            }
+
+                            // get first control point. It's the reflection of the PrevControlPoint
+                            // of the last point. If not existent, use current point (see SVG)
+                            B2DPoint aPrevControl(nLastX, nLastY);
+                            const sal_uInt32 nIndex(aCurrPoly.count() - 1);
+                            const B2DPoint aPrevPoint(aCurrPoly.getB2DPoint(nIndex));
+
+                            if(aCurrPoly.areControlPointsUsed() && aCurrPoly.isPrevControlPointUsed(nIndex))
+                            {
+                                const B2DPoint aPrevControlPoint(aCurrPoly.getPrevControlPoint(nIndex));
+
+                                // use mirrored previous control point
+                                aPrevControl.setX((2.0 * aPrevPoint.getX()) - aPrevControlPoint.getX());
+                                aPrevControl.setY((2.0 * aPrevPoint.getY()) - aPrevControlPoint.getY());
+                            }
+
+                            if(!aPrevControl.equal(aPrevPoint))
+                            {
+                                // there is a prev control point, and we have the already mirrored one
+                                // in aPrevControl. We also need the quadratic control point for this
+                                // new quadratic segment to calculate the 2nd cubic control point
+                                const B2DPoint aQuadControlPoint(
+                                    ((3.0 * aPrevControl.getX()) - aPrevPoint.getX()) / 2.0,
+                                    ((3.0 * aPrevControl.getY()) - aPrevPoint.getY()) / 2.0);
+
+                                // calculate the cubic bezier coefficients from the quadratic ones.
+                                const double nX2Prime((aQuadControlPoint.getX() * 2.0 + nX) / 3.0);
+                                const double nY2Prime((aQuadControlPoint.getY() * 2.0 + nY) / 3.0);
+
+                                // append curved edge, use mirrored cubic control point directly
+                                aCurrPoly.appendBezierSegment(aPrevControl, B2DPoint(nX2Prime, nY2Prime), B2DPoint(nX, nY));
+                            }
+                            else
+                            {
+                                // when no previous control, SVG says to use current point -> straight line.
+                                // Just add end point
+                                aCurrPoly.append(B2DPoint(nX, nY));
+                            }
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+                        }
+                        break;
+                    }
+
+                    case 'a' :
+                    {
+                        bRelative = true;
+                        [[fallthrough]];
+                    }
+                    case 'A' :
+                    {
+                        nPos++;
+                        basegfx::internal::skipSpaces(nPos, rSvgDStatement, nLen);
+
+                        while(nPos < nLen && basegfx::internal::isOnNumberChar(rSvgDStatement, nPos))
+                        {
+                            double nX, nY;
+                            double fRX, fRY, fPhi;
+                            sal_Int32 bLargeArcFlag, bSweepFlag;
+
+                            if(!basegfx::internal::importDoubleAndSpaces(fRX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(fRY, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(fPhi, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importFlagAndSpaces(bLargeArcFlag, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importFlagAndSpaces(bSweepFlag, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
+                            if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;
+
+                            if(bRelative)
+                            {
+                                nX += nLastX;
+                                nY += nLastY;
+                            }
+
+                            if( rtl::math::approxEqual(nX, nLastX) && rtl::math::approxEqual(nY, nLastY) )
+                                continue; // start==end -> skip according to SVG spec
+
+                            if( fRX == 0.0 || fRY == 0.0 )
+                            {
+                                // straight line segment according to SVG spec
+                                aCurrPoly.append(B2DPoint(nX, nY));
+                            }
+                            else
+                            {
+                                // normalize according to SVG spec
+                                fRX=fabs(fRX); fRY=fabs(fRY);
+
+                                // from the SVG spec, appendix F.6.4
+
+                                // |x1'|   |cos phi   sin phi|  |(x1 - x2)/2|
+                                // |y1'| = |-sin phi  cos phi|  |(y1 - y2)/2|
+                                const B2DPoint p1(nLastX, nLastY);
+                                const B2DPoint p2(nX, nY);
+                                B2DHomMatrix aTransform(basegfx::utils::createRotateB2DHomMatrix(
+                                    -deg2rad(fPhi)));
+
+                                const B2DPoint p1_prime( aTransform * B2DPoint(((p1-p2)/2.0)) );
+
+                                //           ______________________________________       rx y1'
+                                // |cx'|  + /  rx^2 ry^2 - rx^2 y1'^2 - ry^2 x1^2           ry
+                                // |cy'| =-/       rx^2y1'^2 + ry^2 x1'^2               - ry x1'
+                                //                                                          rx
+                                // chose + if f_A != f_S
+                                // chose - if f_A  = f_S
+                                B2DPoint aCenter_prime;
+                                const double fRadicant(
+                                    (fRX*fRX*fRY*fRY - fRX*fRX*p1_prime.getY()*p1_prime.getY() - fRY*fRY*p1_prime.getX()*p1_prime.getX())/
+                                    (fRX*fRX*p1_prime.getY()*p1_prime.getY() + fRY*fRY*p1_prime.getX()*p1_prime.getX()));
+                                if( fRadicant < 0.0 )
+                                {
+                                    // no solution - according to SVG
+                                    // spec, scale up ellipse
+                                    // uniformly such that it passes
+                                    // through end points (denominator
+                                    // of radicant solved for fRY,
+                                    // with s=fRX/fRY)
+                                    const double fRatio(fRX/fRY);
+                                    const double fRadicant2(
+                                        p1_prime.getY()*p1_prime.getY() +
+                                        p1_prime.getX()*p1_prime.getX()/(fRatio*fRatio));
+                                    if( fRadicant2 < 0.0 )
+                                    {
+                                        // only trivial solution, one
+                                        // of the axes 0 -> straight
+                                        // line segment according to
+                                        // SVG spec
+                                        aCurrPoly.append(B2DPoint(nX, nY));
+                                        continue;
+                                    }
+
+                                    fRY=sqrt(fRadicant2);
+                                    fRX=fRatio*fRY;
+
+                                    // keep center_prime forced to (0,0)
+                                }
+                                else
+                                {
+                                    const double fFactor(
+                                        (bLargeArcFlag==bSweepFlag ? -1.0 : 1.0) *
+                                        sqrt(fRadicant));
+
+                                    // actually calculate center_prime
+                                    aCenter_prime = B2DPoint(
+                                        fFactor*fRX*p1_prime.getY()/fRY,
+                                        -fFactor*fRY*p1_prime.getX()/fRX);
+                                }
+
+                                //              +           u - v
+                                // angle(u,v) =  arccos( ------------ )     (take the sign of (ux vy - uy vx))
+                                //              -        ||u|| ||v||
+
+                                //                  1    | (x1' - cx')/rx |
+                                // theta1 = angle((   ), |                | )
+                                //                  0    | (y1' - cy')/ry |
+                                const B2DPoint aRadii(fRX,fRY);
+                                double fTheta1(
+                                    B2DVector(1.0,0.0).angle(
+                                        (p1_prime-aCenter_prime)/aRadii));
+
+                                //                 |1|    |  (-x1' - cx')/rx |
+                                // theta2 = angle( | | ,  |                  | )
+                                //                 |0|    |  (-y1' - cy')/ry |
+                                double fTheta2(
+                                    B2DVector(1.0,0.0).angle(
+                                        (-p1_prime-aCenter_prime)/aRadii));
+
+                                // map both angles to [0,2pi)
+                                fTheta1 = fmod(2*M_PI+fTheta1,2*M_PI);
+                                fTheta2 = fmod(2*M_PI+fTheta2,2*M_PI);
+
+                                // make sure the large arc is taken
+                                // (since
+                                // createPolygonFromEllipseSegment()
+                                // normalizes to e.g. cw arc)
+                                if( !bSweepFlag )
+                                    std::swap(fTheta1,fTheta2);
+
+                                // finally, create bezier polygon from this
+                                B2DPolygon aSegment(
+                                    utils::createPolygonFromUnitEllipseSegment(
+                                        fTheta1, fTheta2 ));
+
+                                // transform ellipse by rotation & move to final center
+                                aTransform = basegfx::utils::createScaleB2DHomMatrix(fRX, fRY);
+                                aTransform.translate(aCenter_prime.getX(),
+                                                     aCenter_prime.getY());
+                                aTransform.rotate(deg2rad(fPhi));
+                                const B2DPoint aOffset((p1+p2)/2.0);
+                                aTransform.translate(aOffset.getX(),
+                                                     aOffset.getY());
+                                aSegment.transform(aTransform);
+
+                                // createPolygonFromEllipseSegment()
+                                // always creates arcs that are
+                                // positively oriented - flip polygon
+                                // if we swapped angles above
+                                if( !bSweepFlag )
+                                    aSegment.flip();
+
+                                // remember PointIndex of evtl. added pure helper points
+                                sal_uInt32 nPointIndex(aCurrPoly.count() + 1);
+                                aCurrPoly.append(aSegment);
+
+                                // if asked for, mark pure helper points by adding them to the index list of
+                                // helper points
+                                if(pHelpPointIndexSet && aCurrPoly.count() > 1)
+                                {
+                                    const sal_uInt32 nPolyIndex(o_rPolyPolygon.count());
+
+                                    for(;nPointIndex + 1 < aCurrPoly.count(); nPointIndex++)
+                                    {
+                                        pHelpPointIndexSet->insert(PointIndex(nPolyIndex, nPointIndex));
+                                    }
+                                }
+                            }
+
+                            // set last position
+                            nLastX = nX;
+                            nLastY = nY;
+                        }
+                        break;
+                    }
+
+                    default:
+                    {
+                        SAL_WARN("basegfx", "importFromSvgD(): skipping tags in svg:d element (unknown: \""
+                                << OUString(aCurrChar)
+                                << "\")!");
+                        ++nPos;
+                        break;
+                    }
+                }
+            }
+
+            // if there is polygon data, create non-closed polygon
+            if(aCurrPoly.count())
+            {
+                o_rPolyPolygon.append(aCurrPoly);
+            }
+
+            return true;
+        }
+
+        bool importFromSvgPoints( B2DPolygon&            o_rPoly,
+                                  std::u16string_view rSvgPointsAttribute )
+        {
+            o_rPoly.clear();
+            const sal_Int32 nLen(rSvgPointsAttribute.size());
+            sal_Int32 nPos(0);
+            double nX, nY;
+
+            // skip initial whitespace
+            basegfx::internal::skipSpaces(nPos, rSvgPointsAttribute, nLen);
+
+            while(nPos < nLen)
+            {
+                if(!basegfx::internal::importDoubleAndSpaces(nX, nPos, rSvgPointsAttribute, nLen)) return false;
+                if(!basegfx::internal::importDoubleAndSpaces(nY, nPos, rSvgPointsAttribute, nLen)) return false;
+
+                // add point
+                o_rPoly.append(B2DPoint(nX, nY));
+
+                // skip to next number, or finish
+                basegfx::internal::skipSpaces(nPos, rSvgPointsAttribute, nLen);
+            }
+
+            return true;
+        }
+
+        OUString exportToSvgPoints( const B2DPolygon& rPoly )
+        {
+            SAL_WARN_IF(rPoly.areControlPointsUsed(), "basegfx", "exportToSvgPoints: Only non-bezier polygons allowed (!)");
+            const sal_uInt32 nPointCount(rPoly.count());
+            OUStringBuffer aResult;
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const basegfx::B2DPoint aPoint(rPoly.getB2DPoint(a));
+
+                if(a)
+                {
+                    aResult.append(' ');
+                }
+
+                aResult.append(OUString::number(aPoint.getX())
+                        + ","
+                        + OUString::number(aPoint.getY()));
+            }
+
+            return aResult.makeStringAndClear();
+        }
+
+        OUString exportToSvgD(
+            const B2DPolyPolygon& rPolyPolygon,
+            bool bUseRelativeCoordinates,
+            bool bDetectQuadraticBeziers,
+            bool bHandleRelativeNextPointCompatible,
+            bool bOOXMLMotionPath)
+        {
+            const sal_uInt32 nCount(rPolyPolygon.count());
+            sal_uInt32 nCombinedPointCount = 0;
+            for(sal_uInt32 i(0); i < nCount; i++)
+            {
+                const B2DPolygon& aPolygon(rPolyPolygon.getB2DPolygon(i));
+                nCombinedPointCount += aPolygon.count();
+            }
+
+            OUStringBuffer aResult(std::max<int>(nCombinedPointCount * 32,512));
+            B2DPoint aCurrentSVGPosition(0.0, 0.0); // SVG assumes (0,0) as the initial current point
+
+            for(sal_uInt32 i(0); i < nCount; i++)
+            {
+                const B2DPolygon& aPolygon(rPolyPolygon.getB2DPolygon(i));
+                const sal_uInt32 nPointCount(aPolygon.count());
+
+                if(nPointCount)
+                {
+                    const bool bPolyUsesControlPoints(aPolygon.areControlPointsUsed());
+                    const sal_uInt32 nEdgeCount(aPolygon.isClosed() ? nPointCount : nPointCount - 1);
+                    sal_Unicode aLastSVGCommand(' '); // last SVG command char
+                    B2DPoint aLeft, aRight; // for quadratic bezier test
+
+                    // handle polygon start point
+                    B2DPoint aEdgeStart(aPolygon.getB2DPoint(0));
+                    bool bUseRelativeCoordinatesForFirstPoint(bUseRelativeCoordinates);
+
+                    if(bHandleRelativeNextPointCompatible)
+                    {
+                        // To get around the error that the start point for the next polygon is the
+                        // start point of the current one (and not the last as it was handled up to now)
+                        // do force to write an absolute 'M' command as start for the next polygon
+                        bUseRelativeCoordinatesForFirstPoint = false;
+                    }
+
+                    // Write 'moveto' and the 1st coordinates, set aLastSVGCommand to 'lineto'
+                    putCommandChar(aResult, aLastSVGCommand, 'M', bUseRelativeCoordinatesForFirstPoint, bOOXMLMotionPath);
+                    putNumberChar(aResult, aEdgeStart.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinatesForFirstPoint, bOOXMLMotionPath);
+                    putNumberChar(aResult, aEdgeStart.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinatesForFirstPoint, bOOXMLMotionPath);
+                    aLastSVGCommand =  bUseRelativeCoordinatesForFirstPoint ? 'l' : 'L';
+                    aCurrentSVGPosition = aEdgeStart;
+
+                    for(sal_uInt32 nIndex(0); nIndex < nEdgeCount; nIndex++)
+                    {
+                        // prepare access to next point
+                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
+                        const B2DPoint aEdgeEnd(aPolygon.getB2DPoint(nNextIndex));
+
+                        // handle edge from (aEdgeStart, aEdgeEnd) using indices (nIndex, nNextIndex)
+                        const bool bEdgeIsBezier(bPolyUsesControlPoints
+                            && (aPolygon.isNextControlPointUsed(nIndex) || aPolygon.isPrevControlPointUsed(nNextIndex)));
+
+                        if(bEdgeIsBezier)
+                        {
+                            // handle bezier edge
+                            const B2DPoint aControlEdgeStart(aPolygon.getNextControlPoint(nIndex));
+                            const B2DPoint aControlEdgeEnd(aPolygon.getPrevControlPoint(nNextIndex));
+                            bool bIsQuadraticBezier(false);
+
+                            // check continuity at current edge's start point. For SVG, do NOT use an
+                            // existing continuity since no 'S' or 's' statement should be written. At
+                            // import, that 'previous' control vector is not available. SVG documentation
+                            // says for interpretation:
+
+                            // "(If there is no previous command or if the previous command was
+                            // not a C, c, S or s, assume the first control point is coincident
+                            // with the current point.)"
+
+                            // That's what is done from our import, so avoid exporting it as first statement
+                            // is necessary.
+                            const bool bSymmetricAtEdgeStart(
+                                !bOOXMLMotionPath && nIndex != 0
+                                && aPolygon.getContinuityInPoint(nIndex) == B2VectorContinuity::C2);
+
+                            if(bDetectQuadraticBeziers)
+                            {
+                                // check for quadratic beziers - that's
+                                // the case if both control points are in
+                                // the same place when they are prolonged
+                                // to the common quadratic control point
+
+                                // Left: P = (3P1 - P0) / 2
+                                // Right: P = (3P2 - P3) / 2
+                                aLeft = B2DPoint((3.0 * aControlEdgeStart - aEdgeStart) / 2.0);
+                                aRight= B2DPoint((3.0 * aControlEdgeEnd - aEdgeEnd) / 2.0);
+                                bIsQuadraticBezier = aLeft.equal(aRight);
+                            }
+
+                            if(bIsQuadraticBezier)
+                            {
+                                // approximately equal, export as quadratic bezier
+                                if(bSymmetricAtEdgeStart)
+                                {
+                                    putCommandChar(aResult, aLastSVGCommand, 'T', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                                else
+                                {
+                                    putCommandChar(aResult, aLastSVGCommand, 'Q', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aLeft.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aLeft.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                            }
+                            else
+                            {
+                                // export as cubic bezier
+                                if(bSymmetricAtEdgeStart)
+                                {
+                                    putCommandChar(aResult, aLastSVGCommand, 'S', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aControlEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aControlEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                                else
+                                {
+                                    putCommandChar(aResult, aLastSVGCommand, 'C', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aControlEdgeStart.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aControlEdgeStart.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aControlEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aControlEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                            }
+                        }
+                        else
+                        {
+                            // straight edge
+                            if(nNextIndex == 0)
+                            {
+                                // it's a closed polygon's last edge and it's not a bezier edge, so there is
+                                // no need to write it
+                            }
+                            else
+                            {
+                                const bool bXEqual(rtl::math::approxEqual(aEdgeStart.getX(), aEdgeEnd.getX()));
+                                const bool bYEqual(rtl::math::approxEqual(aEdgeStart.getY(), aEdgeEnd.getY()));
+
+                                if(bXEqual && bYEqual)
+                                {
+                                    // point is a double point; do not export at all
+                                }
+                                else if(bXEqual && !bOOXMLMotionPath)
+                                {
+                                    // export as vertical line
+                                    putCommandChar(aResult, aLastSVGCommand, 'V', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                                else if(bYEqual && !bOOXMLMotionPath)
+                                {
+                                    // export as horizontal line
+                                    putCommandChar(aResult, aLastSVGCommand, 'H', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                                else
+                                {
+                                    // export as line
+                                    putCommandChar(aResult, aLastSVGCommand, 'L', bUseRelativeCoordinates, bOOXMLMotionPath);
+
+                                    putNumberChar(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    putNumberChar(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates, bOOXMLMotionPath);
+                                    aCurrentSVGPosition = aEdgeEnd;
+                                }
+                            }
+                        }
+
+                        // prepare edge start for next loop step
+                        aEdgeStart = aEdgeEnd;
+                    }
+
+                    // close path if closed poly (Z and z are equivalent here, but looks nicer when case is matched)
+                    if(aPolygon.isClosed())
+                    {
+                        putCommandChar(aResult, aLastSVGCommand, 'Z', bUseRelativeCoordinates, bOOXMLMotionPath);
+                    }
+                    else if (bOOXMLMotionPath)
+                    {
+                        putCommandChar(aResult, aLastSVGCommand, 'E', bUseRelativeCoordinates, bOOXMLMotionPath);
+                    }
+
+                    if(!bHandleRelativeNextPointCompatible)
+                    {
+                        // SVG defines that "the next subpath starts at the same initial point as the current subpath",
+                        // so set aCurrentSVGPosition to the 1st point of the current, now ended and written path
+                        aCurrentSVGPosition = aPolygon.getB2DPoint(0);
+                    }
+                }
+            }
+
+            return aResult.makeStringAndClear();
+        }
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b2dtrapezoid.cxx b/basegfx/source/polygon/b2dtrapezoid.cxx
new file mode 100644
index 0000000000..2870c46d82
--- /dev/null
+++ b/basegfx/source/polygon/b2dtrapezoid.cxx
@@ -0,0 +1,1163 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b2dtrapezoid.hxx>
+#include <basegfx/range/b1drange.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+
+#include <osl/diagnose.h>
+
+#include <list>
+
+namespace basegfx::trapezoidhelper
+{
+
+        // helper class to hold a simple edge. This is only used for horizontal edges
+        // currently, thus the YPositions will be equal. I did not create a special
+        // class for this since holding the pointers is more effective and also can be
+        // used as baseclass for the traversing edges
+
+        namespace {
+
+        class TrDeSimpleEdge
+        {
+        protected:
+            // pointers to start and end point
+            const B2DPoint*     mpStart;
+            const B2DPoint*     mpEnd;
+
+        public:
+            // constructor
+            TrDeSimpleEdge(
+                const B2DPoint* pStart,
+                const B2DPoint* pEnd)
+            :   mpStart(pStart),
+                mpEnd(pEnd)
+            {
+            }
+
+            // data read access
+            const B2DPoint& getStart() const { return *mpStart; }
+            const B2DPoint& getEnd() const { return *mpEnd; }
+        };
+
+        }
+
+        // define vector of simple edges
+
+        typedef std::vector< TrDeSimpleEdge > TrDeSimpleEdges;
+
+        // helper class for holding a traversing edge. It will always have some
+        // distance in YPos. The slope (in a numerically useful form, see comments) is
+        // hold and used in SortValue to allow sorting traversing edges by Y, X and slope
+        // (in that order)
+
+        namespace {
+
+        class TrDeEdgeEntry : public TrDeSimpleEdge
+        {
+        private:
+            // the slope in a numerical useful form for sorting
+            sal_uInt32          mnSortValue;
+
+        public:
+            // convenience data read access
+            double getDeltaX() const { return mpEnd->getX() - mpStart->getX(); }
+            double getDeltaY() const { return mpEnd->getY() - mpStart->getY(); }
+
+            // convenience data read access. SortValue is created on demand since
+            // it is not always used
+            sal_uInt32 getSortValue() const
+            {
+                if(mnSortValue != 0)
+                    return mnSortValue;
+
+                // get radiant; has to be in the range ]0.0 .. pi[, thus scale to full
+                // sal_uInt32 range for maximum precision
+                const double fRadiant(atan2(getDeltaY(), getDeltaX()) * (SAL_MAX_UINT32 / M_PI));
+
+                // convert to sal_uInt32 value
+                const_cast< TrDeEdgeEntry* >(this)->mnSortValue = sal_uInt32(fRadiant);
+
+                return mnSortValue;
+            }
+
+            // constructor. SortValue can be given when known, use zero otherwise
+            TrDeEdgeEntry(
+                const B2DPoint* pStart,
+                const B2DPoint* pEnd,
+                sal_uInt32 nSortValue)
+            :   TrDeSimpleEdge(pStart, pEnd),
+                mnSortValue(nSortValue)
+            {
+                // force traversal of deltaY downward
+                if(mpEnd->getY() < mpStart->getY())
+                {
+                    std::swap(mpStart, mpEnd);
+                }
+
+                // no horizontal edges allowed, all need to traverse vertically
+                OSL_ENSURE(mpEnd->getY() > mpStart->getY(), "Illegal TrDeEdgeEntry constructed (!)");
+            }
+
+            // data write access to StartPoint
+            void setStart( const B2DPoint* pNewStart)
+            {
+                OSL_ENSURE(pNewStart != nullptr, "No null pointer allowed here (!)");
+
+                if(mpStart != pNewStart)
+                {
+                    mpStart = pNewStart;
+
+                    // no horizontal edges allowed, all need to traverse vertically
+                    OSL_ENSURE(mpEnd->getY() > mpStart->getY(), "Illegal TrDeEdgeEntry constructed (!)");
+                }
+            }
+
+            // data write access to EndPoint
+            void setEnd( const B2DPoint* pNewEnd)
+            {
+                OSL_ENSURE(pNewEnd != nullptr, "No null pointer allowed here (!)");
+
+                if(mpEnd != pNewEnd)
+                {
+                    mpEnd = pNewEnd;
+
+                    // no horizontal edges allowed, all need to traverse vertically
+                    OSL_ENSURE(mpEnd->getY() > mpStart->getY(), "Illegal TrDeEdgeEntry constructed (!)");
+                }
+            }
+
+            // operator for sort support. Sort by Y, X and slope (in that order)
+            bool operator<(const TrDeEdgeEntry& rComp) const
+            {
+                if(fTools::equal(getStart().getY(), rComp.getStart().getY()))
+                {
+                    if(fTools::equal(getStart().getX(), rComp.getStart().getX()))
+                    {
+                        // when start points are equal, use the direction the edge is pointing
+                        // to. That value is created on demand and derived from atan2 in the
+                        // range ]0.0 .. pi[ (without extremas, we always have a deltaY in this
+                        // class) and scaled to sal_uInt32 range for best precision. 0 means no angle,
+                        // while SAL_MAX_UINT32 means pi. Thus, the higher the value, the more left
+                        // the edge traverses.
+                        return (getSortValue() > rComp.getSortValue());
+                    }
+                    else
+                    {
+                        return fTools::less(getStart().getX(), rComp.getStart().getX());
+                    }
+                }
+                else
+                {
+                    return fTools::less(getStart().getY(), rComp.getStart().getY());
+                }
+            }
+
+            // method for cut support
+            B2DPoint getCutPointForGivenY(double fGivenY) const
+            {
+                // avoid div/0
+                if (getDeltaY() == 0)
+                    return B2DPoint(getStart().getX(), fGivenY);
+                // Calculate cut point locally (do not use interpolate) since it is numerically
+                // necessary to guarantee the new, equal Y-coordinate
+                const double fFactor((fGivenY - getStart().getY()) / getDeltaY());
+                const double fDeltaXNew(fFactor * getDeltaX());
+
+                return B2DPoint(getStart().getX() + fDeltaXNew, fGivenY);
+            }
+        };
+
+        }
+
+        // define double linked list of edges (for fast random insert)
+
+        typedef std::list< TrDeEdgeEntry > TrDeEdgeEntries;
+
+
+
+        // FIXME: templatize this and use it for TrDeEdgeEntries too ...
+
+        namespace {
+
+        /// Class to allow efficient allocation and release of B2DPoints
+        class PointBlockAllocator
+        {
+            static const size_t nBlockSize = 32;
+            size_t nCurPoint;
+            B2DPoint *mpPointBase;
+            /// Special case the first allocation to avoid it.
+            B2DPoint maFirstStackBlock[nBlockSize];
+            std::vector< B2DPoint * > maBlocks;
+        public:
+            PointBlockAllocator() :
+                nCurPoint( nBlockSize ),
+                mpPointBase( maFirstStackBlock )
+            {
+            }
+
+            ~PointBlockAllocator()
+            {
+                while(!maBlocks.empty())
+                {
+                    delete [] maBlocks.back();
+                    maBlocks.pop_back();
+                }
+            }
+
+            B2DPoint *allocatePoint()
+            {
+                if(nCurPoint >= nBlockSize)
+                {
+                    mpPointBase = new B2DPoint[nBlockSize];
+                    maBlocks.push_back(mpPointBase);
+                    nCurPoint = 0;
+                }
+                return mpPointBase + nCurPoint++;
+            }
+
+            B2DPoint *allocatePoint(const B2DTuple &rPoint)
+            {
+                B2DPoint *pPoint = allocatePoint();
+                *pPoint = rPoint;
+                return pPoint;
+            }
+
+            /// This is a very uncommon case but why not ...
+            void freeIfLast(B2DPoint const *pPoint)
+            {
+                // just re-use the last point if we can.
+                if ( nCurPoint > 0 && pPoint == mpPointBase + nCurPoint - 1 )
+                    nCurPoint--;
+            }
+        };
+
+        // helper class to handle the complete trapezoid subdivision of a PolyPolygon
+        class TrapezoidSubdivider
+        {
+        private:
+            // local data
+            TrDeEdgeEntries             maTrDeEdgeEntries;
+            std::vector< B2DPoint >   maPoints;
+            /// new points allocated for cuts
+            PointBlockAllocator         maNewPoints;
+
+            void addEdgeSorted(
+                TrDeEdgeEntries::iterator aCurrent,
+                const TrDeEdgeEntry& rNewEdge)
+            {
+                // Loop while new entry is bigger, use operator<
+                while(aCurrent != maTrDeEdgeEntries.end() && (*aCurrent) < rNewEdge)
+                {
+                    ++aCurrent;
+                }
+
+                // Insert before first which is smaller or equal or at end
+                maTrDeEdgeEntries.insert(aCurrent, rNewEdge);
+            }
+
+            bool splitEdgeAtGivenPoint(
+                TrDeEdgeEntries::reference aEdge,
+                const B2DPoint& rCutPoint,
+                const TrDeEdgeEntries::iterator& aCurrent)
+            {
+                // do not create edges without deltaY: do not split when start is identical
+                if(aEdge.getStart().equal(rCutPoint))
+                {
+                    return false;
+                }
+
+                // do not create edges without deltaY: do not split when end is identical
+                if(aEdge.getEnd().equal(rCutPoint))
+                {
+                    return false;
+                }
+
+                const double fOldDeltaYStart(rCutPoint.getY() - aEdge.getStart().getY());
+
+                if(fTools::lessOrEqual(fOldDeltaYStart, 0.0))
+                {
+                    // do not split: the resulting edge would be horizontal
+                    // correct it to new start point
+                    aEdge.setStart(&rCutPoint);
+                    return false;
+                }
+
+                const double fNewDeltaYStart(aEdge.getEnd().getY() - rCutPoint.getY());
+
+                if(fTools::lessOrEqual(fNewDeltaYStart, 0.0))
+                {
+                    // do not split: the resulting edge would be horizontal
+                    // correct it to new end point
+                    aEdge.setEnd(&rCutPoint);
+                    return false;
+                }
+
+                // Create new entry
+                const TrDeEdgeEntry aNewEdge(
+                    &rCutPoint,
+                    &aEdge.getEnd(),
+                    aEdge.getSortValue());
+
+                // Correct old entry
+                aEdge.setEnd(&rCutPoint);
+
+                // Insert sorted (to avoid new sort)
+                addEdgeSorted(aCurrent, aNewEdge);
+
+                return true;
+            }
+
+            bool testAndCorrectEdgeIntersection(
+                TrDeEdgeEntries::reference aEdgeA,
+                TrDeEdgeEntries::reference aEdgeB,
+                const TrDeEdgeEntries::iterator& aCurrent)
+            {
+                // Exclude simple cases: same start or end point
+                if(aEdgeA.getStart().equal(aEdgeB.getStart()))
+                {
+                    return false;
+                }
+
+                if(aEdgeA.getStart().equal(aEdgeB.getEnd()))
+                {
+                    return false;
+                }
+
+                if(aEdgeA.getEnd().equal(aEdgeB.getStart()))
+                {
+                    return false;
+                }
+
+                if(aEdgeA.getEnd().equal(aEdgeB.getEnd()))
+                {
+                    return false;
+                }
+
+                // Exclude simple cases: one of the edges has no length anymore
+                if(aEdgeA.getStart().equal(aEdgeA.getEnd()))
+                {
+                    return false;
+                }
+
+                if(aEdgeB.getStart().equal(aEdgeB.getEnd()))
+                {
+                    return false;
+                }
+
+                // check if one point is on the other edge (a touch, not a cut)
+                const B2DVector aDeltaB(aEdgeB.getDeltaX(), aEdgeB.getDeltaY());
+
+                if(utils::isPointOnEdge(aEdgeA.getStart(), aEdgeB.getStart(), aDeltaB))
+                {
+                    return splitEdgeAtGivenPoint(aEdgeB, aEdgeA.getStart(), aCurrent);
+                }
+
+                if(utils::isPointOnEdge(aEdgeA.getEnd(), aEdgeB.getStart(), aDeltaB))
+                {
+                    return splitEdgeAtGivenPoint(aEdgeB, aEdgeA.getEnd(), aCurrent);
+                }
+
+                const B2DVector aDeltaA(aEdgeA.getDeltaX(), aEdgeA.getDeltaY());
+
+                if(utils::isPointOnEdge(aEdgeB.getStart(), aEdgeA.getStart(), aDeltaA))
+                {
+                    return splitEdgeAtGivenPoint(aEdgeA, aEdgeB.getStart(), aCurrent);
+                }
+
+                if(utils::isPointOnEdge(aEdgeB.getEnd(), aEdgeA.getStart(), aDeltaA))
+                {
+                    return splitEdgeAtGivenPoint(aEdgeA, aEdgeB.getEnd(), aCurrent);
+                }
+
+                // check for cut inside edges. Use both t-values to choose the more precise
+                // one later
+                double fCutA(0.0);
+                double fCutB(0.0);
+
+                if(utils::findCut(
+                    aEdgeA.getStart(), aDeltaA,
+                    aEdgeB.getStart(), aDeltaB,
+                    CutFlagValue::LINE,
+                    &fCutA,
+                    &fCutB) == CutFlagValue::NONE)
+                    return false;
+
+                // use a simple metric (length criteria) for choosing the numerically
+                // better cut
+                const double fSimpleLengthA(aDeltaA.getX() + aDeltaA.getY());
+                const double fSimpleLengthB(aDeltaB.getX() + aDeltaB.getY());
+                const bool bAIsLonger(fSimpleLengthA > fSimpleLengthB);
+                B2DPoint* pNewPoint = bAIsLonger
+                    ? maNewPoints.allocatePoint(aEdgeA.getStart() + (fCutA * aDeltaA))
+                    : maNewPoints.allocatePoint(aEdgeB.getStart() + (fCutB * aDeltaB));
+
+                // try to split both edges
+                bool bRetval = splitEdgeAtGivenPoint(aEdgeA, *pNewPoint, aCurrent);
+                bRetval |= splitEdgeAtGivenPoint(aEdgeB, *pNewPoint, aCurrent);
+
+                if(!bRetval)
+                    maNewPoints.freeIfLast(pNewPoint);
+
+                return bRetval;
+            }
+
+            void solveHorizontalEdges(TrDeSimpleEdges& rTrDeSimpleEdges)
+            {
+                if(rTrDeSimpleEdges.empty() || maTrDeEdgeEntries.empty())
+                    return;
+
+                // there were horizontal edges. These can be excluded, but
+                // cuts with other edges need to be solved and added before
+                // ignoring them
+                for(const TrDeSimpleEdge & rHorEdge : rTrDeSimpleEdges)
+                {
+                    // get horizontal edge as candidate; prepare its range and fixed Y
+                    const B1DRange aRange(rHorEdge.getStart().getX(), rHorEdge.getEnd().getX());
+                    const double fFixedY(rHorEdge.getStart().getY());
+
+                    // loop over traversing edges
+                    TrDeEdgeEntries::iterator aCurrent(maTrDeEdgeEntries.begin());
+
+                    do
+                    {
+                        // get compare edge
+                        TrDeEdgeEntries::reference aCompare(*aCurrent++);
+
+                        if(fTools::lessOrEqual(aCompare.getEnd().getY(), fFixedY))
+                        {
+                            // edge ends above horizontal edge, continue
+                            continue;
+                        }
+
+                        if(fTools::moreOrEqual(aCompare.getStart().getY(), fFixedY))
+                        {
+                            // edge starts below horizontal edge, continue
+                            continue;
+                        }
+
+                        // vertical overlap, get horizontal range
+                        const B1DRange aCompareRange(aCompare.getStart().getX(), aCompare.getEnd().getX());
+
+                        if(aRange.overlaps(aCompareRange))
+                        {
+                            // possible cut, get cut point
+                            const B2DPoint aSplit(aCompare.getCutPointForGivenY(fFixedY));
+
+                            if(fTools::more(aSplit.getX(), aRange.getMinimum())
+                                && fTools::less(aSplit.getX(), aRange.getMaximum()))
+                            {
+                                // cut is in XRange of horizontal edge, potentially needed cut
+                                B2DPoint* pNewPoint = maNewPoints.allocatePoint(aSplit);
+
+                                if(!splitEdgeAtGivenPoint(aCompare, *pNewPoint, aCurrent))
+                                {
+                                    maNewPoints.freeIfLast(pNewPoint);
+                                }
+                            }
+                        }
+                    }
+                    while(aCurrent != maTrDeEdgeEntries.end()
+                        && fTools::less(aCurrent->getStart().getY(), fFixedY));
+                }
+            }
+
+        public:
+            explicit TrapezoidSubdivider(
+                const B2DPolyPolygon& rSourcePolyPolygon)
+            {
+                B2DPolyPolygon aSource(rSourcePolyPolygon);
+                TrDeSimpleEdges aTrDeSimpleEdges;
+                sal_uInt32 nAllPointCount(0);
+
+                // ensure there are no curves used
+                if(aSource.areControlPointsUsed())
+                {
+                    aSource = aSource.getDefaultAdaptiveSubdivision();
+                }
+
+                for(const auto& aPolygonCandidate : std::as_const(aSource))
+                {
+                    // 1st run: count points
+                    const sal_uInt32 nCount(aPolygonCandidate.count());
+
+                    if(nCount > 2)
+                    {
+                        nAllPointCount += nCount;
+                    }
+                }
+
+                if(nAllPointCount)
+                {
+                    // reserve needed points. CAUTION: maPoints size is NOT to be changed anymore
+                    // after 2nd loop since pointers to it are used in the edges
+                    maPoints.reserve(nAllPointCount);
+
+                    for(const auto& aPolygonCandidate : std::as_const(aSource))
+                    {
+                        // 2nd run: add points
+                        const sal_uInt32 nCount(aPolygonCandidate.count());
+
+                        if(nCount > 2)
+                        {
+                            for(sal_uInt32 b = 0; b < nCount; b++)
+                            {
+                                maPoints.push_back(aPolygonCandidate.getB2DPoint(b));
+                            }
+                        }
+                    }
+
+                    // Moved the edge construction to a 3rd run: doing it in the 2nd run is
+                    // possible (and I used it), but requires a working vector::reserve()
+                    // implementation, else the vector will be reallocated and the pointers
+                    // in the edges may be wrong. Security first here.
+                    sal_uInt32 nStartIndex(0);
+
+                    for(const auto& aPolygonCandidate : std::as_const(aSource))
+                    {
+                        const sal_uInt32 nCount(aPolygonCandidate.count());
+
+                        if(nCount > 2)
+                        {
+                            // get the last point of the current polygon
+                            B2DPoint* pPrev(&maPoints[nCount + nStartIndex - 1]);
+
+                            for(sal_uInt32 b = 0; b < nCount; b++)
+                            {
+                                // get next point
+                                B2DPoint* pCurr(&maPoints[nStartIndex++]);
+
+                                if(fTools::equal(pPrev->getY(), pCurr->getY()))
+                                {
+                                    // horizontal edge, check for single point
+                                    if(!fTools::equal(pPrev->getX(), pCurr->getX()))
+                                    {
+                                        // X-order not needed, just add
+                                        aTrDeSimpleEdges.emplace_back(pPrev, pCurr);
+
+                                        const double fMiddle((pPrev->getY() + pCurr->getY()) * 0.5);
+                                        pPrev->setY(fMiddle);
+                                        pCurr->setY(fMiddle);
+                                    }
+                                }
+                                else
+                                {
+                                    // vertical edge. Positive Y-direction is guaranteed by the
+                                    // TrDeEdgeEntry constructor
+                                    maTrDeEdgeEntries.emplace_back(pPrev, pCurr, 0);
+                                }
+
+                                // prepare next step
+                                pPrev = pCurr;
+                            }
+                        }
+                    }
+                }
+
+                if(!maTrDeEdgeEntries.empty())
+                {
+                    // single and initial sort of traversing edges
+                    maTrDeEdgeEntries.sort();
+
+                    // solve horizontal edges if there are any detected
+                    solveHorizontalEdges(aTrDeSimpleEdges);
+                }
+            }
+
+            void Subdivide(B2DTrapezoidVector& ro_Result)
+            {
+                // This is the central subdivider. The strategy is to use the first two entries
+                // from the traversing edges as a potential trapezoid and do the needed corrections
+                // and adaptations on the way.
+
+                // There always must be two edges with the same YStart value: When adding the polygons
+                // in the constructor, there is always a topmost point from which two edges start; when
+                // the topmost is an edge, there is a start and end of this edge from which two edges
+                // start. All cases have two edges with same StartY (QED).
+
+                // Based on this these edges get corrected when:
+                // - one is longer than the other
+                // - they intersect
+                // - they intersect with other edges
+                // - another edge starts inside the thought trapezoid
+
+                // All this cases again produce a valid state so that the first two edges have a common
+                // Ystart again. Some cases lead to a restart of the process, some allow consuming the
+                // edges and create the intended trapezoid.
+
+                // Be careful when doing changes here: it is essential to keep all possible paths
+                // in valid states and to be numerically correct. This is especially needed e.g.
+                // by using fTools::equal(..) in the more robust small-value incarnation.
+                B1DRange aLeftRange;
+                B1DRange aRightRange;
+
+                if(!maTrDeEdgeEntries.empty())
+                {
+                    // measuring shows that the relation between edges and created trapezoids is
+                    // mostly in the 1:1 range, thus reserve as much trapezoids as edges exist.
+                    ro_Result.reserve(ro_Result.size() + maTrDeEdgeEntries.size());
+                }
+
+                while(!maTrDeEdgeEntries.empty())
+                {
+                    // Prepare current operator and get first edge
+                    TrDeEdgeEntries::iterator aCurrent(maTrDeEdgeEntries.begin());
+                    TrDeEdgeEntries::reference aLeft(*aCurrent++);
+
+                    if(aCurrent == maTrDeEdgeEntries.end())
+                    {
+                        // Should not happen: No 2nd edge; consume the single edge
+                        // to not have an endless loop and start next. During development
+                        // I constantly had breakpoints here, so I am sure enough to add an
+                        // assertion here
+                        OSL_FAIL("Trapezoid decomposer in illegal state (!)");
+                        maTrDeEdgeEntries.pop_front();
+                        continue;
+                    }
+
+                    // get second edge
+                    TrDeEdgeEntries::reference aRight(*aCurrent++);
+
+                    if(!fTools::equal(aLeft.getStart().getY(), aRight.getStart().getY()))
+                    {
+                        // Should not happen: We have a 2nd edge, but YStart is on another
+                        // line; consume the single edge to not have an endless loop and start
+                        // next. During development I constantly had breakpoints here, so I am
+                        // sure enough to add an assertion here
+                        OSL_FAIL("Trapezoid decomposer in illegal state (!)");
+                        maTrDeEdgeEntries.pop_front();
+                        continue;
+                    }
+
+                    // aLeft and aRight build a thought trapezoid now. They have a common
+                    // start line (same Y for start points). Potentially, one of the edges
+                    // is longer than the other. It is only needed to look at the shorter
+                    // length which build the potential trapezoid. To do so, get the end points
+                    // locally and adapt the evtl. longer one. Use only aLeftEnd and aRightEnd
+                    // from here on, not the aLeft.getEnd() or aRight.getEnd() accesses.
+                    B2DPoint aLeftEnd(aLeft.getEnd());
+                    B2DPoint aRightEnd(aRight.getEnd());
+
+                    // check if end points are on the same line. If yes, no adaptation
+                    // needs to be prepared. Also remember which one actually is longer.
+                    const bool bEndOnSameLine(fTools::equal(aLeftEnd.getY(), aRightEnd.getY()));
+                    bool bLeftIsLonger(false);
+
+                    if(!bEndOnSameLine)
+                    {
+                        // check which edge is longer and correct accordingly
+                        bLeftIsLonger = fTools::more(aLeftEnd.getY(), aRightEnd.getY());
+
+                        if(bLeftIsLonger)
+                        {
+                            aLeftEnd = aLeft.getCutPointForGivenY(aRightEnd.getY());
+                        }
+                        else
+                        {
+                            aRightEnd = aRight.getCutPointForGivenY(aLeftEnd.getY());
+                        }
+                    }
+
+                    // check for same start and end points
+                    const bool bSameStartPoint(aLeft.getStart().equal(aRight.getStart()));
+                    const bool bSameEndPoint(aLeftEnd.equal(aRightEnd));
+
+                    // check the simple case that the edges form a 'blind' edge (deadend)
+                    if(bSameStartPoint && bSameEndPoint)
+                    {
+                        // correct the longer edge if prepared
+                        if(!bEndOnSameLine)
+                        {
+                            if(bLeftIsLonger)
+                            {
+                                B2DPoint* pNewPoint = maNewPoints.allocatePoint(aLeftEnd);
+
+                                if(!splitEdgeAtGivenPoint(aLeft, *pNewPoint, aCurrent))
+                                {
+                                    maNewPoints.freeIfLast(pNewPoint);
+                                }
+                            }
+                            else
+                            {
+                                B2DPoint* pNewPoint = maNewPoints.allocatePoint(aRightEnd);
+
+                                if(!splitEdgeAtGivenPoint(aRight, *pNewPoint, aCurrent))
+                                {
+                                    maNewPoints.freeIfLast(pNewPoint);
+                                }
+                            }
+                        }
+
+                        // consume both edges and start next run
+                        maTrDeEdgeEntries.pop_front();
+                        maTrDeEdgeEntries.pop_front();
+
+                        continue;
+                    }
+
+                    // check if the edges self-intersect. This can only happen when
+                    // start and end point are different
+                    bool bRangesSet(false);
+
+                    if(!(bSameStartPoint || bSameEndPoint))
+                    {
+                        // get XRanges of edges
+                        aLeftRange = B1DRange(aLeft.getStart().getX(), aLeftEnd.getX());
+                        aRightRange = B1DRange(aRight.getStart().getX(), aRightEnd.getX());
+                        bRangesSet = true;
+
+                        // use fast range test first
+                        if(aLeftRange.overlaps(aRightRange))
+                        {
+                            // real cut test and correction. If correction was needed,
+                            // start new run
+                            if(testAndCorrectEdgeIntersection(aLeft, aRight, aCurrent))
+                            {
+                                continue;
+                            }
+                        }
+                    }
+
+                    // now we need to check if there are intersections with other edges
+                    // or if other edges start inside the candidate trapezoid
+                    if(aCurrent != maTrDeEdgeEntries.end()
+                        && fTools::less(aCurrent->getStart().getY(), aLeftEnd.getY()))
+                    {
+                        // get XRanges of edges
+                        if(!bRangesSet)
+                        {
+                            aLeftRange = B1DRange(aLeft.getStart().getX(), aLeftEnd.getX());
+                            aRightRange = B1DRange(aRight.getStart().getX(), aRightEnd.getX());
+                        }
+
+                        // build full XRange for fast check
+                        B1DRange aAllRange(aLeftRange);
+                        aAllRange.expand(aRightRange);
+
+                        // prepare loop iterator; aCurrent needs to stay unchanged for
+                        // possibly sorted insertions of new EdgeNodes. Also prepare stop flag
+                        TrDeEdgeEntries::iterator aLoop(aCurrent);
+                        bool bDone(false);
+
+                        do
+                        {
+                            // get compare edge and its XRange
+                            TrDeEdgeEntries::reference aCompare(*aLoop++);
+
+                            // avoid edges using the same start point as one of
+                            // the edges. These can neither have their start point
+                            // in the thought trapezoid nor cut with one of the edges
+                            if(aCompare.getStart().equal(aRight.getStart()))
+                            {
+                                continue;
+                            }
+
+                            // get compare XRange
+                            const B1DRange aCompareRange(aCompare.getStart().getX(), aCompare.getEnd().getX());
+
+                            // use fast range test first
+                            if(aAllRange.overlaps(aCompareRange))
+                            {
+                                // check for start point inside thought trapezoid
+                                if(fTools::more(aCompare.getStart().getY(), aLeft.getStart().getY()))
+                                {
+                                    // calculate the two possible split points at compare's Y
+                                    const B2DPoint aSplitLeft(aLeft.getCutPointForGivenY(aCompare.getStart().getY()));
+                                    const B2DPoint aSplitRight(aRight.getCutPointForGivenY(aCompare.getStart().getY()));
+
+                                    // check for start point of aCompare being inside thought
+                                    // trapezoid
+                                    if(aCompare.getStart().getX() >= aSplitLeft.getX() &&
+                                        aCompare.getStart().getX() <= aSplitRight.getX())
+                                    {
+                                        // is inside, correct and restart loop
+                                        B2DPoint* pNewLeft = maNewPoints.allocatePoint(aSplitLeft);
+
+                                        if(splitEdgeAtGivenPoint(aLeft, *pNewLeft, aCurrent))
+                                        {
+                                            bDone = true;
+                                        }
+                                        else
+                                        {
+                                            maNewPoints.freeIfLast(pNewLeft);
+                                        }
+
+                                        B2DPoint* pNewRight = maNewPoints.allocatePoint(aSplitRight);
+
+                                        if(splitEdgeAtGivenPoint(aRight, *pNewRight, aCurrent))
+                                        {
+                                            bDone = true;
+                                        }
+                                        else
+                                        {
+                                            maNewPoints.freeIfLast(pNewRight);
+                                        }
+                                    }
+                                }
+
+                                if(!bDone && aLeftRange.overlaps(aCompareRange))
+                                {
+                                    // test for concrete cut of compare edge with left edge
+                                    bDone = testAndCorrectEdgeIntersection(aLeft, aCompare, aCurrent);
+                                }
+
+                                if(!bDone && aRightRange.overlaps(aCompareRange))
+                                {
+                                    // test for concrete cut of compare edge with Right edge
+                                    bDone = testAndCorrectEdgeIntersection(aRight, aCompare, aCurrent);
+                                }
+                            }
+                        }
+                        while(!bDone
+                            && aLoop != maTrDeEdgeEntries.end()
+                            && fTools::less(aLoop->getStart().getY(), aLeftEnd.getY()));
+
+                        if(bDone)
+                        {
+                            // something needed to be changed; start next loop
+                            continue;
+                        }
+                    }
+
+                    // when we get here, the intended trapezoid can be used. It needs to
+                    // be corrected possibly (if prepared); but this is no reason not to
+                    // use it in the same loop iteration
+                    if(!bEndOnSameLine)
+                    {
+                        if(bLeftIsLonger)
+                        {
+                            B2DPoint* pNewPoint = maNewPoints.allocatePoint(aLeftEnd);
+
+                            if(!splitEdgeAtGivenPoint(aLeft, *pNewPoint, aCurrent))
+                            {
+                                maNewPoints.freeIfLast(pNewPoint);
+                            }
+                        }
+                        else
+                        {
+                            B2DPoint* pNewPoint = maNewPoints.allocatePoint(aRightEnd);
+
+                            if(!splitEdgeAtGivenPoint(aRight, *pNewPoint, aCurrent))
+                            {
+                                maNewPoints.freeIfLast(pNewPoint);
+                            }
+                        }
+                    }
+
+                    // the two edges start at the same Y, they use the same DeltaY, they
+                    // do not cut themselves and not any other edge in range. Create a
+                    // B2DTrapezoid and consume both edges
+                    ro_Result.emplace_back(
+                            aLeft.getStart().getX(),
+                            aRight.getStart().getX(),
+                            aLeft.getStart().getY(),
+                            aLeftEnd.getX(),
+                            aRightEnd.getX(),
+                            aLeftEnd.getY());
+
+                    maTrDeEdgeEntries.pop_front();
+                    maTrDeEdgeEntries.pop_front();
+                }
+            }
+        };
+
+        }
+} // end of namespace
+
+namespace basegfx
+{
+    B2DTrapezoid::B2DTrapezoid(
+        const double& rfTopXLeft,
+        const double& rfTopXRight,
+        const double& rfTopY,
+        const double& rfBottomXLeft,
+        const double& rfBottomXRight,
+        const double& rfBottomY)
+    :   mfTopXLeft(rfTopXLeft),
+        mfTopXRight(rfTopXRight),
+        mfTopY(rfTopY),
+        mfBottomXLeft(rfBottomXLeft),
+        mfBottomXRight(rfBottomXRight),
+        mfBottomY(rfBottomY)
+    {
+        // guarantee mfTopXRight >= mfTopXLeft
+        if(mfTopXLeft > mfTopXRight)
+        {
+            std::swap(mfTopXLeft, mfTopXRight);
+        }
+
+        // guarantee mfBottomXRight >= mfBottomXLeft
+        if(mfBottomXLeft > mfBottomXRight)
+        {
+            std::swap(mfBottomXLeft, mfBottomXRight);
+        }
+
+        // guarantee mfBottomY >= mfTopY
+        if(mfTopY > mfBottomY)
+        {
+            std::swap(mfTopY, mfBottomY);
+            std::swap(mfTopXLeft, mfBottomXLeft);
+            std::swap(mfTopXRight, mfBottomXRight);
+        }
+    }
+
+    B2DPolygon B2DTrapezoid::getB2DPolygon() const
+    {
+        B2DPolygon aRetval;
+
+        aRetval.append(B2DPoint(getTopXLeft(), getTopY()));
+        aRetval.append(B2DPoint(getTopXRight(), getTopY()));
+        aRetval.append(B2DPoint(getBottomXRight(), getBottomY()));
+        aRetval.append(B2DPoint(getBottomXLeft(), getBottomY()));
+        aRetval.setClosed(true);
+
+        return aRetval;
+    }
+} // end of namespace basegfx
+
+namespace basegfx::utils
+{
+        // convert Source utils::PolyPolygon to trapezoids
+        void trapezoidSubdivide(B2DTrapezoidVector& ro_Result, const B2DPolyPolygon& rSourcePolyPolygon)
+        {
+            trapezoidhelper::TrapezoidSubdivider aTrapezoidSubdivider(rSourcePolyPolygon);
+
+            aTrapezoidSubdivider.Subdivide(ro_Result);
+        }
+
+        void createLineTrapezoidFromEdge(
+            B2DTrapezoidVector& ro_Result,
+            const B2DPoint& rPointA,
+            const B2DPoint& rPointB,
+            double fLineWidth)
+        {
+            if(fTools::lessOrEqual(fLineWidth, 0.0))
+            {
+                // no line width
+                return;
+            }
+
+            if(rPointA.equal(rPointB))
+            {
+                // points are equal, no edge
+                return;
+            }
+
+            const double fHalfLineWidth(0.5 * fLineWidth);
+
+            if(fTools::equal(rPointA.getX(), rPointB.getX()))
+            {
+                // vertical line
+                const double fLeftX(rPointA.getX() - fHalfLineWidth);
+                const double fRightX(rPointA.getX() + fHalfLineWidth);
+
+                ro_Result.emplace_back(
+                        fLeftX,
+                        fRightX,
+                        std::min(rPointA.getY(), rPointB.getY()),
+                        fLeftX,
+                        fRightX,
+                        std::max(rPointA.getY(), rPointB.getY()));
+            }
+            else if(fTools::equal(rPointA.getY(), rPointB.getY()))
+            {
+                // horizontal line
+                const double fLeftX(std::min(rPointA.getX(), rPointB.getX()));
+                const double fRightX(std::max(rPointA.getX(), rPointB.getX()));
+
+                ro_Result.emplace_back(
+                        fLeftX,
+                        fRightX,
+                        rPointA.getY() - fHalfLineWidth,
+                        fLeftX,
+                        fRightX,
+                        rPointA.getY() + fHalfLineWidth);
+            }
+            else
+            {
+                // diagonal line
+                // create perpendicular vector
+                const B2DVector aDelta(rPointB - rPointA);
+                B2DVector aPerpendicular(-aDelta.getY(), aDelta.getX());
+                aPerpendicular.setLength(fHalfLineWidth);
+
+                // create StartLow, StartHigh, EndLow and EndHigh
+                const B2DPoint aStartLow(rPointA + aPerpendicular);
+                const B2DPoint aStartHigh(rPointA - aPerpendicular);
+                const B2DPoint aEndHigh(rPointB - aPerpendicular);
+                const B2DPoint aEndLow(rPointB + aPerpendicular);
+
+                // create EdgeEntries
+                basegfx::trapezoidhelper::TrDeEdgeEntries aTrDeEdgeEntries;
+
+                aTrDeEdgeEntries.emplace_back(&aStartLow, &aStartHigh, 0);
+                aTrDeEdgeEntries.emplace_back(&aStartHigh, &aEndHigh, 0);
+                aTrDeEdgeEntries.emplace_back(&aEndHigh, &aEndLow, 0);
+                aTrDeEdgeEntries.emplace_back(&aEndLow, &aStartLow, 0);
+                aTrDeEdgeEntries.sort();
+
+                // here we know we have exactly four edges, and they do not cut, touch or
+                // intersect. This makes processing much easier. Get the first two as start
+                // edges for the thought trapezoid
+                basegfx::trapezoidhelper::TrDeEdgeEntries::iterator aCurrent(aTrDeEdgeEntries.begin());
+                basegfx::trapezoidhelper::TrDeEdgeEntries::reference aLeft(*aCurrent++);
+                basegfx::trapezoidhelper::TrDeEdgeEntries::reference aRight(*aCurrent++);
+                const bool bEndOnSameLine(fTools::equal(aLeft.getEnd().getY(), aRight.getEnd().getY()));
+
+                if(bEndOnSameLine)
+                {
+                    // create two triangle trapezoids
+                    ro_Result.emplace_back(
+                            aLeft.getStart().getX(),
+                            aRight.getStart().getX(),
+                            aLeft.getStart().getY(),
+                            aLeft.getEnd().getX(),
+                            aRight.getEnd().getX(),
+                            aLeft.getEnd().getY());
+
+                    basegfx::trapezoidhelper::TrDeEdgeEntries::reference aLeft2(*aCurrent++);
+                    basegfx::trapezoidhelper::TrDeEdgeEntries::reference aRight2(*aCurrent++);
+
+                    ro_Result.emplace_back(
+                            aLeft2.getStart().getX(),
+                            aRight2.getStart().getX(),
+                            aLeft2.getStart().getY(),
+                            aLeft2.getEnd().getX(),
+                            aRight2.getEnd().getX(),
+                            aLeft2.getEnd().getY());
+                }
+                else
+                {
+                    // create three trapezoids. Check which edge is longer and
+                    // correct accordingly
+                    const bool bLeftIsLonger(fTools::more(aLeft.getEnd().getY(), aRight.getEnd().getY()));
+
+                    if(bLeftIsLonger)
+                    {
+                        basegfx::trapezoidhelper::TrDeEdgeEntries::reference aRight2(*aCurrent++);
+                        basegfx::trapezoidhelper::TrDeEdgeEntries::reference aLeft2(*aCurrent++);
+                        const B2DPoint aSplitLeft(aLeft.getCutPointForGivenY(aRight.getEnd().getY()));
+                        const B2DPoint aSplitRight(aRight2.getCutPointForGivenY(aLeft.getEnd().getY()));
+
+                        ro_Result.emplace_back(
+                                aLeft.getStart().getX(),
+                                aRight.getStart().getX(),
+                                aLeft.getStart().getY(),
+                                aSplitLeft.getX(),
+                                aRight.getEnd().getX(),
+                                aRight.getEnd().getY());
+
+                        ro_Result.emplace_back(
+                                aSplitLeft.getX(),
+                                aRight.getEnd().getX(),
+                                aRight.getEnd().getY(),
+                                aLeft2.getStart().getX(),
+                                aSplitRight.getX(),
+                                aLeft2.getStart().getY());
+
+                        ro_Result.emplace_back(
+                                aLeft2.getStart().getX(),
+                                aSplitRight.getX(),
+                                aLeft2.getStart().getY(),
+                                aLeft2.getEnd().getX(),
+                                aRight2.getEnd().getX(),
+                                aLeft2.getEnd().getY());
+                    }
+                    else
+                    {
+                        basegfx::trapezoidhelper::TrDeEdgeEntries::reference aLeft2(*aCurrent++);
+                        basegfx::trapezoidhelper::TrDeEdgeEntries::reference aRight2(*aCurrent++);
+                        const B2DPoint aSplitRight(aRight.getCutPointForGivenY(aLeft.getEnd().getY()));
+                        const B2DPoint aSplitLeft(aLeft2.getCutPointForGivenY(aRight.getEnd().getY()));
+
+                        ro_Result.emplace_back(
+                                aLeft.getStart().getX(),
+                                aRight.getStart().getX(),
+                                aLeft.getStart().getY(),
+                                aLeft.getEnd().getX(),
+                                aSplitRight.getX(),
+                                aLeft.getEnd().getY());
+
+                        ro_Result.emplace_back(
+                                aLeft.getEnd().getX(),
+                                aSplitRight.getX(),
+                                aLeft.getEnd().getY(),
+                                aSplitLeft.getX(),
+                                aRight.getEnd().getX(),
+                                aRight2.getStart().getY());
+
+                        ro_Result.emplace_back(
+                                aSplitLeft.getX(),
+                                aRight.getEnd().getX(),
+                                aRight2.getStart().getY(),
+                                aLeft2.getEnd().getX(),
+                                aRight2.getEnd().getX(),
+                                aLeft2.getEnd().getY());
+                    }
+                }
+            }
+        }
+
+        void createLineTrapezoidFromB2DPolygon(
+            B2DTrapezoidVector& ro_Result,
+            const B2DPolygon& rPolygon,
+            double fLineWidth)
+        {
+            if(fTools::lessOrEqual(fLineWidth, 0.0))
+            {
+                return;
+            }
+
+            // ensure there are no curves used
+            B2DPolygon aSource(rPolygon);
+
+            if(aSource.areControlPointsUsed())
+            {
+                const double fPrecisionFactor = 0.25;
+                aSource = adaptiveSubdivideByDistance( aSource, fLineWidth * fPrecisionFactor );
+            }
+
+            const sal_uInt32 nPointCount(aSource.count());
+
+            if(!nPointCount)
+            {
+                return;
+            }
+
+            const sal_uInt32 nEdgeCount(aSource.isClosed() ? nPointCount : nPointCount - 1);
+            B2DPoint aCurrent(aSource.getB2DPoint(0));
+
+            ro_Result.reserve(ro_Result.size() + (3 * nEdgeCount));
+
+            for(sal_uInt32 a(0); a < nEdgeCount; a++)
+            {
+                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                const B2DPoint aNext(aSource.getB2DPoint(nNextIndex));
+
+                createLineTrapezoidFromEdge(ro_Result, aCurrent, aNext, fLineWidth);
+                aCurrent = aNext;
+            }
+        }
+
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b3dpolygon.cxx b/basegfx/source/polygon/b3dpolygon.cxx
new file mode 100644
index 0000000000..ebd9e3f4f7
--- /dev/null
+++ b/basegfx/source/polygon/b3dpolygon.cxx
@@ -0,0 +1,1612 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <osl/diagnose.h>
+#include <basegfx/polygon/b3dpolygon.hxx>
+#include <basegfx/point/b3dpoint.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/color/bcolor.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <cassert>
+#include <memory>
+#include <utility>
+#include <vector>
+#include <algorithm>
+
+namespace {
+
+class CoordinateData3D
+{
+    basegfx::B3DPoint                               maPoint;
+
+public:
+    CoordinateData3D()
+    {
+    }
+
+    explicit CoordinateData3D(const basegfx::B3DPoint& rData)
+    :   maPoint(rData)
+    {
+    }
+
+    const basegfx::B3DPoint& getCoordinate() const
+    {
+        return maPoint;
+    }
+
+    void setCoordinate(const basegfx::B3DPoint& rValue)
+    {
+        if(rValue != maPoint)
+            maPoint = rValue;
+    }
+
+    bool operator==(const CoordinateData3D& rData) const
+    {
+        return (maPoint == rData.getCoordinate());
+    }
+
+    void transform(const basegfx::B3DHomMatrix& rMatrix)
+    {
+        maPoint *= rMatrix;
+    }
+};
+
+class CoordinateDataArray3D
+{
+    typedef std::vector< CoordinateData3D > CoordinateData3DVector;
+
+    CoordinateData3DVector                          maVector;
+
+public:
+    explicit CoordinateDataArray3D(sal_uInt32 nCount)
+    :   maVector(nCount)
+    {
+    }
+
+    CoordinateDataArray3D(const CoordinateDataArray3D& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   maVector(rOriginal.maVector.begin() + nIndex, rOriginal.maVector.begin() + (nIndex + nCount))
+    {
+    }
+
+    ::basegfx::B3DVector getNormal() const
+    {
+        ::basegfx::B3DVector aRetval;
+        const sal_uInt32 nPointCount(maVector.size());
+
+        if(nPointCount > 2)
+        {
+            sal_uInt32 nISmallest(0);
+            sal_uInt32 a(0);
+            const basegfx::B3DPoint* pSmallest(&maVector[0].getCoordinate());
+            const basegfx::B3DPoint* pNext(nullptr);
+            const basegfx::B3DPoint* pPrev(nullptr);
+
+            // To guarantee a correctly oriented point, choose an outmost one
+            // which then cannot be concave
+            for(a = 1; a < nPointCount; a++)
+            {
+                const basegfx::B3DPoint& rCandidate = maVector[a].getCoordinate();
+
+                if((rCandidate.getX() < pSmallest->getX())
+                    || (rCandidate.getX() == pSmallest->getX() && rCandidate.getY() < pSmallest->getY())
+                    || (rCandidate.getX() == pSmallest->getX() && rCandidate.getY() == pSmallest->getY() && rCandidate.getZ() < pSmallest->getZ()))
+                {
+                    nISmallest = a;
+                    pSmallest = &rCandidate;
+                }
+            }
+
+            // look for a next point different from minimal one
+            for(a = (nISmallest + 1) % nPointCount; a != nISmallest; a = (a + 1) % nPointCount)
+            {
+                const basegfx::B3DPoint& rCandidate = maVector[a].getCoordinate();
+
+                if(!rCandidate.equal(*pSmallest))
+                {
+                    pNext = &rCandidate;
+                    break;
+                }
+            }
+
+            // look for a previous point different from minimal one
+            for(a = (nISmallest + nPointCount - 1) % nPointCount; a != nISmallest; a = (a + nPointCount - 1) % nPointCount)
+            {
+                const basegfx::B3DPoint& rCandidate = maVector[a].getCoordinate();
+
+                if(!rCandidate.equal(*pSmallest))
+                {
+                    pPrev = &rCandidate;
+                    break;
+                }
+            }
+
+            // we always have a minimal point. If we also have a different next and previous,
+            // we can calculate the normal
+            if(pNext && pPrev)
+            {
+                const basegfx::B3DVector aPrev(*pPrev - *pSmallest);
+                const basegfx::B3DVector aNext(*pNext - *pSmallest);
+
+                aRetval = cross(aPrev, aNext);
+                aRetval.normalize();
+            }
+        }
+
+        return aRetval;
+    }
+
+    sal_uInt32 count() const
+    {
+        return maVector.size();
+    }
+
+    bool operator==(const CoordinateDataArray3D& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    const basegfx::B3DPoint& getCoordinate(sal_uInt32 nIndex) const
+    {
+        return maVector[nIndex].getCoordinate();
+    }
+
+    void setCoordinate(sal_uInt32 nIndex, const basegfx::B3DPoint& rValue)
+    {
+        maVector[nIndex].setCoordinate(rValue);
+    }
+
+    void insert(sal_uInt32 nIndex, const CoordinateData3D& rValue, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // add nCount copies of rValue
+            CoordinateData3DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            maVector.insert(aIndex, nCount, rValue);
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const CoordinateDataArray3D& rSource)
+    {
+        const sal_uInt32 nCount(rSource.maVector.size());
+
+        if(nCount)
+        {
+            // insert data
+            CoordinateData3DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            CoordinateData3DVector::const_iterator aStart(rSource.maVector.begin());
+            CoordinateData3DVector::const_iterator aEnd(rSource.maVector.end());
+            maVector.insert(aIndex, aStart, aEnd);
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // remove point data
+            CoordinateData3DVector::iterator aStart(maVector.begin());
+            aStart += nIndex;
+            const CoordinateData3DVector::iterator aEnd(aStart + nCount);
+            maVector.erase(aStart, aEnd);
+        }
+    }
+
+    void flip()
+    {
+        if(maVector.size() <= 1)
+            return;
+
+        const sal_uInt32 nHalfSize(maVector.size() >> 1);
+        CoordinateData3DVector::iterator aStart(maVector.begin());
+        CoordinateData3DVector::iterator aEnd(maVector.end() - 1);
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            std::swap(*aStart, *aEnd);
+            ++aStart;
+            --aEnd;
+        }
+    }
+
+    void transform(const ::basegfx::B3DHomMatrix& rMatrix)
+    {
+        for (auto & elem : maVector)
+        {
+            elem.transform(rMatrix);
+        }
+    }
+};
+
+class BColorArray
+{
+    typedef std::vector< ::basegfx::BColor > BColorDataVector;
+
+    BColorDataVector                                    maVector;
+    sal_uInt32                                          mnUsedEntries;
+
+public:
+    explicit BColorArray(sal_uInt32 nCount)
+    :   maVector(nCount),
+        mnUsedEntries(0)
+    {
+    }
+
+    BColorArray(const BColorArray& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   mnUsedEntries(0)
+    {
+        BColorDataVector::const_iterator aStart(rOriginal.maVector.begin());
+        aStart += nIndex;
+        BColorDataVector::const_iterator aEnd(aStart);
+        assert(nCount <= rOriginal.maVector.size());
+        aEnd += nCount;
+        maVector.reserve(nCount);
+
+        for(; aStart != aEnd; ++aStart)
+        {
+            if(!aStart->equalZero())
+                mnUsedEntries++;
+
+            maVector.push_back(*aStart);
+        }
+    }
+
+    bool operator==(const BColorArray& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    bool isUsed() const
+    {
+        return (mnUsedEntries != 0);
+    }
+
+    const ::basegfx::BColor& getBColor(sal_uInt32 nIndex) const
+    {
+        return maVector[nIndex];
+    }
+
+    void setBColor(sal_uInt32 nIndex, const ::basegfx::BColor& rValue)
+    {
+        bool bWasUsed(mnUsedEntries && !maVector[nIndex].equalZero());
+        bool bIsUsed(!rValue.equalZero());
+
+        if(bWasUsed)
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+            }
+            else
+            {
+                maVector[nIndex] = ::basegfx::BColor::getEmptyBColor();
+                mnUsedEntries--;
+            }
+        }
+        else
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+                mnUsedEntries++;
+            }
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::BColor& rValue, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // add nCount copies of rValue
+            BColorDataVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            maVector.insert(aIndex, nCount, rValue);
+
+            if(!rValue.equalZero())
+                mnUsedEntries += nCount;
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const BColorArray& rSource)
+    {
+        const sal_uInt32 nCount(rSource.maVector.size());
+
+        if(nCount)
+        {
+            // insert data
+            BColorDataVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            BColorDataVector::const_iterator aStart(rSource.maVector.begin());
+            BColorDataVector::const_iterator aEnd(rSource.maVector.end());
+            maVector.insert(aIndex, aStart, aEnd);
+
+            mnUsedEntries += std::count_if(aStart, aEnd,
+                [](BColorDataVector::const_reference rData) { return !rData.equalZero(); });
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            const BColorDataVector::iterator aDeleteStart(maVector.begin() + nIndex);
+            const BColorDataVector::iterator aDeleteEnd(aDeleteStart + nCount);
+
+            auto nDeleteUsed = std::count_if(aDeleteStart, aDeleteEnd,
+                [](BColorDataVector::const_reference rData) { return !rData.equalZero(); });
+            mnUsedEntries -= std::min(mnUsedEntries, static_cast<sal_uInt32>(nDeleteUsed));
+
+            // remove point data
+            maVector.erase(aDeleteStart, aDeleteEnd);
+        }
+    }
+
+    void flip()
+    {
+        if(maVector.size() <= 1)
+            return;
+
+        const sal_uInt32 nHalfSize(maVector.size() >> 1);
+        BColorDataVector::iterator aStart(maVector.begin());
+        BColorDataVector::iterator aEnd(maVector.end() - 1);
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            std::swap(*aStart, *aEnd);
+            ++aStart;
+            --aEnd;
+        }
+    }
+};
+
+class NormalsArray3D
+{
+    typedef std::vector< ::basegfx::B3DVector > NormalsData3DVector;
+
+    NormalsData3DVector                                 maVector;
+    sal_uInt32                                          mnUsedEntries;
+
+public:
+    explicit NormalsArray3D(sal_uInt32 nCount)
+    :   maVector(nCount),
+        mnUsedEntries(0)
+    {
+    }
+
+    NormalsArray3D(const NormalsArray3D& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   mnUsedEntries(0)
+    {
+        NormalsData3DVector::const_iterator aStart(rOriginal.maVector.begin());
+        aStart += nIndex;
+        NormalsData3DVector::const_iterator aEnd(aStart);
+        aEnd += nCount;
+        maVector.reserve(nCount);
+
+        for(; aStart != aEnd; ++aStart)
+        {
+            if(!aStart->equalZero())
+                mnUsedEntries++;
+
+            maVector.push_back(*aStart);
+        }
+    }
+
+    bool operator==(const NormalsArray3D& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    bool isUsed() const
+    {
+        return (mnUsedEntries != 0);
+    }
+
+    const ::basegfx::B3DVector& getNormal(sal_uInt32 nIndex) const
+    {
+        return maVector[nIndex];
+    }
+
+    void setNormal(sal_uInt32 nIndex, const ::basegfx::B3DVector& rValue)
+    {
+        bool bWasUsed(mnUsedEntries && !maVector[nIndex].equalZero());
+        bool bIsUsed(!rValue.equalZero());
+
+        if(bWasUsed)
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+            }
+            else
+            {
+                maVector[nIndex] = ::basegfx::B3DVector::getEmptyVector();
+                mnUsedEntries--;
+            }
+        }
+        else
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+                mnUsedEntries++;
+            }
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::B3DVector& rValue, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // add nCount copies of rValue
+            NormalsData3DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            maVector.insert(aIndex, nCount, rValue);
+
+            if(!rValue.equalZero())
+                mnUsedEntries += nCount;
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const NormalsArray3D& rSource)
+    {
+        const sal_uInt32 nCount(rSource.maVector.size());
+
+        if(nCount)
+        {
+            // insert data
+            NormalsData3DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            NormalsData3DVector::const_iterator aStart(rSource.maVector.begin());
+            NormalsData3DVector::const_iterator aEnd(rSource.maVector.end());
+            maVector.insert(aIndex, aStart, aEnd);
+
+            mnUsedEntries += std::count_if(aStart, aEnd,
+                [](NormalsData3DVector::const_reference rData) { return !rData.equalZero(); });
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            const NormalsData3DVector::iterator aDeleteStart(maVector.begin() + nIndex);
+            const NormalsData3DVector::iterator aDeleteEnd(aDeleteStart + nCount);
+
+            auto nDeleteUsed = std::count_if(aDeleteStart, aDeleteEnd,
+                [](NormalsData3DVector::const_reference rData) { return !rData.equalZero(); });
+            mnUsedEntries -= std::min(mnUsedEntries, static_cast<sal_uInt32>(nDeleteUsed));
+
+            // remove point data
+            maVector.erase(aDeleteStart, aDeleteEnd);
+        }
+    }
+
+    void flip()
+    {
+        if(maVector.size() <= 1)
+            return;
+
+        const sal_uInt32 nHalfSize(maVector.size() >> 1);
+        NormalsData3DVector::iterator aStart(maVector.begin());
+        NormalsData3DVector::iterator aEnd(maVector.end() - 1);
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            std::swap(*aStart, *aEnd);
+            ++aStart;
+            --aEnd;
+        }
+    }
+
+    void transform(const basegfx::B3DHomMatrix& rMatrix)
+    {
+        for (auto & elem : maVector)
+        {
+            elem *= rMatrix;
+        }
+    }
+};
+
+class TextureCoordinate2D
+{
+    typedef std::vector< ::basegfx::B2DPoint > TextureData2DVector;
+
+    TextureData2DVector                                 maVector;
+    sal_uInt32                                          mnUsedEntries;
+
+public:
+    explicit TextureCoordinate2D(sal_uInt32 nCount)
+    :   maVector(nCount),
+        mnUsedEntries(0)
+    {
+    }
+
+    TextureCoordinate2D(const TextureCoordinate2D& rOriginal, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   mnUsedEntries(0)
+    {
+        TextureData2DVector::const_iterator aStart(rOriginal.maVector.begin());
+        aStart += nIndex;
+        TextureData2DVector::const_iterator aEnd(aStart);
+        aEnd += nCount;
+        maVector.reserve(nCount);
+
+        for(; aStart != aEnd; ++aStart)
+        {
+            if(!aStart->equalZero())
+                mnUsedEntries++;
+
+            maVector.push_back(*aStart);
+        }
+    }
+
+    bool operator==(const TextureCoordinate2D& rCandidate) const
+    {
+        return (maVector == rCandidate.maVector);
+    }
+
+    bool isUsed() const
+    {
+        return (mnUsedEntries != 0);
+    }
+
+    const ::basegfx::B2DPoint& getTextureCoordinate(sal_uInt32 nIndex) const
+    {
+        return maVector[nIndex];
+    }
+
+    void setTextureCoordinate(sal_uInt32 nIndex, const ::basegfx::B2DPoint& rValue)
+    {
+        bool bWasUsed(mnUsedEntries && !maVector[nIndex].equalZero());
+        bool bIsUsed(!rValue.equalZero());
+
+        if(bWasUsed)
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+            }
+            else
+            {
+                maVector[nIndex] = ::basegfx::B2DPoint::getEmptyPoint();
+                mnUsedEntries--;
+            }
+        }
+        else
+        {
+            if(bIsUsed)
+            {
+                maVector[nIndex] = rValue;
+                mnUsedEntries++;
+            }
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::B2DPoint& rValue, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // add nCount copies of rValue
+            TextureData2DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            maVector.insert(aIndex, nCount, rValue);
+
+            if(!rValue.equalZero())
+                mnUsedEntries += nCount;
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const TextureCoordinate2D& rSource)
+    {
+        const sal_uInt32 nCount(rSource.maVector.size());
+
+        if(nCount)
+        {
+            // insert data
+            TextureData2DVector::iterator aIndex(maVector.begin());
+            aIndex += nIndex;
+            TextureData2DVector::const_iterator aStart(rSource.maVector.begin());
+            TextureData2DVector::const_iterator aEnd(rSource.maVector.end());
+            maVector.insert(aIndex, aStart, aEnd);
+
+            mnUsedEntries += std::count_if(aStart, aEnd,
+                [](TextureData2DVector::const_reference rData) { return !rData.equalZero(); });
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            const TextureData2DVector::iterator aDeleteStart(maVector.begin() + nIndex);
+            const TextureData2DVector::iterator aDeleteEnd(aDeleteStart + nCount);
+
+            auto nDeleteUsed = std::count_if(aDeleteStart, aDeleteEnd,
+                [](TextureData2DVector::const_reference rData) { return !rData.equalZero(); });
+            mnUsedEntries -= std::min(mnUsedEntries, static_cast<sal_uInt32>(nDeleteUsed));
+
+            // remove point data
+            maVector.erase(aDeleteStart, aDeleteEnd);
+        }
+    }
+
+    void flip()
+    {
+        if(maVector.size() <= 1)
+            return;
+
+        const sal_uInt32 nHalfSize(maVector.size() >> 1);
+        TextureData2DVector::iterator aStart(maVector.begin());
+        TextureData2DVector::iterator aEnd(maVector.end() - 1);
+
+        for(sal_uInt32 a(0); a < nHalfSize; a++)
+        {
+            std::swap(*aStart, *aEnd);
+            ++aStart;
+            --aEnd;
+        }
+    }
+
+    void transform(const ::basegfx::B2DHomMatrix& rMatrix)
+    {
+        for (auto & elem : maVector)
+        {
+            elem *= rMatrix;
+        }
+    }
+};
+
+}
+
+class ImplB3DPolygon
+{
+    // The point vector. This vector exists always and defines the
+    // count of members.
+    CoordinateDataArray3D                           maPoints;
+
+    // The BColor vector. This vectors are created on demand
+    // and may be zero.
+    std::unique_ptr<BColorArray>                    mpBColors;
+
+    // The Normals vector. This vectors are created on demand
+    // and may be zero.
+    std::unique_ptr<NormalsArray3D>                 mpNormals;
+
+    // The TextureCoordinates vector. This vectors are created on demand
+    // and may be zero.
+    std::unique_ptr<TextureCoordinate2D>            mpTextureCoordinates;
+
+    // The calculated plane normal. mbPlaneNormalValid says if it's valid.
+    ::basegfx::B3DVector                            maPlaneNormal;
+
+    // flag which decides if this polygon is opened or closed
+    bool                                            mbIsClosed : 1;
+
+    // flag which says if maPlaneNormal is up-to-date
+    bool                                            mbPlaneNormalValid : 1;
+
+protected:
+    void invalidatePlaneNormal()
+    {
+        if(mbPlaneNormalValid)
+        {
+            mbPlaneNormalValid = false;
+        }
+    }
+
+public:
+    // This constructor is only used from the static identity polygon, thus
+    // the RefCount is set to 1 to never 'delete' this static incarnation.
+    ImplB3DPolygon()
+    :   maPoints(0),
+        maPlaneNormal(::basegfx::B3DVector::getEmptyVector()),
+        mbIsClosed(false),
+        mbPlaneNormalValid(true)
+    {
+        // complete initialization with defaults
+    }
+
+    ImplB3DPolygon(const ImplB3DPolygon& rToBeCopied)
+    :   maPoints(rToBeCopied.maPoints),
+        maPlaneNormal(rToBeCopied.maPlaneNormal),
+        mbIsClosed(rToBeCopied.mbIsClosed),
+        mbPlaneNormalValid(rToBeCopied.mbPlaneNormalValid)
+    {
+        // complete initialization using copy
+        if(rToBeCopied.mpBColors && rToBeCopied.mpBColors->isUsed())
+        {
+            mpBColors.reset( new BColorArray(*rToBeCopied.mpBColors) );
+        }
+
+        if(rToBeCopied.mpNormals && rToBeCopied.mpNormals->isUsed())
+        {
+            mpNormals.reset( new NormalsArray3D(*rToBeCopied.mpNormals) );
+        }
+
+        if(rToBeCopied.mpTextureCoordinates && rToBeCopied.mpTextureCoordinates->isUsed())
+        {
+            mpTextureCoordinates.reset( new TextureCoordinate2D(*rToBeCopied.mpTextureCoordinates) );
+        }
+    }
+
+    ImplB3DPolygon(const ImplB3DPolygon& rToBeCopied, sal_uInt32 nIndex, sal_uInt32 nCount)
+    :   maPoints(rToBeCopied.maPoints, nIndex, nCount),
+        maPlaneNormal(::basegfx::B3DVector::getEmptyVector()),
+        mbIsClosed(rToBeCopied.mbIsClosed),
+        mbPlaneNormalValid(false)
+    {
+        // complete initialization using partly copy
+        if(rToBeCopied.mpBColors && rToBeCopied.mpBColors->isUsed())
+        {
+            mpBColors.reset( new BColorArray(*rToBeCopied.mpBColors, nIndex, nCount) );
+
+            if(!mpBColors->isUsed())
+            {
+                mpBColors.reset();
+            }
+        }
+
+        if(rToBeCopied.mpNormals && rToBeCopied.mpNormals->isUsed())
+        {
+            mpNormals.reset( new NormalsArray3D(*rToBeCopied.mpNormals, nIndex, nCount) );
+
+            if(!mpNormals->isUsed())
+            {
+                mpNormals.reset();
+            }
+        }
+
+        if(rToBeCopied.mpTextureCoordinates && rToBeCopied.mpTextureCoordinates->isUsed())
+        {
+            mpTextureCoordinates.reset( new TextureCoordinate2D(*rToBeCopied.mpTextureCoordinates, nIndex, nCount) );
+
+            if(!mpTextureCoordinates->isUsed())
+            {
+                mpTextureCoordinates.reset();
+            }
+        }
+    }
+
+    sal_uInt32 count() const
+    {
+        return maPoints.count();
+    }
+
+    bool isClosed() const
+    {
+        return mbIsClosed;
+    }
+
+    void setClosed(bool bNew)
+    {
+        if(bNew != mbIsClosed)
+        {
+            mbIsClosed = bNew;
+        }
+    }
+
+    bool impBColorsAreEqual(const ImplB3DPolygon& rCandidate) const
+    {
+        bool bBColorsAreEqual(true);
+
+        if(mpBColors)
+        {
+            if(rCandidate.mpBColors)
+            {
+                bBColorsAreEqual = (*mpBColors == *rCandidate.mpBColors);
+            }
+            else
+            {
+                // candidate has no BColors, so it's assumed all unused.
+                bBColorsAreEqual = !mpBColors->isUsed();
+            }
+        }
+        else
+        {
+            if(rCandidate.mpBColors)
+            {
+                // we have no TextureCoordinates, so it's assumed all unused.
+                bBColorsAreEqual = !rCandidate.mpBColors->isUsed();
+            }
+        }
+
+        return bBColorsAreEqual;
+    }
+
+    bool impNormalsAreEqual(const ImplB3DPolygon& rCandidate) const
+    {
+        bool bNormalsAreEqual(true);
+
+        if(mpNormals)
+        {
+            if(rCandidate.mpNormals)
+            {
+                bNormalsAreEqual = (*mpNormals == *rCandidate.mpNormals);
+            }
+            else
+            {
+                // candidate has no normals, so it's assumed all unused.
+                bNormalsAreEqual = !mpNormals->isUsed();
+            }
+        }
+        else
+        {
+            if(rCandidate.mpNormals)
+            {
+                // we have no normals, so it's assumed all unused.
+                bNormalsAreEqual = !rCandidate.mpNormals->isUsed();
+            }
+        }
+
+        return bNormalsAreEqual;
+    }
+
+    bool impTextureCoordinatesAreEqual(const ImplB3DPolygon& rCandidate) const
+    {
+        bool bTextureCoordinatesAreEqual(true);
+
+        if(mpTextureCoordinates)
+        {
+            if(rCandidate.mpTextureCoordinates)
+            {
+                bTextureCoordinatesAreEqual = (*mpTextureCoordinates == *rCandidate.mpTextureCoordinates);
+            }
+            else
+            {
+                // candidate has no TextureCoordinates, so it's assumed all unused.
+                bTextureCoordinatesAreEqual = !mpTextureCoordinates->isUsed();
+            }
+        }
+        else
+        {
+            if(rCandidate.mpTextureCoordinates)
+            {
+                // we have no TextureCoordinates, so it's assumed all unused.
+                bTextureCoordinatesAreEqual = !rCandidate.mpTextureCoordinates->isUsed();
+            }
+        }
+
+        return bTextureCoordinatesAreEqual;
+    }
+
+    bool operator==(const ImplB3DPolygon& rCandidate) const
+    {
+        if(mbIsClosed == rCandidate.mbIsClosed)
+        {
+            if(maPoints == rCandidate.maPoints)
+            {
+                if(impBColorsAreEqual(rCandidate))
+                {
+                    if(impNormalsAreEqual(rCandidate))
+                    {
+                        if(impTextureCoordinatesAreEqual(rCandidate))
+                        {
+                            return true;
+                        }
+                    }
+                }
+            }
+        }
+
+        return false;
+    }
+
+    const ::basegfx::B3DPoint& getPoint(sal_uInt32 nIndex) const
+    {
+        return maPoints.getCoordinate(nIndex);
+    }
+
+    void setPoint(sal_uInt32 nIndex, const ::basegfx::B3DPoint& rValue)
+    {
+        maPoints.setCoordinate(nIndex, rValue);
+        invalidatePlaneNormal();
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::B3DPoint& rPoint, sal_uInt32 nCount)
+    {
+        if(!nCount)
+            return;
+
+        CoordinateData3D aCoordinate(rPoint);
+        maPoints.insert(nIndex, aCoordinate, nCount);
+        invalidatePlaneNormal();
+
+        if(mpBColors)
+        {
+            mpBColors->insert(nIndex, ::basegfx::BColor::getEmptyBColor(), nCount);
+        }
+
+        if(mpNormals)
+        {
+            mpNormals->insert(nIndex, ::basegfx::B3DVector::getEmptyVector(), nCount);
+        }
+
+        if(mpTextureCoordinates)
+        {
+            mpTextureCoordinates->insert(nIndex, ::basegfx::B2DPoint::getEmptyPoint(), nCount);
+        }
+    }
+
+    const ::basegfx::BColor& getBColor(sal_uInt32 nIndex) const
+    {
+        if(mpBColors)
+        {
+            return mpBColors->getBColor(nIndex);
+        }
+        else
+        {
+            return ::basegfx::BColor::getEmptyBColor();
+        }
+    }
+
+    void setBColor(sal_uInt32 nIndex, const ::basegfx::BColor& rValue)
+    {
+        if(!mpBColors)
+        {
+            if(!rValue.equalZero())
+            {
+                mpBColors.reset( new BColorArray(maPoints.count()) );
+                mpBColors->setBColor(nIndex, rValue);
+            }
+        }
+        else
+        {
+            mpBColors->setBColor(nIndex, rValue);
+
+            if(!mpBColors->isUsed())
+            {
+                mpBColors.reset();
+            }
+        }
+    }
+
+    bool areBColorsUsed() const
+    {
+        return (mpBColors && mpBColors->isUsed());
+    }
+
+    void clearBColors()
+    {
+        mpBColors.reset();
+    }
+
+    const ::basegfx::B3DVector& getNormal() const
+    {
+        if(!mbPlaneNormalValid)
+        {
+            const_cast< ImplB3DPolygon* >(this)->maPlaneNormal = maPoints.getNormal();
+            const_cast< ImplB3DPolygon* >(this)->mbPlaneNormalValid = true;
+        }
+
+        return maPlaneNormal;
+    }
+
+    const ::basegfx::B3DVector& getNormal(sal_uInt32 nIndex) const
+    {
+        if(mpNormals)
+        {
+            return mpNormals->getNormal(nIndex);
+        }
+        else
+        {
+            return ::basegfx::B3DVector::getEmptyVector();
+        }
+    }
+
+    void setNormal(sal_uInt32 nIndex, const ::basegfx::B3DVector& rValue)
+    {
+        if(!mpNormals)
+        {
+            if(!rValue.equalZero())
+            {
+                mpNormals.reset( new NormalsArray3D(maPoints.count()) );
+                mpNormals->setNormal(nIndex, rValue);
+            }
+        }
+        else
+        {
+            mpNormals->setNormal(nIndex, rValue);
+
+            if(!mpNormals->isUsed())
+            {
+                mpNormals.reset();
+            }
+        }
+    }
+
+    void transformNormals(const ::basegfx::B3DHomMatrix& rMatrix)
+    {
+        if(mpNormals)
+        {
+            mpNormals->transform(rMatrix);
+        }
+    }
+
+    bool areNormalsUsed() const
+    {
+        return (mpNormals && mpNormals->isUsed());
+    }
+
+    void clearNormals()
+    {
+        mpNormals.reset();
+    }
+
+    const ::basegfx::B2DPoint& getTextureCoordinate(sal_uInt32 nIndex) const
+    {
+        if(mpTextureCoordinates)
+        {
+            return mpTextureCoordinates->getTextureCoordinate(nIndex);
+        }
+        else
+        {
+            return ::basegfx::B2DPoint::getEmptyPoint();
+        }
+    }
+
+    void setTextureCoordinate(sal_uInt32 nIndex, const ::basegfx::B2DPoint& rValue)
+    {
+        if(!mpTextureCoordinates)
+        {
+            if(!rValue.equalZero())
+            {
+                mpTextureCoordinates.reset( new TextureCoordinate2D(maPoints.count()) );
+                mpTextureCoordinates->setTextureCoordinate(nIndex, rValue);
+            }
+        }
+        else
+        {
+            mpTextureCoordinates->setTextureCoordinate(nIndex, rValue);
+
+            if(!mpTextureCoordinates->isUsed())
+            {
+                mpTextureCoordinates.reset();
+            }
+        }
+    }
+
+    bool areTextureCoordinatesUsed() const
+    {
+        return (mpTextureCoordinates && mpTextureCoordinates->isUsed());
+    }
+
+    void clearTextureCoordinates()
+    {
+        mpTextureCoordinates.reset();
+    }
+
+    void transformTextureCoordinates(const ::basegfx::B2DHomMatrix& rMatrix)
+    {
+        if(mpTextureCoordinates)
+        {
+            mpTextureCoordinates->transform(rMatrix);
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const ImplB3DPolygon& rSource)
+    {
+        const sal_uInt32 nCount(rSource.maPoints.count());
+
+        if(!nCount)
+            return;
+
+        maPoints.insert(nIndex, rSource.maPoints);
+        invalidatePlaneNormal();
+
+        if(rSource.mpBColors && rSource.mpBColors->isUsed())
+        {
+            if(!mpBColors)
+            {
+                mpBColors.reset( new BColorArray(maPoints.count()) );
+            }
+
+            mpBColors->insert(nIndex, *rSource.mpBColors);
+        }
+        else
+        {
+            if(mpBColors)
+            {
+                mpBColors->insert(nIndex, ::basegfx::BColor::getEmptyBColor(), nCount);
+            }
+        }
+
+        if(rSource.mpNormals && rSource.mpNormals->isUsed())
+        {
+            if(!mpNormals)
+            {
+                mpNormals.reset( new NormalsArray3D(maPoints.count()) );
+            }
+
+            mpNormals->insert(nIndex, *rSource.mpNormals);
+        }
+        else
+        {
+            if(mpNormals)
+            {
+                mpNormals->insert(nIndex, ::basegfx::B3DVector::getEmptyVector(), nCount);
+            }
+        }
+
+        if(rSource.mpTextureCoordinates && rSource.mpTextureCoordinates->isUsed())
+        {
+            if(!mpTextureCoordinates)
+            {
+                mpTextureCoordinates.reset( new TextureCoordinate2D(maPoints.count()) );
+            }
+
+            mpTextureCoordinates->insert(nIndex, *rSource.mpTextureCoordinates);
+        }
+        else
+        {
+            if(mpTextureCoordinates)
+            {
+                mpTextureCoordinates->insert(nIndex, ::basegfx::B2DPoint::getEmptyPoint(), nCount);
+            }
+        }
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(!nCount)
+            return;
+
+        maPoints.remove(nIndex, nCount);
+        invalidatePlaneNormal();
+
+        if(mpBColors)
+        {
+            mpBColors->remove(nIndex, nCount);
+
+            if(!mpBColors->isUsed())
+            {
+                mpBColors.reset();
+            }
+        }
+
+        if(mpNormals)
+        {
+            mpNormals->remove(nIndex, nCount);
+
+            if(!mpNormals->isUsed())
+            {
+                mpNormals.reset();
+            }
+        }
+
+        if(mpTextureCoordinates)
+        {
+            mpTextureCoordinates->remove(nIndex, nCount);
+
+            if(!mpTextureCoordinates->isUsed())
+            {
+                mpTextureCoordinates.reset();
+            }
+        }
+    }
+
+    void flip()
+    {
+        if(maPoints.count() <= 1)
+            return;
+
+        maPoints.flip();
+
+        if(mbPlaneNormalValid)
+        {
+            // mirror plane normal
+            maPlaneNormal = -maPlaneNormal;
+        }
+
+        if(mpBColors)
+        {
+            mpBColors->flip();
+        }
+
+        if(mpNormals)
+        {
+            mpNormals->flip();
+        }
+
+        if(mpTextureCoordinates)
+        {
+            mpTextureCoordinates->flip();
+        }
+    }
+
+    bool hasDoublePoints() const
+    {
+        if(mbIsClosed)
+        {
+            // check for same start and end point
+            const sal_uInt32 nIndex(maPoints.count() - 1);
+
+            if(maPoints.getCoordinate(0) == maPoints.getCoordinate(nIndex))
+            {
+                const bool bBColorEqual(!mpBColors || (mpBColors->getBColor(0) == mpBColors->getBColor(nIndex)));
+
+                if(bBColorEqual)
+                {
+                    const bool bNormalsEqual(!mpNormals || (mpNormals->getNormal(0) == mpNormals->getNormal(nIndex)));
+
+                    if(bNormalsEqual)
+                    {
+                        const bool bTextureCoordinatesEqual(!mpTextureCoordinates || (mpTextureCoordinates->getTextureCoordinate(0) == mpTextureCoordinates->getTextureCoordinate(nIndex)));
+
+                        if(bTextureCoordinatesEqual)
+                        {
+                            return true;
+                        }
+                    }
+                }
+            }
+        }
+
+        // test for range
+        for(sal_uInt32 a(0); a < maPoints.count() - 1; a++)
+        {
+            if(maPoints.getCoordinate(a) == maPoints.getCoordinate(a + 1))
+            {
+                const bool bBColorEqual(!mpBColors || (mpBColors->getBColor(a) == mpBColors->getBColor(a + 1)));
+
+                if(bBColorEqual)
+                {
+                    const bool bNormalsEqual(!mpNormals || (mpNormals->getNormal(a) == mpNormals->getNormal(a + 1)));
+
+                    if(bNormalsEqual)
+                    {
+                        const bool bTextureCoordinatesEqual(!mpTextureCoordinates || (mpTextureCoordinates->getTextureCoordinate(a) == mpTextureCoordinates->getTextureCoordinate(a + 1)));
+
+                        if(bTextureCoordinatesEqual)
+                        {
+                            return true;
+                        }
+                    }
+                }
+            }
+        }
+
+        return false;
+    }
+
+    void removeDoublePointsAtBeginEnd()
+    {
+        // Only remove DoublePoints at Begin and End when poly is closed
+        if(!mbIsClosed)
+            return;
+
+        bool bRemove;
+
+        do
+        {
+            bRemove = false;
+
+            if(maPoints.count() > 1)
+            {
+                const sal_uInt32 nIndex(maPoints.count() - 1);
+                bRemove = (maPoints.getCoordinate(0) == maPoints.getCoordinate(nIndex));
+
+                if(bRemove && mpBColors && mpBColors->getBColor(0) != mpBColors->getBColor(nIndex))
+                {
+                    bRemove = false;
+                }
+
+                if(bRemove && mpNormals && mpNormals->getNormal(0) != mpNormals->getNormal(nIndex))
+                {
+                    bRemove = false;
+                }
+
+                if(bRemove && mpTextureCoordinates && mpTextureCoordinates->getTextureCoordinate(0) != mpTextureCoordinates->getTextureCoordinate(nIndex))
+                {
+                    bRemove = false;
+                }
+            }
+
+            if(bRemove)
+            {
+                const sal_uInt32 nIndex(maPoints.count() - 1);
+                remove(nIndex, 1);
+            }
+        } while(bRemove);
+    }
+
+    void removeDoublePointsWholeTrack()
+    {
+        sal_uInt32 nIndex(0);
+
+        // test as long as there are at least two points and as long as the index
+        // is smaller or equal second last point
+        while((maPoints.count() > 1) && (nIndex <= maPoints.count() - 2))
+        {
+            const sal_uInt32 nNextIndex(nIndex + 1);
+            bool bRemove(maPoints.getCoordinate(nIndex) == maPoints.getCoordinate(nNextIndex));
+
+            if(bRemove && mpBColors && mpBColors->getBColor(nIndex) != mpBColors->getBColor(nNextIndex))
+            {
+                bRemove = false;
+            }
+
+            if(bRemove && mpNormals && mpNormals->getNormal(nIndex) != mpNormals->getNormal(nNextIndex))
+            {
+                bRemove = false;
+            }
+
+            if(bRemove && mpTextureCoordinates && mpTextureCoordinates->getTextureCoordinate(nIndex) != mpTextureCoordinates->getTextureCoordinate(nNextIndex))
+            {
+                bRemove = false;
+            }
+
+            if(bRemove)
+            {
+                // if next is same as index and the control vectors are unused, delete index
+                remove(nIndex, 1);
+            }
+            else
+            {
+                // if different, step forward
+                nIndex++;
+            }
+        }
+    }
+
+    void transform(const ::basegfx::B3DHomMatrix& rMatrix)
+    {
+        maPoints.transform(rMatrix);
+
+        // Here, it seems to be possible to transform a valid plane normal and to avoid
+        // invalidation, but it's not true. If the transformation contains shears or e.g.
+        // perspective projection, the orthogonality to the transformed plane will not
+        // be preserved. It may be possible to test that at the matrix to not invalidate in
+        // all cases or to extract a matrix which does not 'shear' the vector which is
+        // a normal in this case. As long as this is not sure, i will just invalidate.
+        invalidatePlaneNormal();
+    }
+};
+
+namespace basegfx
+{
+    namespace {
+
+    B3DPolygon::ImplType const & getDefaultPolygon() {
+        static B3DPolygon::ImplType const singleton;
+        return singleton;
+    }
+
+    }
+
+    B3DPolygon::B3DPolygon() :
+        mpPolygon(getDefaultPolygon())
+    {
+    }
+
+    B3DPolygon::B3DPolygon(const B3DPolygon&) = default;
+
+    B3DPolygon::B3DPolygon(B3DPolygon&&) = default;
+
+    B3DPolygon::~B3DPolygon() = default;
+
+    B3DPolygon& B3DPolygon::operator=(const B3DPolygon&) = default;
+
+    B3DPolygon& B3DPolygon::operator=(B3DPolygon&&) = default;
+
+    bool B3DPolygon::operator==(const B3DPolygon& rPolygon) const
+    {
+        if(mpPolygon.same_object(rPolygon.mpPolygon))
+            return true;
+
+        return (*mpPolygon == *rPolygon.mpPolygon);
+    }
+
+    sal_uInt32 B3DPolygon::count() const
+    {
+        return mpPolygon->count();
+    }
+
+    basegfx::B3DPoint const & B3DPolygon::getB3DPoint(sal_uInt32 nIndex) const
+    {
+        OSL_ENSURE(nIndex < mpPolygon->count(), "B3DPolygon access outside range (!)");
+
+        return mpPolygon->getPoint(nIndex);
+    }
+
+    void B3DPolygon::setB3DPoint(sal_uInt32 nIndex, const basegfx::B3DPoint& rValue)
+    {
+        OSL_ENSURE(nIndex < std::as_const(mpPolygon)->count(), "B3DPolygon access outside range (!)");
+
+        if(getB3DPoint(nIndex) != rValue)
+            mpPolygon->setPoint(nIndex, rValue);
+    }
+
+    BColor const & B3DPolygon::getBColor(sal_uInt32 nIndex) const
+    {
+        OSL_ENSURE(nIndex < mpPolygon->count(), "B3DPolygon access outside range (!)");
+
+        return mpPolygon->getBColor(nIndex);
+    }
+
+    void B3DPolygon::setBColor(sal_uInt32 nIndex, const BColor& rValue)
+    {
+        OSL_ENSURE(nIndex < std::as_const(mpPolygon)->count(), "B3DPolygon access outside range (!)");
+
+        if(std::as_const(mpPolygon)->getBColor(nIndex) != rValue)
+            mpPolygon->setBColor(nIndex, rValue);
+    }
+
+    bool B3DPolygon::areBColorsUsed() const
+    {
+        return mpPolygon->areBColorsUsed();
+    }
+
+    void B3DPolygon::clearBColors()
+    {
+        if(std::as_const(mpPolygon)->areBColorsUsed())
+            mpPolygon->clearBColors();
+    }
+
+    B3DVector const & B3DPolygon::getNormal() const
+    {
+        return mpPolygon->getNormal();
+    }
+
+    B3DVector const & B3DPolygon::getNormal(sal_uInt32 nIndex) const
+    {
+        OSL_ENSURE(nIndex < mpPolygon->count(), "B3DPolygon access outside range (!)");
+
+        return mpPolygon->getNormal(nIndex);
+    }
+
+    void B3DPolygon::setNormal(sal_uInt32 nIndex, const B3DVector& rValue)
+    {
+        OSL_ENSURE(nIndex < std::as_const(mpPolygon)->count(), "B3DPolygon access outside range (!)");
+
+        if(std::as_const(mpPolygon)->getNormal(nIndex) != rValue)
+            mpPolygon->setNormal(nIndex, rValue);
+    }
+
+    void B3DPolygon::transformNormals(const B3DHomMatrix& rMatrix)
+    {
+        if(std::as_const(mpPolygon)->areNormalsUsed() && !rMatrix.isIdentity())
+            mpPolygon->transformNormals(rMatrix);
+    }
+
+    bool B3DPolygon::areNormalsUsed() const
+    {
+        return mpPolygon->areNormalsUsed();
+    }
+
+    void B3DPolygon::clearNormals()
+    {
+        if(std::as_const(mpPolygon)->areNormalsUsed())
+            mpPolygon->clearNormals();
+    }
+
+    B2DPoint const & B3DPolygon::getTextureCoordinate(sal_uInt32 nIndex) const
+    {
+        OSL_ENSURE(nIndex < mpPolygon->count(), "B3DPolygon access outside range (!)");
+
+        return mpPolygon->getTextureCoordinate(nIndex);
+    }
+
+    void B3DPolygon::setTextureCoordinate(sal_uInt32 nIndex, const B2DPoint& rValue)
+    {
+        OSL_ENSURE(nIndex < std::as_const(mpPolygon)->count(), "B3DPolygon access outside range (!)");
+
+        if(std::as_const(mpPolygon)->getTextureCoordinate(nIndex) != rValue)
+            mpPolygon->setTextureCoordinate(nIndex, rValue);
+    }
+
+    void B3DPolygon::transformTextureCoordinates(const B2DHomMatrix& rMatrix)
+    {
+        if(std::as_const(mpPolygon)->areTextureCoordinatesUsed() && !rMatrix.isIdentity())
+            mpPolygon->transformTextureCoordinates(rMatrix);
+    }
+
+    bool B3DPolygon::areTextureCoordinatesUsed() const
+    {
+        return mpPolygon->areTextureCoordinatesUsed();
+    }
+
+    void B3DPolygon::clearTextureCoordinates()
+    {
+        if(std::as_const(mpPolygon)->areTextureCoordinatesUsed())
+            mpPolygon->clearTextureCoordinates();
+    }
+
+    void B3DPolygon::append(const basegfx::B3DPoint& rPoint, sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolygon->insert(std::as_const(mpPolygon)->count(), rPoint, nCount);
+    }
+
+    void B3DPolygon::append(const B3DPolygon& rPoly, sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(!rPoly.count())
+            return;
+
+        if(!nCount)
+        {
+            nCount = rPoly.count();
+        }
+
+        if(nIndex == 0 && nCount == rPoly.count())
+        {
+            mpPolygon->insert(std::as_const(mpPolygon)->count(), *rPoly.mpPolygon);
+        }
+        else
+        {
+            OSL_ENSURE(nIndex + nCount <= rPoly.mpPolygon->count(), "B3DPolygon Append outside range (!)");
+            ImplB3DPolygon aTempPoly(*rPoly.mpPolygon, nIndex, nCount);
+            mpPolygon->insert(std::as_const(mpPolygon)->count(), aTempPoly);
+        }
+    }
+
+    void B3DPolygon::remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        OSL_ENSURE(nIndex + nCount <= std::as_const(mpPolygon)->count(), "B3DPolygon Remove outside range (!)");
+
+        if(nCount)
+            mpPolygon->remove(nIndex, nCount);
+    }
+
+    void B3DPolygon::clear()
+    {
+        mpPolygon = getDefaultPolygon();
+    }
+
+    bool B3DPolygon::isClosed() const
+    {
+        return mpPolygon->isClosed();
+    }
+
+    void B3DPolygon::setClosed(bool bNew)
+    {
+        if(isClosed() != bNew)
+            mpPolygon->setClosed(bNew);
+    }
+
+    void B3DPolygon::flip()
+    {
+        if(count() > 1)
+            mpPolygon->flip();
+    }
+
+    bool B3DPolygon::hasDoublePoints() const
+    {
+        return (mpPolygon->count() > 1 && mpPolygon->hasDoublePoints());
+    }
+
+    void B3DPolygon::removeDoublePoints()
+    {
+        if(hasDoublePoints())
+        {
+            mpPolygon->removeDoublePointsAtBeginEnd();
+            mpPolygon->removeDoublePointsWholeTrack();
+        }
+    }
+
+    void B3DPolygon::transform(const basegfx::B3DHomMatrix& rMatrix)
+    {
+        if(std::as_const(mpPolygon)->count() && !rMatrix.isIdentity())
+        {
+            mpPolygon->transform(rMatrix);
+        }
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b3dpolygontools.cxx b/basegfx/source/polygon/b3dpolygontools.cxx
new file mode 100644
index 0000000000..7c92f5ddce
--- /dev/null
+++ b/basegfx/source/polygon/b3dpolygontools.cxx
@@ -0,0 +1,826 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <osl/diagnose.h>
+#include <basegfx/polygon/b3dpolygontools.hxx>
+#include <basegfx/polygon/b3dpolygon.hxx>
+#include <basegfx/polygon/b3dpolypolygon.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/range/b3drange.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/tuple/b3ituple.hxx>
+#include <cassert>
+#include <numeric>
+
+namespace basegfx::utils
+{
+        // B3DPolygon tools
+        void checkClosed(B3DPolygon& rCandidate)
+        {
+            while(rCandidate.count() > 1
+                && rCandidate.getB3DPoint(0).equal(rCandidate.getB3DPoint(rCandidate.count() - 1)))
+            {
+                rCandidate.setClosed(true);
+                rCandidate.remove(rCandidate.count() - 1);
+            }
+        }
+
+        sal_uInt32 getIndexOfSuccessor(sal_uInt32 nIndex, const B3DPolygon& rCandidate)
+        {
+            OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");
+
+            if(nIndex + 1 < rCandidate.count())
+            {
+                return nIndex + 1;
+            }
+            else
+            {
+                return 0;
+            }
+        }
+
+        B3DRange getRange(const B3DPolygon& rCandidate)
+        {
+            B3DRange aRetval;
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            for(sal_uInt32 a(0); a < nPointCount; a++)
+            {
+                const B3DPoint aTestPoint(rCandidate.getB3DPoint(a));
+                aRetval.expand(aTestPoint);
+            }
+
+            return aRetval;
+        }
+
+        double getLength(const B3DPolygon& rCandidate)
+        {
+            double fRetval(0.0);
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+
+                for(sal_uInt32 a(0); a < nLoopCount; a++)
+                {
+                    const sal_uInt32 nNextIndex(getIndexOfSuccessor(a, rCandidate));
+                    const B3DPoint aCurrentPoint(rCandidate.getB3DPoint(a));
+                    const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
+                    const B3DVector aVector(aNextPoint - aCurrentPoint);
+                    fRetval += aVector.getLength();
+                }
+            }
+
+            return fRetval;
+        }
+
+        void applyLineDashing(
+            const B3DPolygon& rCandidate,
+            const std::vector<double>& rDotDashArray,
+            B3DPolyPolygon* pLineTarget,
+            double fDotDashLength)
+        {
+            // clear targets in any case
+            if(pLineTarget)
+            {
+                pLineTarget->clear();
+            }
+
+            // provide callback as lambda
+            auto aLineCallback(
+                nullptr == pLineTarget
+                ? std::function<void(const basegfx::B3DPolygon&)>()
+                : [&pLineTarget](const basegfx::B3DPolygon& rSnippet){ pLineTarget->append(rSnippet); });
+
+            // call version that uses callbacks
+            applyLineDashing(
+                rCandidate,
+                rDotDashArray,
+                aLineCallback,
+                fDotDashLength);
+        }
+
+        static void implHandleSnippet(
+            const B3DPolygon& rSnippet,
+            const std::function<void(const basegfx::B3DPolygon& rSnippet)>& rTargetCallback,
+            B3DPolygon& rFirst,
+            B3DPolygon& rLast)
+        {
+            if(rSnippet.isClosed())
+            {
+                if(!rFirst.count())
+                {
+                    rFirst = rSnippet;
+                }
+                else
+                {
+                    if(rLast.count())
+                    {
+                        rTargetCallback(rLast);
+                    }
+
+                    rLast = rSnippet;
+                }
+            }
+            else
+            {
+                rTargetCallback(rSnippet);
+            }
+        }
+
+        static void implHandleFirstLast(
+            const std::function<void(const basegfx::B3DPolygon& rSnippet)>& rTargetCallback,
+            B3DPolygon& rFirst,
+            B3DPolygon& rLast)
+        {
+            if(rFirst.count() && rLast.count()
+                && rFirst.getB3DPoint(0).equal(rLast.getB3DPoint(rLast.count() - 1)))
+            {
+                // start of first and end of last are the same -> merge them
+                rLast.append(rFirst);
+                rLast.removeDoublePoints();
+                rFirst.clear();
+            }
+
+            if(rLast.count())
+            {
+                rTargetCallback(rLast);
+            }
+
+            if(rFirst.count())
+            {
+                rTargetCallback(rFirst);
+            }
+        }
+
+        void applyLineDashing(
+            const B3DPolygon& rCandidate,
+            const std::vector<double>& rDotDashArray,
+            const std::function<void(const basegfx::B3DPolygon& rSnippet)>& rLineTargetCallback,
+            double fDotDashLength)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+            const sal_uInt32 nDotDashCount(rDotDashArray.size());
+
+            if(fTools::lessOrEqual(fDotDashLength, 0.0))
+            {
+                fDotDashLength = std::accumulate(rDotDashArray.begin(), rDotDashArray.end(), 0.0);
+            }
+
+            if(fTools::lessOrEqual(fDotDashLength, 0.0) || !rLineTargetCallback || !nPointCount)
+            {
+                // parameters make no sense, just add source to targets
+                if (rLineTargetCallback)
+                    rLineTargetCallback(rCandidate);
+                return;
+            }
+
+            // precalculate maximal acceptable length of candidate polygon assuming
+            // we want to create a maximum of fNumberOfAllowedSnippets. In 3D
+            // use less for fNumberOfAllowedSnippets, ca. 6553.6, double due to line & gap.
+            // Less in 3D due to potentially blowing up to rounded line segments.
+            static const double fNumberOfAllowedSnippets(6553.5 * 2.0);
+            const double fAllowedLength((fNumberOfAllowedSnippets * fDotDashLength) / double(rDotDashArray.size()));
+            const double fCandidateLength(basegfx::utils::getLength(rCandidate));
+            std::vector<double> aDotDashArray(rDotDashArray);
+
+            if(fCandidateLength > fAllowedLength)
+            {
+                // we would produce more than fNumberOfAllowedSnippets, so
+                // adapt aDotDashArray to exactly produce assumed number. Also
+                // assert this to let the caller know about it.
+                // If this asserts: Please think about checking your DotDashArray
+                // before calling this function or evtl. use the callback version
+                // to *not* produce that much of data. Even then, you may still
+                // think about producing too much runtime (!)
+                assert(true && "applyLineDashing: potentially too expensive to do the requested dismantle - please consider stretched LineDash pattern (!)");
+
+                // calculate correcting factor, apply to aDotDashArray and fDotDashLength
+                // to enlarge these as needed
+                const double fFactor(fCandidateLength / fAllowedLength);
+                std::for_each(aDotDashArray.begin(), aDotDashArray.end(), [&fFactor](double &f){ f *= fFactor; });
+            }
+
+            // prepare current edge's start
+            B3DPoint aCurrentPoint(rCandidate.getB3DPoint(0));
+            const bool bIsClosed(rCandidate.isClosed());
+            const sal_uInt32 nEdgeCount(bIsClosed ? nPointCount : nPointCount - 1);
+
+            // prepare DotDashArray iteration and the line/gap switching bool
+            sal_uInt32 nDotDashIndex(0);
+            bool bIsLine(true);
+            double fDotDashMovingLength(aDotDashArray[0]);
+            B3DPolygon aSnippet;
+
+            // remember 1st and last snippets to try to merge after execution
+            // is complete and hand to callback
+            B3DPolygon aFirstLine, aLastLine;
+
+            // iterate over all edges
+            for(sal_uInt32 a(0); a < nEdgeCount; a++)
+            {
+                // update current edge
+                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
+                const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
+                const double fEdgeLength(B3DVector(aNextPoint - aCurrentPoint).getLength());
+
+                if(!fTools::equalZero(fEdgeLength))
+                {
+                    double fLastDotDashMovingLength(0.0);
+                    while(fTools::less(fDotDashMovingLength, fEdgeLength))
+                    {
+                        // new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
+                        if(bIsLine)
+                        {
+                            if(!aSnippet.count())
+                            {
+                                aSnippet.append(interpolate(aCurrentPoint, aNextPoint, fLastDotDashMovingLength / fEdgeLength));
+                            }
+
+                            aSnippet.append(interpolate(aCurrentPoint, aNextPoint, fDotDashMovingLength / fEdgeLength));
+
+                            implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
+
+                            aSnippet.clear();
+                        }
+
+                        // prepare next DotDashArray step and flip line/gap flag
+                        fLastDotDashMovingLength = fDotDashMovingLength;
+                        fDotDashMovingLength += aDotDashArray[(++nDotDashIndex) % nDotDashCount];
+                        bIsLine = !bIsLine;
+                    }
+
+                    // append snippet [fLastDotDashMovingLength, fEdgeLength]
+                    if(bIsLine)
+                    {
+                        if(!aSnippet.count())
+                        {
+                            aSnippet.append(interpolate(aCurrentPoint, aNextPoint, fLastDotDashMovingLength / fEdgeLength));
+                        }
+
+                        aSnippet.append(aNextPoint);
+                    }
+
+                    // prepare move to next edge
+                    fDotDashMovingLength -= fEdgeLength;
+                }
+
+                // prepare next edge step (end point gets new start point)
+                aCurrentPoint = aNextPoint;
+            }
+
+            // append last intermediate results (if exists)
+            if(aSnippet.count())
+            {
+                if(bIsLine)
+                {
+                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
+                }
+            }
+
+            if(bIsClosed)
+            {
+                implHandleFirstLast(rLineTargetCallback, aFirstLine, aLastLine);
+            }
+        }
+
+        B3DPolygon applyDefaultNormalsSphere( const B3DPolygon& rCandidate, const B3DPoint& rCenter)
+        {
+            B3DPolygon aRetval(rCandidate);
+
+            for(sal_uInt32 a(0); a < aRetval.count(); a++)
+            {
+                B3DVector aVector(aRetval.getB3DPoint(a) - rCenter);
+                aVector.normalize();
+                aRetval.setNormal(a, aVector);
+            }
+
+            return aRetval;
+        }
+
+        B3DPolygon invertNormals( const B3DPolygon& rCandidate)
+        {
+            B3DPolygon aRetval(rCandidate);
+
+            if(aRetval.areNormalsUsed())
+            {
+                for(sal_uInt32 a(0); a < aRetval.count(); a++)
+                {
+                    aRetval.setNormal(a, -aRetval.getNormal(a));
+                }
+            }
+
+            return aRetval;
+        }
+
+        B3DPolygon applyDefaultTextureCoordinatesParallel( const B3DPolygon& rCandidate, const B3DRange& rRange, bool bChangeX, bool bChangeY)
+        {
+            B3DPolygon aRetval(rCandidate);
+
+            if(bChangeX || bChangeY)
+            {
+                // create projection of standard texture coordinates in (X, Y) onto
+                // the 3d coordinates straight
+                const double fWidth(rRange.getWidth());
+                const double fHeight(rRange.getHeight());
+                const bool bWidthSet(!fTools::equalZero(fWidth));
+                const bool bHeightSet(!fTools::equalZero(fHeight));
+                const double fOne(1.0);
+
+                for(sal_uInt32 a(0); a < aRetval.count(); a++)
+                {
+                    const B3DPoint aPoint(aRetval.getB3DPoint(a));
+                    B2DPoint aTextureCoordinate(aRetval.getTextureCoordinate(a));
+
+                    if(bChangeX)
+                    {
+                        if(bWidthSet)
+                        {
+                            aTextureCoordinate.setX((aPoint.getX() - rRange.getMinX()) / fWidth);
+                        }
+                        else
+                        {
+                            aTextureCoordinate.setX(0.0);
+                        }
+                    }
+
+                    if(bChangeY)
+                    {
+                        if(bHeightSet)
+                        {
+                            aTextureCoordinate.setY(fOne - ((aPoint.getY() - rRange.getMinY()) / fHeight));
+                        }
+                        else
+                        {
+                            aTextureCoordinate.setY(fOne);
+                        }
+                    }
+
+                    aRetval.setTextureCoordinate(a, aTextureCoordinate);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B3DPolygon applyDefaultTextureCoordinatesSphere( const B3DPolygon& rCandidate, const B3DPoint& rCenter, bool bChangeX, bool bChangeY)
+        {
+            B3DPolygon aRetval(rCandidate);
+
+            if(bChangeX || bChangeY)
+            {
+                // create texture coordinates using sphere projection to cartesian coordinates,
+                // use object's center as base
+                const double fOne(1.0);
+                const sal_uInt32 nPointCount(aRetval.count());
+                bool bPolarPoints(false);
+                sal_uInt32 a;
+
+                // create center cartesian coordinates to have a possibility to decide if on boundary
+                // transitions which value to choose
+                const B3DRange aPlaneRange(getRange(rCandidate));
+                const B3DPoint aPlaneCenter(aPlaneRange.getCenter() - rCenter);
+                const double fXCenter(fOne - ((atan2(aPlaneCenter.getZ(), aPlaneCenter.getX()) + M_PI) / (2 * M_PI)));
+
+                for(a = 0; a < nPointCount; a++)
+                {
+                    const B3DVector aVector(aRetval.getB3DPoint(a) - rCenter);
+                    const double fY(fOne - ((atan2(aVector.getY(), aVector.getXZLength()) + M_PI_2) / M_PI));
+                    B2DPoint aTexCoor(aRetval.getTextureCoordinate(a));
+
+                    if(fTools::equalZero(fY))
+                    {
+                        // point is a north polar point, no useful X-coordinate can be created.
+                        if(bChangeY)
+                        {
+                            aTexCoor.setY(0.0);
+
+                            if(bChangeX)
+                            {
+                                bPolarPoints = true;
+                            }
+                        }
+                    }
+                    else if(fTools::equal(fY, fOne))
+                    {
+                        // point is a south polar point, no useful X-coordinate can be created. Set
+                        // Y-coordinate, though
+                        if(bChangeY)
+                        {
+                            aTexCoor.setY(fOne);
+
+                            if(bChangeX)
+                            {
+                                bPolarPoints = true;
+                            }
+                        }
+                    }
+                    else
+                    {
+                        double fX(fOne - ((atan2(aVector.getZ(), aVector.getX()) + M_PI) / (2 * M_PI)));
+
+                        // correct cartesian point coordinate dependent from center value
+                        if(fX > fXCenter + 0.5)
+                        {
+                            fX -= fOne;
+                        }
+                        else if(fX < fXCenter - 0.5)
+                        {
+                            fX += fOne;
+                        }
+
+                        if(bChangeX)
+                        {
+                            aTexCoor.setX(fX);
+                        }
+
+                        if(bChangeY)
+                        {
+                            aTexCoor.setY(fY);
+                        }
+                    }
+
+                    aRetval.setTextureCoordinate(a, aTexCoor);
+                }
+
+                if(bPolarPoints)
+                {
+                    // correct X-texture coordinates if polar points are contained. Those
+                    // coordinates cannot be correct, so use prev or next X-coordinate
+                    for(a = 0; a < nPointCount; a++)
+                    {
+                        B2DPoint aTexCoor(aRetval.getTextureCoordinate(a));
+
+                        if(fTools::equalZero(aTexCoor.getY()) || fTools::equal(aTexCoor.getY(), fOne))
+                        {
+                            // get prev, next TexCoor and test for pole
+                            const B2DPoint aPrevTexCoor(aRetval.getTextureCoordinate(a ? a - 1 : nPointCount - 1));
+                            const B2DPoint aNextTexCoor(aRetval.getTextureCoordinate((a + 1) % nPointCount));
+                            const bool bPrevPole(fTools::equalZero(aPrevTexCoor.getY()) || fTools::equal(aPrevTexCoor.getY(), fOne));
+                            const bool bNextPole(fTools::equalZero(aNextTexCoor.getY()) || fTools::equal(aNextTexCoor.getY(), fOne));
+
+                            if(!bPrevPole && !bNextPole)
+                            {
+                                // both no poles, mix them
+                                aTexCoor.setX((aPrevTexCoor.getX() + aNextTexCoor.getX()) / 2.0);
+                            }
+                            else if(!bNextPole)
+                            {
+                                // copy next
+                                aTexCoor.setX(aNextTexCoor.getX());
+                            }
+                            else
+                            {
+                                // copy prev, even if it's a pole, hopefully it is already corrected
+                                aTexCoor.setX(aPrevTexCoor.getX());
+                            }
+
+                            aRetval.setTextureCoordinate(a, aTexCoor);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        bool isInside(const B3DPolygon& rCandidate, const B3DPoint& rPoint, bool bWithBorder)
+        {
+            if(bWithBorder && isPointOnPolygon(rCandidate, rPoint))
+            {
+                return true;
+            }
+            else
+            {
+                bool bRetval(false);
+                const B3DVector aPlaneNormal(rCandidate.getNormal());
+
+                if(!aPlaneNormal.equalZero())
+                {
+                    const sal_uInt32 nPointCount(rCandidate.count());
+
+                    if(nPointCount)
+                    {
+                        B3DPoint aCurrentPoint(rCandidate.getB3DPoint(nPointCount - 1));
+                        const double fAbsX(fabs(aPlaneNormal.getX()));
+                        const double fAbsY(fabs(aPlaneNormal.getY()));
+                        const double fAbsZ(fabs(aPlaneNormal.getZ()));
+
+                        if(fAbsX > fAbsY && fAbsX > fAbsZ)
+                        {
+                            // normal points mostly in X-Direction, use YZ-Polygon projection for check
+                            // x -> y, y -> z
+                            for(sal_uInt32 a(0); a < nPointCount; a++)
+                            {
+                                const B3DPoint aPreviousPoint(aCurrentPoint);
+                                aCurrentPoint = rCandidate.getB3DPoint(a);
+
+                                // cross-over in Z?
+                                const bool bCompZA(fTools::more(aPreviousPoint.getZ(), rPoint.getZ()));
+                                const bool bCompZB(fTools::more(aCurrentPoint.getZ(), rPoint.getZ()));
+
+                                if(bCompZA != bCompZB)
+                                {
+                                    // cross-over in Y?
+                                    const bool bCompYA(fTools::more(aPreviousPoint.getY(), rPoint.getY()));
+                                    const bool bCompYB(fTools::more(aCurrentPoint.getY(), rPoint.getY()));
+
+                                    if(bCompYA == bCompYB)
+                                    {
+                                        if(bCompYA)
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                    else
+                                    {
+                                        const double fCompare(
+                                            aCurrentPoint.getY() - (aCurrentPoint.getZ() - rPoint.getZ()) *
+                                            (aPreviousPoint.getY() - aCurrentPoint.getY()) /
+                                            (aPreviousPoint.getZ() - aCurrentPoint.getZ()));
+
+                                        if(fTools::more(fCompare, rPoint.getY()))
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                        else if(fAbsY > fAbsX && fAbsY > fAbsZ)
+                        {
+                            // normal points mostly in Y-Direction, use XZ-Polygon projection for check
+                            // x -> x, y -> z
+                            for(sal_uInt32 a(0); a < nPointCount; a++)
+                            {
+                                const B3DPoint aPreviousPoint(aCurrentPoint);
+                                aCurrentPoint = rCandidate.getB3DPoint(a);
+
+                                // cross-over in Z?
+                                const bool bCompZA(fTools::more(aPreviousPoint.getZ(), rPoint.getZ()));
+                                const bool bCompZB(fTools::more(aCurrentPoint.getZ(), rPoint.getZ()));
+
+                                if(bCompZA != bCompZB)
+                                {
+                                    // cross-over in X?
+                                    const bool bCompXA(fTools::more(aPreviousPoint.getX(), rPoint.getX()));
+                                    const bool bCompXB(fTools::more(aCurrentPoint.getX(), rPoint.getX()));
+
+                                    if(bCompXA == bCompXB)
+                                    {
+                                        if(bCompXA)
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                    else
+                                    {
+                                        const double fCompare(
+                                            aCurrentPoint.getX() - (aCurrentPoint.getZ() - rPoint.getZ()) *
+                                            (aPreviousPoint.getX() - aCurrentPoint.getX()) /
+                                            (aPreviousPoint.getZ() - aCurrentPoint.getZ()));
+
+                                        if(fTools::more(fCompare, rPoint.getX()))
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                        else
+                        {
+                            // normal points mostly in Z-Direction, use XY-Polygon projection for check
+                            // x -> x, y -> y
+                            for(sal_uInt32 a(0); a < nPointCount; a++)
+                            {
+                                const B3DPoint aPreviousPoint(aCurrentPoint);
+                                aCurrentPoint = rCandidate.getB3DPoint(a);
+
+                                // cross-over in Y?
+                                const bool bCompYA(fTools::more(aPreviousPoint.getY(), rPoint.getY()));
+                                const bool bCompYB(fTools::more(aCurrentPoint.getY(), rPoint.getY()));
+
+                                if(bCompYA != bCompYB)
+                                {
+                                    // cross-over in X?
+                                    const bool bCompXA(fTools::more(aPreviousPoint.getX(), rPoint.getX()));
+                                    const bool bCompXB(fTools::more(aCurrentPoint.getX(), rPoint.getX()));
+
+                                    if(bCompXA == bCompXB)
+                                    {
+                                        if(bCompXA)
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                    else
+                                    {
+                                        const double fCompare(
+                                            aCurrentPoint.getX() - (aCurrentPoint.getY() - rPoint.getY()) *
+                                            (aPreviousPoint.getX() - aCurrentPoint.getX()) /
+                                            (aPreviousPoint.getY() - aCurrentPoint.getY()));
+
+                                        if(fTools::more(fCompare, rPoint.getX()))
+                                        {
+                                            bRetval = !bRetval;
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+                }
+
+                return bRetval;
+            }
+        }
+
+        bool isPointOnLine(const B3DPoint& rStart, const B3DPoint& rEnd, const B3DPoint& rCandidate, bool bWithPoints)
+        {
+            if(rCandidate.equal(rStart) || rCandidate.equal(rEnd))
+            {
+                // candidate is in epsilon around start or end -> inside
+                return bWithPoints;
+            }
+            else if(rStart.equal(rEnd))
+            {
+                // start and end are equal, but candidate is outside their epsilon -> outside
+                return false;
+            }
+            else
+            {
+                const B3DVector aEdgeVector(rEnd - rStart);
+                const B3DVector aTestVector(rCandidate - rStart);
+
+                if(areParallel(aEdgeVector, aTestVector))
+                {
+                    double fParamTestOnCurr(0.0);
+
+                    if(aEdgeVector.getX() > aEdgeVector.getY())
+                    {
+                        if(aEdgeVector.getX() > aEdgeVector.getZ())
+                        {
+                            // X is biggest
+                            fParamTestOnCurr = aTestVector.getX() / aEdgeVector.getX();
+                        }
+                        else
+                        {
+                            // Z is biggest
+                            fParamTestOnCurr = aTestVector.getZ() / aEdgeVector.getZ();
+                        }
+                    }
+                    else
+                    {
+                        if(aEdgeVector.getY() > aEdgeVector.getZ())
+                        {
+                            // Y is biggest
+                            fParamTestOnCurr = aTestVector.getY() / aEdgeVector.getY();
+                        }
+                        else
+                        {
+                            // Z is biggest
+                            fParamTestOnCurr = aTestVector.getZ() / aEdgeVector.getZ();
+                        }
+                    }
+
+                    if(fTools::more(fParamTestOnCurr, 0.0) && fTools::less(fParamTestOnCurr, 1.0))
+                    {
+                        return true;
+                    }
+                }
+
+                return false;
+            }
+        }
+
+        bool isPointOnPolygon(const B3DPolygon& rCandidate, const B3DPoint& rPoint)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                B3DPoint aCurrentPoint(rCandidate.getB3DPoint(0));
+
+                for(sal_uInt32 a(0); a < nLoopCount; a++)
+                {
+                    const B3DPoint aNextPoint(rCandidate.getB3DPoint((a + 1) % nPointCount));
+
+                    if(isPointOnLine(aCurrentPoint, aNextPoint, rPoint, true/*bWithPoints*/))
+                    {
+                        return true;
+                    }
+
+                    aCurrentPoint = aNextPoint;
+                }
+            }
+            else if(nPointCount)
+            {
+                return rPoint.equal(rCandidate.getB3DPoint(0));
+            }
+
+            return false;
+        }
+
+        bool getCutBetweenLineAndPlane(const B3DVector& rPlaneNormal, const B3DPoint& rPlanePoint, const B3DPoint& rEdgeStart, const B3DPoint& rEdgeEnd, double& fCut)
+        {
+            if(!rPlaneNormal.equalZero() && !rEdgeStart.equal(rEdgeEnd))
+            {
+                const B3DVector aTestEdge(rEdgeEnd - rEdgeStart);
+                const double fScalarEdge(rPlaneNormal.scalar(aTestEdge));
+
+                if(!fTools::equalZero(fScalarEdge))
+                {
+                    const B3DVector aCompareEdge(rPlanePoint - rEdgeStart);
+                    const double fScalarCompare(rPlaneNormal.scalar(aCompareEdge));
+
+                    fCut = fScalarCompare / fScalarEdge;
+                    return true;
+                }
+            }
+
+            return false;
+        }
+
+        // snap points of horizontal or vertical edges to discrete values
+        B3DPolygon snapPointsOfHorizontalOrVerticalEdges(const B3DPolygon& rCandidate)
+        {
+            const sal_uInt32 nPointCount(rCandidate.count());
+
+            if(nPointCount > 1)
+            {
+                // Start by copying the source polygon to get a writeable copy. The closed state is
+                // copied by aRetval's initialisation, too, so no need to copy it in this method
+                B3DPolygon aRetval(rCandidate);
+
+                // prepare geometry data. Get rounded from original
+                B3ITuple aPrevTuple(basegfx::fround(rCandidate.getB3DPoint(nPointCount - 1)));
+                B3DPoint aCurrPoint(rCandidate.getB3DPoint(0));
+                B3ITuple aCurrTuple(basegfx::fround(aCurrPoint));
+
+                // loop over all points. This will also snap the implicit closing edge
+                // even when not closed, but that's no problem here
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    // get next point. Get rounded from original
+                    const bool bLastRun(a + 1 == nPointCount);
+                    const sal_uInt32 nNextIndex(bLastRun ? 0 : a + 1);
+                    const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
+                    const B3ITuple aNextTuple(basegfx::fround(aNextPoint));
+
+                    // get the states
+                    const bool bPrevVertical(aPrevTuple.getX() == aCurrTuple.getX());
+                    const bool bNextVertical(aNextTuple.getX() == aCurrTuple.getX());
+                    const bool bPrevHorizontal(aPrevTuple.getY() == aCurrTuple.getY());
+                    const bool bNextHorizontal(aNextTuple.getY() == aCurrTuple.getY());
+                    const bool bSnapX(bPrevVertical || bNextVertical);
+                    const bool bSnapY(bPrevHorizontal || bNextHorizontal);
+
+                    if(bSnapX || bSnapY)
+                    {
+                        const B3DPoint aSnappedPoint(
+                            bSnapX ? aCurrTuple.getX() : aCurrPoint.getX(),
+                            bSnapY ? aCurrTuple.getY() : aCurrPoint.getY(),
+                            aCurrPoint.getZ());
+
+                        aRetval.setB3DPoint(a, aSnappedPoint);
+                    }
+
+                    // prepare next point
+                    if(!bLastRun)
+                    {
+                        aPrevTuple = aCurrTuple;
+                        aCurrPoint = aNextPoint;
+                        aCurrTuple = aNextTuple;
+                    }
+                }
+
+                return aRetval;
+            }
+            else
+            {
+                return rCandidate;
+            }
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b3dpolypolygon.cxx b/basegfx/source/polygon/b3dpolypolygon.cxx
new file mode 100644
index 0000000000..017906eef5
--- /dev/null
+++ b/basegfx/source/polygon/b3dpolypolygon.cxx
@@ -0,0 +1,400 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <osl/diagnose.h>
+#include <basegfx/polygon/b3dpolypolygon.hxx>
+#include <basegfx/polygon/b3dpolygon.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <utility>
+#include <vector>
+
+class ImplB3DPolyPolygon
+{
+    typedef std::vector< ::basegfx::B3DPolygon >  PolygonVector;
+
+    PolygonVector                                   maPolygons;
+
+public:
+    ImplB3DPolyPolygon()
+    {
+    }
+
+    explicit ImplB3DPolyPolygon(const ::basegfx::B3DPolygon& rToBeCopied) :
+        maPolygons(1,rToBeCopied)
+    {
+    }
+
+    bool operator==(const ImplB3DPolyPolygon& rPolygonList) const
+    {
+        // same polygon count?
+        if(maPolygons.size() != rPolygonList.maPolygons.size())
+            return false;
+
+        // compare polygon content
+        if(maPolygons != rPolygonList.maPolygons)
+            return false;
+
+        return true;
+    }
+
+    const ::basegfx::B3DPolygon& getB3DPolygon(sal_uInt32 nIndex) const
+    {
+        return maPolygons[nIndex];
+    }
+
+    void setB3DPolygon(sal_uInt32 nIndex, const ::basegfx::B3DPolygon& rPolygon)
+    {
+        maPolygons[nIndex] = rPolygon;
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::B3DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // add nCount copies of rPolygon
+            PolygonVector::iterator aIndex(maPolygons.begin());
+            if( nIndex )
+                aIndex += nIndex;
+            maPolygons.insert(aIndex, nCount, rPolygon);
+        }
+    }
+
+    void insert(sal_uInt32 nIndex, const ::basegfx::B3DPolyPolygon& rPolyPolygon)
+    {
+        // add all polygons from rPolyPolygon
+        PolygonVector::iterator aIndex(maPolygons.begin());
+        if( nIndex )
+            aIndex += nIndex;
+        maPolygons.insert(aIndex, rPolyPolygon.begin(), rPolyPolygon.end());
+    }
+
+    void remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        if(nCount)
+        {
+            // remove polygon data
+            PolygonVector::iterator aStart(maPolygons.begin());
+            aStart += nIndex;
+            const PolygonVector::iterator aEnd(aStart + nCount);
+
+            maPolygons.erase(aStart, aEnd);
+        }
+    }
+
+    sal_uInt32 count() const
+    {
+        return maPolygons.size();
+    }
+
+    void flip()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.flip();
+    }
+
+    void removeDoublePoints()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.removeDoublePoints();
+    }
+
+    void transform(const ::basegfx::B3DHomMatrix& rMatrix)
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.transform(rMatrix);
+    }
+
+    void clearBColors()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.clearBColors();
+    }
+
+    void transformNormals(const ::basegfx::B3DHomMatrix& rMatrix)
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.transformNormals(rMatrix);
+    }
+
+    void clearNormals()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.clearNormals();
+    }
+
+    void transformTextureCoordinates(const ::basegfx::B2DHomMatrix& rMatrix)
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.transformTextureCoordinates(rMatrix);
+    }
+
+    void clearTextureCoordinates()
+    {
+        for (auto& aPolygon : maPolygons)
+            aPolygon.clearTextureCoordinates();
+    }
+
+    const basegfx::B3DPolygon* begin() const
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data();
+    }
+
+    const basegfx::B3DPolygon* end() const
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data() + maPolygons.size();
+    }
+
+    basegfx::B3DPolygon* begin()
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data();
+    }
+
+    basegfx::B3DPolygon* end()
+    {
+        if (maPolygons.empty())
+            return nullptr;
+        else
+            return maPolygons.data() + maPolygons.size();
+    }
+};
+
+namespace basegfx
+{
+    namespace {
+
+    B3DPolyPolygon::ImplType const & getDefaultPolyPolygon() {
+        static B3DPolyPolygon::ImplType const singleton;
+        return singleton;
+    }
+
+    }
+
+    B3DPolyPolygon::B3DPolyPolygon() :
+        mpPolyPolygon(getDefaultPolyPolygon())
+    {
+    }
+
+    B3DPolyPolygon::B3DPolyPolygon(const B3DPolyPolygon&) = default;
+
+    B3DPolyPolygon::B3DPolyPolygon(B3DPolyPolygon&&) = default;
+
+    B3DPolyPolygon::B3DPolyPolygon(const B3DPolygon& rPolygon) :
+        mpPolyPolygon( ImplB3DPolyPolygon(rPolygon) )
+    {
+    }
+
+    B3DPolyPolygon::~B3DPolyPolygon() = default;
+
+    B3DPolyPolygon& B3DPolyPolygon::operator=(const B3DPolyPolygon&) = default;
+
+    B3DPolyPolygon& B3DPolyPolygon::operator=(B3DPolyPolygon&&) = default;
+
+    bool B3DPolyPolygon::operator==(const B3DPolyPolygon& rPolyPolygon) const
+    {
+        if(mpPolyPolygon.same_object(rPolyPolygon.mpPolyPolygon))
+            return true;
+
+        return ((*mpPolyPolygon) == (*rPolyPolygon.mpPolyPolygon));
+    }
+
+    bool B3DPolyPolygon::operator!=(const B3DPolyPolygon& rPolyPolygon) const
+    {
+        return !(*this == rPolyPolygon);
+    }
+
+    sal_uInt32 B3DPolyPolygon::count() const
+    {
+        return mpPolyPolygon->count();
+    }
+
+    B3DPolygon const & B3DPolyPolygon::getB3DPolygon(sal_uInt32 nIndex) const
+    {
+        OSL_ENSURE(nIndex < mpPolyPolygon->count(), "B3DPolyPolygon access outside range (!)");
+
+        return mpPolyPolygon->getB3DPolygon(nIndex);
+    }
+
+    void B3DPolyPolygon::setB3DPolygon(sal_uInt32 nIndex, const B3DPolygon& rPolygon)
+    {
+        OSL_ENSURE(nIndex < std::as_const(mpPolyPolygon)->count(), "B3DPolyPolygon access outside range (!)");
+
+        if(getB3DPolygon(nIndex) != rPolygon)
+            mpPolyPolygon->setB3DPolygon(nIndex, rPolygon);
+    }
+
+    bool B3DPolyPolygon::areBColorsUsed() const
+    {
+        for(sal_uInt32 a(0); a < mpPolyPolygon->count(); a++)
+        {
+            if(mpPolyPolygon->getB3DPolygon(a).areBColorsUsed())
+            {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    void B3DPolyPolygon::clearBColors()
+    {
+        if(areBColorsUsed())
+            mpPolyPolygon->clearBColors();
+    }
+
+    void B3DPolyPolygon::transformNormals(const B3DHomMatrix& rMatrix)
+    {
+        if(!rMatrix.isIdentity())
+            mpPolyPolygon->transformNormals(rMatrix);
+    }
+
+    bool B3DPolyPolygon::areNormalsUsed() const
+    {
+        for(sal_uInt32 a(0); a < mpPolyPolygon->count(); a++)
+        {
+            if(mpPolyPolygon->getB3DPolygon(a).areNormalsUsed())
+            {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    void B3DPolyPolygon::clearNormals()
+    {
+        if(areNormalsUsed())
+            mpPolyPolygon->clearNormals();
+    }
+
+    void B3DPolyPolygon::transformTextureCoordinates(const B2DHomMatrix& rMatrix)
+    {
+        if(!rMatrix.isIdentity())
+            mpPolyPolygon->transformTextureCoordinates(rMatrix);
+    }
+
+    bool B3DPolyPolygon::areTextureCoordinatesUsed() const
+    {
+        for(sal_uInt32 a(0); a < mpPolyPolygon->count(); a++)
+        {
+            if(mpPolyPolygon->getB3DPolygon(a).areTextureCoordinatesUsed())
+            {
+                return true;
+            }
+        }
+
+        return false;
+    }
+
+    void B3DPolyPolygon::clearTextureCoordinates()
+    {
+        if(areTextureCoordinatesUsed())
+            mpPolyPolygon->clearTextureCoordinates();
+    }
+
+    void B3DPolyPolygon::append(const B3DPolygon& rPolygon, sal_uInt32 nCount)
+    {
+        if(nCount)
+            mpPolyPolygon->insert(std::as_const(mpPolyPolygon)->count(), rPolygon, nCount);
+    }
+
+    void B3DPolyPolygon::append(const B3DPolyPolygon& rPolyPolygon)
+    {
+        if(rPolyPolygon.count())
+            mpPolyPolygon->insert(std::as_const(mpPolyPolygon)->count(), rPolyPolygon);
+    }
+
+    void B3DPolyPolygon::remove(sal_uInt32 nIndex, sal_uInt32 nCount)
+    {
+        OSL_ENSURE(nIndex + nCount <= std::as_const(mpPolyPolygon)->count(), "B3DPolyPolygon Remove outside range (!)");
+
+        if(nCount)
+            mpPolyPolygon->remove(nIndex, nCount);
+    }
+
+    void B3DPolyPolygon::clear()
+    {
+        mpPolyPolygon = getDefaultPolyPolygon();
+    }
+
+    void B3DPolyPolygon::flip()
+    {
+        mpPolyPolygon->flip();
+    }
+
+    bool B3DPolyPolygon::hasDoublePoints() const
+    {
+        bool bRetval(false);
+
+        for(sal_uInt32 a(0); !bRetval && a < mpPolyPolygon->count(); a++)
+        {
+            if(mpPolyPolygon->getB3DPolygon(a).hasDoublePoints())
+            {
+                bRetval = true;
+            }
+        }
+
+        return bRetval;
+    }
+
+    void B3DPolyPolygon::removeDoublePoints()
+    {
+        if(hasDoublePoints())
+            mpPolyPolygon->removeDoublePoints();
+    }
+
+    void B3DPolyPolygon::transform(const B3DHomMatrix& rMatrix)
+    {
+        if(std::as_const(mpPolyPolygon)->count() && !rMatrix.isIdentity())
+        {
+            mpPolyPolygon->transform(rMatrix);
+        }
+    }
+
+    const B3DPolygon* B3DPolyPolygon::begin() const
+    {
+        return mpPolyPolygon->begin();
+    }
+
+    const B3DPolygon* B3DPolyPolygon::end() const
+    {
+        return mpPolyPolygon->end();
+    }
+
+    B3DPolygon* B3DPolyPolygon::begin()
+    {
+        return mpPolyPolygon->begin();
+    }
+
+    B3DPolygon* B3DPolyPolygon::end()
+    {
+        return mpPolyPolygon->end();
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/polygon/b3dpolypolygontools.cxx b/basegfx/source/polygon/b3dpolypolygontools.cxx
new file mode 100644
index 0000000000..ffd8bded4d
--- /dev/null
+++ b/basegfx/source/polygon/b3dpolypolygontools.cxx
@@ -0,0 +1,585 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/polygon/b3dpolypolygontools.hxx>
+#include <basegfx/range/b3drange.hxx>
+#include <basegfx/polygon/b3dpolypolygon.hxx>
+#include <basegfx/polygon/b3dpolygon.hxx>
+#include <basegfx/polygon/b3dpolygontools.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <com/sun/star/drawing/DoubleSequence.hpp>
+#include <com/sun/star/drawing/PolyPolygonShape3D.hpp>
+
+// predefines
+#define nMinSegments sal_uInt32(1)
+#define nMaxSegments sal_uInt32(512)
+
+namespace basegfx::utils
+{
+        // B3DPolyPolygon tools
+        B3DRange getRange(const B3DPolyPolygon& rCandidate)
+        {
+            B3DRange aRetval;
+
+            for(const auto& rPolygon : rCandidate )
+            {
+                aRetval.expand(getRange(rPolygon));
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon const & createUnitCubePolyPolygon()
+        {
+            static auto const singleton = [] {
+                    B3DPolyPolygon aRetval;
+                    B3DPolygon aTemp;
+                    aTemp.append(B3DPoint(0.0, 0.0, 1.0));
+                    aTemp.append(B3DPoint(0.0, 1.0, 1.0));
+                    aTemp.append(B3DPoint(1.0, 1.0, 1.0));
+                    aTemp.append(B3DPoint(1.0, 0.0, 1.0));
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    aTemp.clear();
+                    aTemp.append(B3DPoint(0.0, 0.0, 0.0));
+                    aTemp.append(B3DPoint(0.0, 1.0, 0.0));
+                    aTemp.append(B3DPoint(1.0, 1.0, 0.0));
+                    aTemp.append(B3DPoint(1.0, 0.0, 0.0));
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    aTemp.clear();
+                    aTemp.append(B3DPoint(0.0, 0.0, 0.0));
+                    aTemp.append(B3DPoint(0.0, 0.0, 1.0));
+                    aRetval.append(aTemp);
+
+                    aTemp.clear();
+                    aTemp.append(B3DPoint(0.0, 1.0, 0.0));
+                    aTemp.append(B3DPoint(0.0, 1.0, 1.0));
+                    aRetval.append(aTemp);
+
+                    aTemp.clear();
+                    aTemp.append(B3DPoint(1.0, 1.0, 0.0));
+                    aTemp.append(B3DPoint(1.0, 1.0, 1.0));
+                    aRetval.append(aTemp);
+
+                    aTemp.clear();
+                    aTemp.append(B3DPoint(1.0, 0.0, 0.0));
+                    aTemp.append(B3DPoint(1.0, 0.0, 1.0));
+                    aRetval.append(aTemp);
+                    return aRetval;
+                }();
+            return singleton;
+        }
+
+        B3DPolyPolygon const & createUnitCubeFillPolyPolygon()
+        {
+            static auto const singleton = [] {
+                    B3DPolyPolygon aRetval;
+                    B3DPolygon aTemp;
+
+                    // all points
+                    const B3DPoint A(0.0, 0.0, 0.0);
+                    const B3DPoint B(0.0, 1.0, 0.0);
+                    const B3DPoint C(1.0, 1.0, 0.0);
+                    const B3DPoint D(1.0, 0.0, 0.0);
+                    const B3DPoint E(0.0, 0.0, 1.0);
+                    const B3DPoint F(0.0, 1.0, 1.0);
+                    const B3DPoint G(1.0, 1.0, 1.0);
+                    const B3DPoint H(1.0, 0.0, 1.0);
+
+                    // create bottom
+                    aTemp.append(D);
+                    aTemp.append(A);
+                    aTemp.append(E);
+                    aTemp.append(H);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    // create front
+                    aTemp.clear();
+                    aTemp.append(B);
+                    aTemp.append(A);
+                    aTemp.append(D);
+                    aTemp.append(C);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    // create left
+                    aTemp.clear();
+                    aTemp.append(E);
+                    aTemp.append(A);
+                    aTemp.append(B);
+                    aTemp.append(F);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    // create top
+                    aTemp.clear();
+                    aTemp.append(C);
+                    aTemp.append(G);
+                    aTemp.append(F);
+                    aTemp.append(B);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    // create right
+                    aTemp.clear();
+                    aTemp.append(H);
+                    aTemp.append(G);
+                    aTemp.append(C);
+                    aTemp.append(D);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+
+                    // create back
+                    aTemp.clear();
+                    aTemp.append(F);
+                    aTemp.append(G);
+                    aTemp.append(H);
+                    aTemp.append(E);
+                    aTemp.setClosed(true);
+                    aRetval.append(aTemp);
+                    return aRetval;
+                }();
+            return singleton;
+        }
+
+        B3DPolyPolygon createCubePolyPolygonFromB3DRange( const B3DRange& rRange)
+        {
+            B3DPolyPolygon aRetval;
+
+            if(!rRange.isEmpty())
+            {
+                aRetval = createUnitCubePolyPolygon();
+                B3DHomMatrix aTrans;
+                aTrans.scale(rRange.getWidth(), rRange.getHeight(), rRange.getDepth());
+                aTrans.translate(rRange.getMinX(), rRange.getMinY(), rRange.getMinZ());
+                aRetval.transform(aTrans);
+                aRetval.removeDoublePoints();
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon createCubeFillPolyPolygonFromB3DRange( const B3DRange& rRange)
+        {
+            B3DPolyPolygon aRetval;
+
+            if(!rRange.isEmpty())
+            {
+                aRetval = createUnitCubeFillPolyPolygon();
+                B3DHomMatrix aTrans;
+                aTrans.scale(rRange.getWidth(), rRange.getHeight(), rRange.getDepth());
+                aTrans.translate(rRange.getMinX(), rRange.getMinY(), rRange.getMinZ());
+                aRetval.transform(aTrans);
+                aRetval.removeDoublePoints();
+            }
+
+            return aRetval;
+        }
+
+        // helper for getting the 3D Point from given cartesian coordinates. fHor is defined from
+        // [M_PI_2 .. -M_PI_2], fVer from [0.0 .. 2PI]
+        static B3DPoint getPointFromCartesian(double fHor, double fVer)
+        {
+            const double fCosVer(cos(fVer));
+            return B3DPoint(fCosVer * cos(fHor), sin(fVer), fCosVer * -sin(fHor));
+        }
+
+        B3DPolyPolygon createUnitSpherePolyPolygon(
+            sal_uInt32 nHorSeg, sal_uInt32 nVerSeg,
+            double fVerStart, double fVerStop,
+            double fHorStart, double fHorStop)
+        {
+            B3DPolyPolygon aRetval;
+            sal_uInt32 a, b;
+
+            if(!nHorSeg)
+            {
+                nHorSeg = fround(fabs(fHorStop - fHorStart) / (M_PI / 12.0));
+            }
+
+            // min/max limitations
+            nHorSeg = std::clamp(nHorSeg, nMinSegments, nMaxSegments);
+
+            if(!nVerSeg)
+            {
+                nVerSeg = fround(fabs(fVerStop - fVerStart) / (M_PI / 12.0));
+            }
+
+            // min/max limitations
+            nVerSeg = std::clamp(nVerSeg, nMinSegments, nMaxSegments);
+
+            // create constants
+            const double fVerDiffPerStep((fVerStop - fVerStart) / static_cast<double>(nVerSeg));
+            const double fHorDiffPerStep((fHorStop - fHorStart) / static_cast<double>(nHorSeg));
+            bool bHorClosed(fTools::equal(fHorStop - fHorStart, 2 * M_PI));
+            bool bVerFromTop(fTools::equal(fVerStart, M_PI_2));
+            bool bVerToBottom(fTools::equal(fVerStop, -M_PI_2));
+
+            // create horizontal rings
+            const sal_uInt32 nLoopVerInit(bVerFromTop ? 1 : 0);
+            const sal_uInt32 nLoopVerLimit(bVerToBottom ? nVerSeg : nVerSeg + 1);
+            const sal_uInt32 nLoopHorLimit(bHorClosed ? nHorSeg : nHorSeg + 1);
+
+            for(a = nLoopVerInit; a < nLoopVerLimit; a++)
+            {
+                const double fVer(fVerStart + (static_cast<double>(a) * fVerDiffPerStep));
+                B3DPolygon aNew;
+
+                for(b = 0; b < nLoopHorLimit; b++)
+                {
+                    const double fHor(fHorStart + (static_cast<double>(b) * fHorDiffPerStep));
+                    aNew.append(getPointFromCartesian(fHor, fVer));
+                }
+
+                aNew.setClosed(bHorClosed);
+                aRetval.append(aNew);
+            }
+
+            // create vertical half-rings
+            for(a = 0; a < nLoopHorLimit; a++)
+            {
+                const double fHor(fHorStart + (static_cast<double>(a) * fHorDiffPerStep));
+                B3DPolygon aNew;
+
+                if(bVerFromTop)
+                {
+                    aNew.append(B3DPoint(0.0, 1.0, 0.0));
+                }
+
+                for(b = nLoopVerInit; b < nLoopVerLimit; b++)
+                {
+                    const double fVer(fVerStart + (static_cast<double>(b) * fVerDiffPerStep));
+                    aNew.append(getPointFromCartesian(fHor, fVer));
+                }
+
+                if(bVerToBottom)
+                {
+                    aNew.append(B3DPoint(0.0, -1.0, 0.0));
+                }
+
+                aRetval.append(aNew);
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon createSpherePolyPolygonFromB3DRange( const B3DRange& rRange,
+            sal_uInt32 nHorSeg, sal_uInt32 nVerSeg,
+            double fVerStart, double fVerStop,
+            double fHorStart, double fHorStop)
+        {
+            B3DPolyPolygon aRetval(createUnitSpherePolyPolygon(nHorSeg, nVerSeg, fVerStart, fVerStop, fHorStart, fHorStop));
+
+            if(aRetval.count())
+            {
+                // move and scale whole construct which is now in [-1.0 .. 1.0] in all directions
+                B3DHomMatrix aTrans;
+                aTrans.translate(1.0, 1.0, 1.0);
+                aTrans.scale(rRange.getWidth() / 2.0, rRange.getHeight() / 2.0, rRange.getDepth() / 2.0);
+                aTrans.translate(rRange.getMinX(), rRange.getMinY(), rRange.getMinZ());
+                aRetval.transform(aTrans);
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon createUnitSphereFillPolyPolygon(
+            sal_uInt32 nHorSeg, sal_uInt32 nVerSeg,
+            bool bNormals,
+            double fVerStart, double fVerStop,
+            double fHorStart, double fHorStop)
+        {
+            B3DPolyPolygon aRetval;
+
+            if(!nHorSeg)
+            {
+                nHorSeg = fround(fabs(fHorStop - fHorStart) / (M_PI / 12.0));
+            }
+
+            // min/max limitations
+            nHorSeg = std::clamp(nHorSeg, nMinSegments, nMaxSegments);
+
+            if(!nVerSeg)
+            {
+                nVerSeg = fround(fabs(fVerStop - fVerStart) / (M_PI / 12.0));
+            }
+
+            // min/max limitations
+            nVerSeg = std::clamp(nVerSeg, nMinSegments, nMaxSegments);
+
+            // vertical loop
+            for(sal_uInt32 a(0); a < nVerSeg; a++)
+            {
+                const double fVer1(fVerStart + (((fVerStop - fVerStart) * a) / nVerSeg));
+                const double fVer2(fVerStart + (((fVerStop - fVerStart) * (a + 1)) / nVerSeg));
+
+                // horizontal loop
+                for(sal_uInt32 b(0); b < nHorSeg; b++)
+                {
+                    const double fHor1(fHorStart + (((fHorStop - fHorStart) * b) / nHorSeg));
+                    const double fHor2(fHorStart + (((fHorStop - fHorStart) * (b + 1)) / nHorSeg));
+                    B3DPolygon aNew;
+
+                    aNew.append(getPointFromCartesian(fHor1, fVer1));
+                    aNew.append(getPointFromCartesian(fHor2, fVer1));
+                    aNew.append(getPointFromCartesian(fHor2, fVer2));
+                    aNew.append(getPointFromCartesian(fHor1, fVer2));
+
+                    if(bNormals)
+                    {
+                        for(sal_uInt32 c(0); c < aNew.count(); c++)
+                        {
+                            aNew.setNormal(c, ::basegfx::B3DVector(aNew.getB3DPoint(c)));
+                        }
+                    }
+
+                    aNew.setClosed(true);
+                    aRetval.append(aNew);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon createSphereFillPolyPolygonFromB3DRange( const B3DRange& rRange,
+            sal_uInt32 nHorSeg, sal_uInt32 nVerSeg,
+            bool bNormals,
+            double fVerStart, double fVerStop,
+            double fHorStart, double fHorStop)
+        {
+            B3DPolyPolygon aRetval(createUnitSphereFillPolyPolygon(nHorSeg, nVerSeg, bNormals, fVerStart, fVerStop, fHorStart, fHorStop));
+
+            if(aRetval.count())
+            {
+                // move and scale whole construct which is now in [-1.0 .. 1.0] in all directions
+                B3DHomMatrix aTrans;
+                aTrans.translate(1.0, 1.0, 1.0);
+                aTrans.scale(rRange.getWidth() / 2.0, rRange.getHeight() / 2.0, rRange.getDepth() / 2.0);
+                aTrans.translate(rRange.getMinX(), rRange.getMinY(), rRange.getMinZ());
+                aRetval.transform(aTrans);
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon applyDefaultNormalsSphere( const B3DPolyPolygon& rCandidate, const B3DPoint& rCenter)
+        {
+            B3DPolyPolygon aRetval;
+
+            for( const auto& rB3DPolygon : rCandidate)
+            {
+                aRetval.append(applyDefaultNormalsSphere(rB3DPolygon, rCenter));
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon invertNormals( const B3DPolyPolygon& rCandidate)
+        {
+            B3DPolyPolygon aRetval;
+
+            for( const auto& rB3DPolygon : rCandidate )
+            {
+                aRetval.append(invertNormals(rB3DPolygon));
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon applyDefaultTextureCoordinatesParallel( const B3DPolyPolygon& rCandidate, const B3DRange& rRange, bool bChangeX, bool bChangeY)
+        {
+            B3DPolyPolygon aRetval;
+
+            for( const auto& rB3DPolygon : rCandidate)
+            {
+                aRetval.append(applyDefaultTextureCoordinatesParallel(rB3DPolygon, rRange, bChangeX, bChangeY));
+            }
+
+            return aRetval;
+        }
+
+        B3DPolyPolygon applyDefaultTextureCoordinatesSphere( const B3DPolyPolygon& rCandidate, const B3DPoint& rCenter, bool bChangeX, bool bChangeY)
+        {
+            B3DPolyPolygon aRetval;
+
+            for( const auto& rB3DPolygon : rCandidate )
+            {
+                aRetval.append(applyDefaultTextureCoordinatesSphere(rB3DPolygon, rCenter, bChangeX, bChangeY));
+            }
+
+            return aRetval;
+        }
+
+        bool isInside(const B3DPolyPolygon& rCandidate, const B3DPoint& rPoint)
+        {
+            const sal_uInt32 nPolygonCount(rCandidate.count());
+
+            if(nPolygonCount == 1)
+            {
+                return isInside(rCandidate.getB3DPolygon(0), rPoint, false/*bWithBorder*/);
+            }
+            else
+            {
+                sal_Int32 nInsideCount(0);
+
+                for(const auto& rPolygon : rCandidate )
+                {
+                    const bool bInside(isInside(rPolygon, rPoint, false/*bWithBorder*/));
+
+                    if(bInside)
+                    {
+                        nInsideCount++;
+                    }
+                }
+
+                return (nInsideCount % 2);
+            }
+        }
+
+/// converters for css::drawing::PolyPolygonShape3D
+        B3DPolyPolygon UnoPolyPolygonShape3DToB3DPolyPolygon(
+            const css::drawing::PolyPolygonShape3D& rPolyPolygonShape3DSource)
+        {
+            B3DPolyPolygon aRetval;
+            const sal_Int32 nOuterSequenceCount(rPolyPolygonShape3DSource.SequenceX.getLength());
+
+            if(nOuterSequenceCount)
+            {
+                assert(nOuterSequenceCount == rPolyPolygonShape3DSource.SequenceY.getLength()
+                           && nOuterSequenceCount
+                                  == rPolyPolygonShape3DSource.SequenceZ.getLength()&&
+                       "UnoPolyPolygonShape3DToB3DPolygon: Not all double sequences have the same "
+                       "length (!)" );
+
+                const css::drawing::DoubleSequence* pInnerSequenceX = rPolyPolygonShape3DSource.SequenceX.getConstArray();
+                const css::drawing::DoubleSequence* pInnerSequenceY = rPolyPolygonShape3DSource.SequenceY.getConstArray();
+                const css::drawing::DoubleSequence* pInnerSequenceZ = rPolyPolygonShape3DSource.SequenceZ.getConstArray();
+
+                for(sal_Int32 a(0); a < nOuterSequenceCount; a++)
+                {
+                    basegfx::B3DPolygon aNewPolygon;
+                    const sal_Int32 nInnerSequenceCount(pInnerSequenceX->getLength());
+                    assert(nInnerSequenceCount == pInnerSequenceY->getLength()
+                           && nInnerSequenceCount == pInnerSequenceZ->getLength()
+                           && "UnoPolyPolygonShape3DToB3DPolygon: Not all double sequences have "
+                              "the same length (!)");
+
+                    const double* pArrayX = pInnerSequenceX->getConstArray();
+                    const double* pArrayY = pInnerSequenceY->getConstArray();
+                    const double* pArrayZ = pInnerSequenceZ->getConstArray();
+
+                    for(sal_Int32 b(0); b < nInnerSequenceCount; b++)
+                    {
+                        aNewPolygon.append(basegfx::B3DPoint(*pArrayX++,*pArrayY++,*pArrayZ++));
+                    }
+
+                    pInnerSequenceX++;
+                    pInnerSequenceY++;
+                    pInnerSequenceZ++;
+
+                    // #i101520# correction is needed for imported polygons of old format,
+                    // see callers
+                    basegfx::utils::checkClosed(aNewPolygon);
+
+                    aRetval.append(aNewPolygon);
+                }
+            }
+
+            return aRetval;
+        }
+
+        void B3DPolyPolygonToUnoPolyPolygonShape3D(
+            const B3DPolyPolygon& rPolyPolygonSource,
+            css::drawing::PolyPolygonShape3D& rPolyPolygonShape3DRetval)
+        {
+            const sal_uInt32 nPolygonCount(rPolyPolygonSource.count());
+
+            if(nPolygonCount)
+            {
+                rPolyPolygonShape3DRetval.SequenceX.realloc(nPolygonCount);
+                rPolyPolygonShape3DRetval.SequenceY.realloc(nPolygonCount);
+                rPolyPolygonShape3DRetval.SequenceZ.realloc(nPolygonCount);
+
+                css::drawing::DoubleSequence* pOuterSequenceX = rPolyPolygonShape3DRetval.SequenceX.getArray();
+                css::drawing::DoubleSequence* pOuterSequenceY = rPolyPolygonShape3DRetval.SequenceY.getArray();
+                css::drawing::DoubleSequence* pOuterSequenceZ = rPolyPolygonShape3DRetval.SequenceZ.getArray();
+
+                for(sal_uInt32 a(0); a < nPolygonCount; a++)
+                {
+                    const basegfx::B3DPolygon& aPoly(rPolyPolygonSource.getB3DPolygon(a));
+                    const sal_uInt32 nPointCount(aPoly.count());
+
+                    if(nPointCount)
+                    {
+                        const bool bIsClosed(aPoly.isClosed());
+                        const sal_uInt32 nTargetCount(bIsClosed ? nPointCount + 1 : nPointCount);
+                        pOuterSequenceX->realloc(nTargetCount);
+                        pOuterSequenceY->realloc(nTargetCount);
+                        pOuterSequenceZ->realloc(nTargetCount);
+
+                        double* pInnerSequenceX = pOuterSequenceX->getArray();
+                        double* pInnerSequenceY = pOuterSequenceY->getArray();
+                        double* pInnerSequenceZ = pOuterSequenceZ->getArray();
+
+                        for(sal_uInt32 b(0); b < nPointCount; b++)
+                        {
+                            const basegfx::B3DPoint aPoint(aPoly.getB3DPoint(b));
+
+                            *pInnerSequenceX++ = aPoint.getX();
+                            *pInnerSequenceY++ = aPoint.getY();
+                            *pInnerSequenceZ++ = aPoint.getZ();
+                        }
+
+                        if(bIsClosed)
+                        {
+                            const basegfx::B3DPoint aPoint(aPoly.getB3DPoint(0));
+
+                            *pInnerSequenceX++ = aPoint.getX();
+                            *pInnerSequenceY++ = aPoint.getY();
+                            *pInnerSequenceZ++ = aPoint.getZ();
+                        }
+                    }
+                    else
+                    {
+                        pOuterSequenceX->realloc(0);
+                        pOuterSequenceY->realloc(0);
+                        pOuterSequenceZ->realloc(0);
+                    }
+
+                    pOuterSequenceX++;
+                    pOuterSequenceY++;
+                    pOuterSequenceZ++;
+                }
+            }
+            else
+            {
+                rPolyPolygonShape3DRetval.SequenceX.realloc(0);
+                rPolyPolygonShape3DRetval.SequenceY.realloc(0);
+                rPolyPolygonShape3DRetval.SequenceZ.realloc(0);
+            }
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/range/b2dpolyrange.cxx b/basegfx/source/range/b2dpolyrange.cxx
new file mode 100644
index 0000000000..beb506fc8e
--- /dev/null
+++ b/basegfx/source/range/b2dpolyrange.cxx
@@ -0,0 +1,153 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/range/b2dpolyrange.hxx>
+
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/range/b2drangeclipper.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+
+#include <algorithm>
+#include <vector>
+
+namespace basegfx
+{
+    class ImplB2DPolyRange
+    {
+    public:
+        ImplB2DPolyRange()
+        {}
+
+        bool operator==(const ImplB2DPolyRange& rRHS) const
+        {
+            return maRanges == rRHS.maRanges && maOrient == rRHS.maOrient;
+        }
+
+        sal_uInt32 count() const
+        {
+            return maRanges.size();
+        }
+
+        B2DPolyRange::ElementType getElement(sal_uInt32 nIndex) const
+        {
+            return std::make_tuple(maRanges[nIndex], maOrient[nIndex]);
+        }
+
+        void appendElement(const B2DRange& rRange, B2VectorOrientation eOrient)
+        {
+            maRanges.push_back(rRange);
+            maOrient.push_back(eOrient);
+            maBounds.expand(rRange);
+        }
+
+        void clear()
+        {
+            std::vector<B2DRange>().swap(maRanges);
+            std::vector<B2VectorOrientation>().swap(maOrient);
+
+            maBounds.reset();
+        }
+
+        bool overlaps( const B2DRange& rRange ) const
+        {
+            if( !maBounds.overlaps( rRange ) )
+                return false;
+
+            const std::vector<B2DRange>::const_iterator aEnd( maRanges.end() );
+            return std::any_of( maRanges.begin(),
+                                 aEnd,
+                                 [&rRange](const B2DRange& aRange) { return aRange.overlaps(rRange); } );
+        }
+
+        B2DPolyPolygon solveCrossovers() const
+        {
+            return utils::solveCrossovers(maRanges,maOrient);
+        }
+
+        void transform(const basegfx::B2DHomMatrix& rTranslate)
+        {
+            maBounds.transform(rTranslate);
+            for (auto &a : maRanges)
+                a.transform(rTranslate);
+        }
+
+    private:
+        B2DRange                         maBounds;
+        std::vector<B2DRange>            maRanges;
+        std::vector<B2VectorOrientation> maOrient;
+    };
+
+    B2DPolyRange::B2DPolyRange() = default;
+
+    B2DPolyRange::~B2DPolyRange() = default;
+
+    B2DPolyRange::B2DPolyRange( const B2DPolyRange& ) = default;
+
+    B2DPolyRange& B2DPolyRange::operator=( const B2DPolyRange& ) = default;
+
+    bool B2DPolyRange::operator==(const B2DPolyRange& rRange) const
+    {
+        if(mpImpl.same_object(rRange.mpImpl))
+            return true;
+
+        return ((*mpImpl) == (*rRange.mpImpl));
+    }
+
+    bool B2DPolyRange::operator!=(const B2DPolyRange& rRange) const
+    {
+        return !(*this == rRange);
+    }
+
+    sal_uInt32 B2DPolyRange::count() const
+    {
+        return mpImpl->count();
+    }
+
+    B2DPolyRange::ElementType B2DPolyRange::getElement(sal_uInt32 nIndex) const
+    {
+        return mpImpl->getElement(nIndex);
+    }
+
+    void B2DPolyRange::appendElement(const B2DRange& rRange, B2VectorOrientation eOrient)
+    {
+        mpImpl->appendElement(rRange, eOrient);
+    }
+
+    void B2DPolyRange::clear()
+    {
+        mpImpl->clear();
+    }
+
+    bool B2DPolyRange::overlaps( const B2DRange& rRange ) const
+    {
+        return mpImpl->overlaps(rRange);
+    }
+
+    void B2DPolyRange::transform(const basegfx::B2DHomMatrix& rTranslate)
+    {
+        mpImpl->transform(rTranslate);
+    }
+
+    B2DPolyPolygon B2DPolyRange::solveCrossovers() const
+    {
+        return mpImpl->solveCrossovers();
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/range/b2drange.cxx b/basegfx/source/range/b2drange.cxx
new file mode 100644
index 0000000000..1f20cce90a
--- /dev/null
+++ b/basegfx/source/range/b2drange.cxx
@@ -0,0 +1,81 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/range/b2irange.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+
+namespace basegfx
+{
+    B2DRange::B2DRange(const B2IRange& rRange)
+    {
+        if (!rRange.isEmpty())
+        {
+            maRangeX = basegfx::BasicRange<ValueType, TraitsType>(rRange.getMinX());
+            maRangeY = basegfx::BasicRange<ValueType, TraitsType>(rRange.getMinY());
+
+            maRangeX.expand(rRange.getMaxX());
+            maRangeY.expand(rRange.getMaxY());
+        }
+    }
+
+    void B2DRange::transform(const B2DHomMatrix& rMatrix)
+    {
+        if(!isEmpty() && !rMatrix.isIdentity())
+        {
+            const B2DRange aSource(*this);
+            reset();
+            expand(rMatrix * B2DPoint(aSource.getMinX(), aSource.getMinY()));
+            expand(rMatrix * B2DPoint(aSource.getMaxX(), aSource.getMinY()));
+            expand(rMatrix * B2DPoint(aSource.getMinX(), aSource.getMaxY()));
+            expand(rMatrix * B2DPoint(aSource.getMaxX(), aSource.getMaxY()));
+        }
+    }
+
+    B2DRange& B2DRange::operator*=(const basegfx::B2DHomMatrix& rMatrix)
+    {
+        transform(rMatrix);
+        return *this;
+    }
+
+    const B2DRange& B2DRange::getUnitB2DRange()
+    {
+        static const B2DRange aUnitB2DRange(0.0, 0.0, 1.0, 1.0);
+
+        return aUnitB2DRange;
+    }
+
+    B2IRange fround(const B2DRange& rRange)
+    {
+        return rRange.isEmpty() ?
+            B2IRange() :
+            B2IRange(fround(rRange.getMinimum()),
+                     fround(rRange.getMaximum()));
+    }
+
+    B2DRange operator*( const ::basegfx::B2DHomMatrix& rMat, const B2DRange& rB2DRange )
+    {
+        B2DRange aRes( rB2DRange );
+        aRes *= rMat;
+        return aRes;
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/range/b2drangeclipper.cxx b/basegfx/source/range/b2drangeclipper.cxx
new file mode 100644
index 0000000000..401ff20caa
--- /dev/null
+++ b/basegfx/source/range/b2drangeclipper.cxx
@@ -0,0 +1,877 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <osl/diagnose.h>
+
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/range/b2drangeclipper.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/range/b2drectangle.hxx>
+
+#include <o3tl/vector_pool.hxx>
+
+#include <algorithm>
+#include <cassert>
+#include <list>
+#include <iterator>
+
+namespace basegfx
+{
+    namespace
+    {
+        // Generating a poly-polygon from a bunch of rectangles
+
+        // Helper functionality for sweep-line algorithm
+        // ====================================================
+
+        class ImplPolygon;
+        typedef o3tl::vector_pool<ImplPolygon> VectorOfPolygons;
+
+        /** This class represents an active edge
+
+            As the sweep line traverses across the overall area,
+            rectangle edges parallel to it generate events, and
+            rectangle edges orthogonal to it generate active
+            edges. This class represents the latter.
+         */
+        class ActiveEdge
+        {
+        public:
+
+            enum EdgeDirection {
+                /// edge proceeds to the left
+                PROCEED_LEFT=0,
+                /// edge proceeds to the right
+                PROCEED_RIGHT=1
+            };
+
+            /** Create active edge
+
+                @param rRect
+                Rectangle this edge is part of
+
+                @param fInvariantCoord
+                The invariant coordinate value of this edge
+
+                @param eEdgeType
+                Is fInvariantCoord the lower or the higher value, for
+                this rect?
+             */
+            ActiveEdge( const B2DRectangle& rRect,
+                        const double&       fInvariantCoord,
+                        std::ptrdiff_t      nPolyIdx,
+                        EdgeDirection       eEdgeDirection ) :
+                mfInvariantCoord(fInvariantCoord),
+                mpAssociatedRect( &rRect ),
+                mnPolygonIdx( nPolyIdx ),
+                meEdgeDirection( eEdgeDirection )
+            {}
+
+            double              getInvariantCoord() const { return mfInvariantCoord; }
+            const B2DRectangle& getRect() const { return *mpAssociatedRect; }
+            std::ptrdiff_t      getTargetPolygonIndex() const { return mnPolygonIdx; }
+            void                setTargetPolygonIndex( std::ptrdiff_t nIdx ) { mnPolygonIdx = nIdx; }
+            EdgeDirection       getEdgeDirection() const { return meEdgeDirection; }
+
+        private:
+            /** The invariant coordinate value of this edge (e.g. the
+                common y value, for a horizontal edge)
+             */
+            double              mfInvariantCoord;
+
+            /** Associated rectangle
+
+                This on the one hand saves some storage space (the
+                vector of rectangles is persistent, anyway), and on
+                the other hand provides an identifier to match active
+                edges and x events (see below)
+
+                Ptr because class needs to be assignable
+             */
+            const B2DRectangle* mpAssociatedRect;
+
+            /** Index of the polygon this edge is currently involved
+                with.
+
+                Note that this can change for some kinds of edge
+                intersection, as the algorithm tends to swap
+                associated polygons there.
+
+                -1 denotes no assigned polygon
+             */
+            std::ptrdiff_t      mnPolygonIdx;
+
+            /// 'left' or 'right'
+            EdgeDirection       meEdgeDirection;
+        };
+
+        // Needs to be list - various places hold ptrs to elements
+        typedef std::list< ActiveEdge > ListOfEdges;
+
+        /** Element of the sweep line event list
+
+            As the sweep line traverses across the overall area,
+            rectangle edges parallel to it generate events, and
+            rectangle edges orthogonal to it generate active
+            edges. This class represents the former.
+
+            The class defines an element of the sweep line list. The
+            sweep line's position jumps in steps defined by the
+            coordinates of the sorted SweepLineEvent entries.
+         */
+        class SweepLineEvent
+        {
+        public:
+            /** The two possible sweep line rectangle edges differ by
+                one coordinate value - the starting edge has the
+                lower, the finishing edge the higher value.
+             */
+            enum EdgeType {
+                /// edge with lower coordinate value
+                STARTING_EDGE=0,
+                /// edge with higher coordinate value
+                FINISHING_EDGE=1
+            };
+
+            /** The two possible sweep line directions
+             */
+            enum EdgeDirection {
+                PROCEED_UP=0,
+                PROCEED_DOWN=1
+            };
+
+            /** Create sweep line event
+
+                @param fPos
+                Coordinate position of the event
+
+                @param rRect
+                Rectangle this event is generated for.
+
+                @param eEdgeType
+                Is fPos the lower or the higher value, for the
+                rectangle this event is generated for?
+             */
+            SweepLineEvent( double              fPos,
+                            const B2DRectangle& rRect,
+                            EdgeType            eEdgeType,
+                            EdgeDirection       eDirection) :
+                mfPos( fPos ),
+                mpAssociatedRect( &rRect ),
+                meEdgeType( eEdgeType ),
+                meEdgeDirection( eDirection )
+            {}
+
+            double              getPos() const { return mfPos; }
+            const B2DRectangle& getRect() const { return *mpAssociatedRect; }
+            EdgeType            getEdgeType() const { return meEdgeType; }
+            EdgeDirection       getEdgeDirection() const { return meEdgeDirection; }
+
+            /// For STL sort
+            bool operator<( const SweepLineEvent& rRHS ) const { return mfPos < rRHS.mfPos; }
+
+        private:
+            /// position of the event, in the direction of the line sweep
+            double                mfPos;
+
+            /** Rectangle this event is generated for
+
+                This on the one hand saves some storage space (the
+                vector of rectangles is persistent, anyway), and on
+                the other hand provides an identifier to match active
+                edges and events (see below)
+
+                Ptr because class needs to be assignable
+             */
+            const B2DRectangle*   mpAssociatedRect;
+
+            /// 'upper' or 'lower' edge of original rectangle.
+            EdgeType              meEdgeType;
+
+            /// 'up' or 'down'
+            EdgeDirection         meEdgeDirection;
+        };
+
+        typedef std::vector< SweepLineEvent > VectorOfEvents;
+
+        /** Smart point container for B2DMultiRange::getPolyPolygon()
+
+            This class provides methods needed only here, and is used
+            as a place to store some additional information per
+            polygon. Also, most of the intersection logic is
+            implemented here.
+         */
+        class ImplPolygon
+        {
+        public:
+            /** Create polygon
+             */
+            ImplPolygon() :
+                mpLeadingRightEdge(nullptr),
+                mnIdx(-1),
+                mbIsFinished(false)
+            {
+                // completely ad-hoc. but what the hell.
+                maPoints.reserve(11);
+            }
+
+            void setPolygonPoolIndex( std::ptrdiff_t nIdx ) { mnIdx = nIdx; }
+
+            /// Add point to the end of the existing points
+            void append( const B2DPoint& rPoint )
+            {
+                OSL_PRECOND( maPoints.empty() ||
+                             maPoints.back().getX() == rPoint.getX() ||
+                             maPoints.back().getY() == rPoint.getY(),
+                             "ImplPolygon::append(): added point violates 90 degree line angle constraint!" );
+
+                if( maPoints.empty() ||
+                    maPoints.back() != rPoint )
+                {
+                    // avoid duplicate points
+                    maPoints.push_back( rPoint );
+                }
+            }
+
+            /** Perform the intersection of this polygon with an
+                active edge.
+
+                @param rEvent
+                The vertical line event that generated the
+                intersection
+
+                @param rActiveEdge
+                The active edge that generated the intersection
+
+                @param rPolygonPool
+                Polygon pool, we sometimes need to allocate a new one
+
+                @param bIsFinishingEdge
+                True, when this is hitting the last edge of the
+                vertical sweep - every vertical sweep starts and ends
+                with upper and lower edge of the _same_ rectangle.
+
+                @return the new current polygon (that's the one
+                processing must proceed with, when going through the
+                list of upcoming active edges).
+             */
+            std::ptrdiff_t intersect( SweepLineEvent const & rEvent,
+                                      ActiveEdge&            rActiveEdge,
+                                      VectorOfPolygons&      rPolygonPool,
+                                      B2DPolyPolygon&        rRes,
+                                      bool                   isFinishingEdge )
+            {
+                OSL_PRECOND( !mbIsFinished,
+                             "ImplPolygon::intersect(): called on already finished polygon!" );
+                OSL_PRECOND( !isFinishingEdge || &rEvent.getRect() == &rActiveEdge.getRect(),
+                             "ImplPolygon::intersect(): inconsistent ending!" );
+
+                const B2DPoint aIntersectionPoint( rEvent.getPos(),
+                                                   rActiveEdge.getInvariantCoord() );
+
+                // intersection point, goes to our polygon
+                // unconditionally
+                append(aIntersectionPoint);
+
+                if( isFinishingEdge )
+                {
+                    // isSweepLineEnteringRect ?
+                    if( rEvent.getEdgeType() == SweepLineEvent::STARTING_EDGE)
+                        handleFinalOwnRightEdge(rActiveEdge);
+                    else
+                        handleFinalOwnLeftEdge(rActiveEdge,
+                                               rPolygonPool,
+                                               rRes);
+
+                    // we're done with this rect & sweep line
+                    return -1;
+                }
+                else if( metOwnEdge(rEvent,rActiveEdge) )
+                {
+                    handleInitialOwnEdge(rEvent, rActiveEdge);
+
+                    // point already added, all init done, continue
+                    // with same poly
+                    return mnIdx;
+                }
+                else
+                {
+                    OSL_ENSURE( rActiveEdge.getTargetPolygonIndex() != -1,
+                                "ImplPolygon::intersect(): non-trivial intersection hit empty polygon!" );
+
+                    const bool isHittingLeftEdge(
+                        rActiveEdge.getEdgeDirection() == ActiveEdge::PROCEED_LEFT);
+
+                    if( isHittingLeftEdge )
+                        return handleComplexLeftEdge(rActiveEdge,
+                                                     aIntersectionPoint,
+                                                     rPolygonPool,
+                                                     rRes);
+                    else
+                        return handleComplexRightEdge(rActiveEdge,
+                                                      aIntersectionPoint,
+                                                      rPolygonPool);
+                }
+            }
+
+        private:
+            void handleInitialOwnEdge(SweepLineEvent const & rEvent,
+                                      ActiveEdge const & rActiveEdge) const
+            {
+                const bool isActiveEdgeProceedLeft(
+                    rActiveEdge.getEdgeDirection() == ActiveEdge::PROCEED_LEFT);
+                const bool isSweepLineEnteringRect(
+                    rEvent.getEdgeType() == SweepLineEvent::STARTING_EDGE);
+
+                OSL_ENSURE( isSweepLineEnteringRect == isActiveEdgeProceedLeft,
+                            "ImplPolygon::intersect(): sweep initial own edge hit: wrong polygon order" );
+
+                OSL_ENSURE( isSweepLineEnteringRect ||
+                            mpLeadingRightEdge == &rActiveEdge,
+                            "ImplPolygon::intersect(): sweep initial own edge hit: wrong leading edge" );
+            }
+
+            void handleFinalOwnRightEdge(ActiveEdge& rActiveEdge)
+            {
+                OSL_ENSURE( rActiveEdge.getEdgeDirection() == ActiveEdge::PROCEED_RIGHT,
+                            "ImplPolygon::handleInitialOwnRightEdge(): start edge wrong polygon order" );
+
+                rActiveEdge.setTargetPolygonIndex(mnIdx);
+                mpLeadingRightEdge = &rActiveEdge;
+            }
+
+            void handleFinalOwnLeftEdge(ActiveEdge const & rActiveEdge,
+                                        VectorOfPolygons&  rPolygonPool,
+                                        B2DPolyPolygon&    rRes)
+            {
+                OSL_ENSURE( rActiveEdge.getEdgeDirection() == ActiveEdge::PROCEED_LEFT,
+                            "ImplPolygon::handleFinalOwnLeftEdge(): end edge wrong polygon order" );
+
+                const bool isHittingOurTail(
+                    rActiveEdge.getTargetPolygonIndex() == mnIdx);
+
+                if( isHittingOurTail )
+                    finish(rRes); // just finish. no fuss.
+                else
+                {
+                    // temp poly hits final left edge
+                    const std::ptrdiff_t nTmpIdx=rActiveEdge.getTargetPolygonIndex();
+                    ImplPolygon& rTmp=rPolygonPool.get(nTmpIdx);
+
+                    // active edge's polygon has points
+                    // already. ours need to go in front of them.
+                    maPoints.insert(maPoints.end(),
+                                    rTmp.maPoints.begin(),
+                                    rTmp.maPoints.end());
+
+                    // adjust leading edges, we're switching the polygon
+                    ActiveEdge* const pFarEdge=rTmp.mpLeadingRightEdge;
+
+                    mpLeadingRightEdge = pFarEdge;
+                    pFarEdge->setTargetPolygonIndex(mnIdx);
+
+                    // nTmpIdx is an empty shell, get rid of it
+                    rPolygonPool.free(nTmpIdx);
+                }
+            }
+
+            std::ptrdiff_t handleComplexLeftEdge(ActiveEdge&       rActiveEdge,
+                                                 const B2DPoint&   rIntersectionPoint,
+                                                 VectorOfPolygons& rPolygonPool,
+                                                 B2DPolyPolygon&   rRes)
+            {
+                const bool isHittingOurTail(
+                    rActiveEdge.getTargetPolygonIndex() == mnIdx);
+                if( isHittingOurTail )
+                {
+                    finish(rRes);
+
+                    // so "this" is done - need new polygon to collect
+                    // further points
+                    const std::ptrdiff_t nIdxNewPolygon=rPolygonPool.alloc();
+                    rPolygonPool.get(nIdxNewPolygon).setPolygonPoolIndex(nIdxNewPolygon);
+                    rPolygonPool.get(nIdxNewPolygon).append(rIntersectionPoint);
+
+                    rActiveEdge.setTargetPolygonIndex(nIdxNewPolygon);
+
+                    return nIdxNewPolygon;
+                }
+                else
+                {
+                    const std::ptrdiff_t nTmpIdx=rActiveEdge.getTargetPolygonIndex();
+                    ImplPolygon& rTmp=rPolygonPool.get(nTmpIdx);
+
+                    // active edge's polygon has points
+                    // already. ours need to go in front of them.
+                    maPoints.insert(maPoints.end(),
+                                    rTmp.maPoints.begin(),
+                                    rTmp.maPoints.end());
+
+                    rTmp.maPoints.clear();
+                    rTmp.append(rIntersectionPoint);
+
+                    // adjust leading edges, we're switching the polygon
+                    ActiveEdge* const pFarEdge=rTmp.mpLeadingRightEdge;
+                    ActiveEdge* const pNearEdge=&rActiveEdge;
+
+                    rTmp.mpLeadingRightEdge = nullptr;
+                    pNearEdge->setTargetPolygonIndex(nTmpIdx);
+
+                    mpLeadingRightEdge = pFarEdge;
+                    pFarEdge->setTargetPolygonIndex(mnIdx);
+
+                    return nTmpIdx;
+                }
+            }
+
+            std::ptrdiff_t handleComplexRightEdge(ActiveEdge&       rActiveEdge,
+                                                  const B2DPoint&   rIntersectionPoint,
+                                                  VectorOfPolygons& rPolygonPool)
+            {
+                const std::ptrdiff_t nTmpIdx=rActiveEdge.getTargetPolygonIndex();
+                ImplPolygon& rTmp=rPolygonPool.get(nTmpIdx);
+
+                rTmp.append(rIntersectionPoint);
+
+                rActiveEdge.setTargetPolygonIndex(mnIdx);
+                mpLeadingRightEdge = &rActiveEdge;
+
+                rTmp.mpLeadingRightEdge = nullptr;
+
+                return nTmpIdx;
+            }
+
+            /// True when sweep line hits our own active edge
+            static bool metOwnEdge(SweepLineEvent const & rEvent,
+                                   ActiveEdge const &     rActiveEdge)
+            {
+                const bool bHitOwnEdge=&rEvent.getRect() == &rActiveEdge.getRect();
+                return bHitOwnEdge;
+            }
+
+            /// Retrieve B2DPolygon from this object
+            B2DPolygon getPolygon() const
+            {
+                B2DPolygon aRes;
+                for (auto const& aPoint : maPoints)
+                    aRes.append(aPoint, 1);
+                aRes.setClosed( true );
+                return aRes;
+            }
+
+            /** Finish this polygon, push to result set.
+             */
+            void finish(B2DPolyPolygon& rRes)
+            {
+                OSL_PRECOND( maPoints.empty() ||
+                             maPoints.front().getX() == maPoints.back().getX() ||
+                             maPoints.front().getY() == maPoints.back().getY(),
+                             "ImplPolygon::finish(): first and last point violate 90 degree line angle constraint!" );
+
+                mbIsFinished = true;
+                mpLeadingRightEdge = nullptr;
+
+                rRes.append(getPolygon());
+            }
+
+            /** Refers to the current leading edge element of this
+                polygon, or NULL. The leading edge denotes the 'front'
+                of the polygon vertex sequence, i.e. the coordinates
+                at the polygon's leading edge are returned from
+                maPoints.front()
+             */
+            ActiveEdge*           mpLeadingRightEdge;
+
+            /// current index into vector pool
+            std::ptrdiff_t        mnIdx;
+
+            /// Container for the actual polygon points
+            std::vector<B2DPoint> maPoints;
+
+            /// When true, this polygon is 'done', i.e. nothing must be added anymore.
+            bool                  mbIsFinished;
+        };
+
+        /** Init sweep line event list
+
+            This method fills the event list with the sweep line
+            events generated from the input rectangles, and sorts them
+            with increasing x.
+         */
+        void setupSweepLineEventListFromRanges( VectorOfEvents& o_rEventVector,
+                                                const std::vector<B2DRange>& rRanges,
+                                                const std::vector<B2VectorOrientation>& rOrientations )
+        {
+            // we need exactly 2*rectVec.size() events: one for the
+            // left, and one for the right edge of each rectangle
+            o_rEventVector.clear();
+            o_rEventVector.reserve( 2*rRanges.size() );
+
+            // generate events
+            // ===============
+
+            // first pass: add all left edges in increasing order
+            std::vector<B2DRange>::const_iterator aCurrRect=rRanges.begin();
+            std::vector<B2VectorOrientation>::const_iterator aCurrOrientation=rOrientations.begin();
+            const std::vector<B2DRange>::const_iterator aEnd=rRanges.end();
+            const std::vector<B2VectorOrientation>::const_iterator aEndOrientation=rOrientations.end();
+            while( aCurrRect != aEnd && aCurrOrientation != aEndOrientation )
+            {
+                const B2DRectangle& rCurrRect( *aCurrRect++ );
+
+                o_rEventVector.emplace_back( rCurrRect.getMinX(),
+                                    rCurrRect,
+                                    SweepLineEvent::STARTING_EDGE,
+                                    (*aCurrOrientation++) == B2VectorOrientation::Positive ?
+                                    SweepLineEvent::PROCEED_UP : SweepLineEvent::PROCEED_DOWN );
+            }
+
+            // second pass: add all right edges in reversed order
+            std::vector<B2DRange>::const_reverse_iterator aCurrRectR=rRanges.rbegin();
+            std::vector<B2VectorOrientation>::const_reverse_iterator aCurrOrientationR=rOrientations.rbegin();
+            const std::vector<B2DRange>::const_reverse_iterator aEndR=rRanges.rend();
+            while( aCurrRectR != aEndR )
+            {
+                const B2DRectangle& rCurrRect( *aCurrRectR++ );
+
+                o_rEventVector.emplace_back( rCurrRect.getMaxX(),
+                                    rCurrRect,
+                                    SweepLineEvent::FINISHING_EDGE,
+                                    (*aCurrOrientationR++) == B2VectorOrientation::Positive ?
+                                    SweepLineEvent::PROCEED_DOWN : SweepLineEvent::PROCEED_UP );
+            }
+
+            // sort events
+            // ===========
+
+            // since we use stable_sort, the order of events with the
+            // same x value will not change. The elaborate two-pass
+            // add above thus ensures, that for each two rectangles
+            // with similar left and right x coordinates, the
+            // rectangle whose left event comes first will have its
+            // right event come last. This is advantageous for the
+            // clip algorithm below, see handleRightEdgeCrossing().
+
+            std::stable_sort( o_rEventVector.begin(),
+                              o_rEventVector.end() );
+        }
+
+        /** Insert two active edge segments for the given rectangle.
+
+            This method creates two active edge segments from the
+            given rect, and inserts them into the active edge list,
+            such that this stays sorted (if it was before).
+
+            @param io_rEdgeList
+            Active edge list to insert into
+
+            @param io_rPolygons
+            Vector of polygons. Each rectangle added creates one
+            tentative result polygon in this vector, and the edge list
+            entries holds a reference to that polygon (this _requires_
+            that the polygon vector does not reallocate, i.e. it must
+            have at least the maximal number of rectangles reserved)
+
+            @param o_CurrentPolygon
+            The then-current polygon when processing this sweep line
+            event
+
+            @param rCurrEvent
+            The actual event that caused this call
+         */
+        void createActiveEdgesFromStartEvent( ListOfEdges &          io_rEdgeList,
+                                              VectorOfPolygons &     io_rPolygonPool,
+                                              SweepLineEvent const & rCurrEvent )
+        {
+            ListOfEdges         aNewEdges;
+            const B2DRectangle& rRect=rCurrEvent.getRect();
+            const bool          bGoesDown=rCurrEvent.getEdgeDirection() == SweepLineEvent::PROCEED_DOWN;
+
+            // start event - new rect starts here, needs polygon to
+            // collect points into
+            const std::ptrdiff_t nIdxPolygon=io_rPolygonPool.alloc();
+            io_rPolygonPool.get(nIdxPolygon).setPolygonPoolIndex(nIdxPolygon);
+
+            // upper edge
+            aNewEdges.emplace_back(
+                    rRect,
+                    rRect.getMinY(),
+                    bGoesDown ? nIdxPolygon : -1,
+                    bGoesDown ? ActiveEdge::PROCEED_LEFT : ActiveEdge::PROCEED_RIGHT );
+            // lower edge
+            aNewEdges.emplace_back(
+                    rRect,
+                    rRect.getMaxY(),
+                    bGoesDown ? -1 : nIdxPolygon,
+                    bGoesDown ? ActiveEdge::PROCEED_RIGHT : ActiveEdge::PROCEED_LEFT );
+
+            // furthermore, have to respect a special tie-breaking
+            // rule here, for edges which share the same y value:
+            // newly added upper edges must be inserted _before_ any
+            // other edge with the same y value, and newly added lower
+            // edges must be _after_ all other edges with the same
+            // y. This ensures that the left vertical edge processing
+            // below encounters the upper edge of the current rect
+            // first, and the lower edge last, which automatically
+            // starts and finishes this rect correctly (as only then,
+            // the polygon will have their associated active edges
+            // set).
+            const double                nMinY( rRect.getMinY() );
+            const double                nMaxY( rRect.getMaxY() );
+            ListOfEdges::iterator       aCurr( io_rEdgeList.begin() );
+            const ListOfEdges::iterator aEnd ( io_rEdgeList.end() );
+            while( aCurr != aEnd )
+            {
+                const double nCurrY( aCurr->getInvariantCoord() );
+
+                if( nCurrY >= nMinY &&
+                    aNewEdges.size() == 2 ) // only add, if not yet done.
+                {
+                    // insert upper edge _before_ aCurr. Thus, it will
+                    // be the first entry for a range of equal y
+                    // values. Using splice here, since we hold
+                    // references to the moved list element!
+                    io_rEdgeList.splice( aCurr,
+                                         aNewEdges,
+                                         aNewEdges.begin() );
+                }
+
+                if( nCurrY > nMaxY )
+                {
+                    // insert lower edge _before_ aCurr. Thus, it will
+                    // be the last entry for a range of equal y values
+                    // (aCurr is the first entry strictly larger than
+                    // nMaxY). Using splice here, since we hold
+                    // references to the moved list element!
+                    io_rEdgeList.splice( aCurr,
+                                         aNewEdges,
+                                         aNewEdges.begin() );
+                    // done with insertion, can early-exit here.
+                    return;
+                }
+
+                ++aCurr;
+            }
+
+            // append remainder of aNewList (might still contain 2 or
+            // 1 elements, depending of the contents of io_rEdgeList).
+            io_rEdgeList.splice( aCurr,
+                                 aNewEdges );
+        }
+
+        bool isSameRect(ActiveEdge const &        rEdge,
+                               basegfx::B2DRange const & rRect)
+        {
+            return &rEdge.getRect() == &rRect;
+        }
+
+        // wow what a hack. necessary because stl's list::erase does
+        // not eat reverse_iterator
+        template<typename Cont, typename Iter> Iter eraseFromList(Cont&, const Iter&);
+        template<> ListOfEdges::iterator eraseFromList(
+            ListOfEdges& rList, const ListOfEdges::iterator& aIter)
+        {
+            return rList.erase(aIter);
+        }
+        template<> ListOfEdges::reverse_iterator eraseFromList(
+            ListOfEdges& rList, const ListOfEdges::reverse_iterator& aIter)
+        {
+            return ListOfEdges::reverse_iterator(
+                    rList.erase(std::prev(aIter.base())));
+        }
+
+        template<int bPerformErase,
+                 typename Iterator> void processActiveEdges(
+            Iterator          first,
+            Iterator          last,
+            ListOfEdges&      rActiveEdgeList,
+            SweepLineEvent const & rCurrEvent,
+            VectorOfPolygons& rPolygonPool,
+            B2DPolyPolygon&   rRes )
+        {
+            const basegfx::B2DRange& rCurrRect=rCurrEvent.getRect();
+
+            // fast-forward to rCurrEvent's first active edge (holds
+            // for both starting and finishing sweep line events, a
+            // rect is regarded _outside_ any rects whose events have
+            // started earlier
+            first = std::find_if(first, last,
+                                 [&rCurrRect](ActiveEdge& anEdge) { return isSameRect(anEdge, rCurrRect); });
+
+            if(first == last)
+                return;
+
+            int nCount=0;
+            std::ptrdiff_t nCurrPolyIdx=-1;
+            while(first != last)
+            {
+                if( nCurrPolyIdx == -1 )
+                    nCurrPolyIdx=first->getTargetPolygonIndex();
+
+                assert(nCurrPolyIdx != -1);
+
+                // second encounter of my rect -> second edge
+                // encountered, done
+                const bool bExit=
+                    nCount &&
+                    isSameRect(*first,
+                               rCurrRect);
+
+                // deal with current active edge
+                nCurrPolyIdx =
+                    rPolygonPool.get(nCurrPolyIdx).intersect(
+                        rCurrEvent,
+                        *first,
+                        rPolygonPool,
+                        rRes,
+                        bExit);
+
+                // prune upper & lower active edges, if requested
+                if( bPerformErase && (bExit || !nCount) )
+                    first = eraseFromList(rActiveEdgeList,first);
+                else
+                    ++first;
+
+                // delayed exit, had to prune first
+                if( bExit )
+                    return;
+
+                ++nCount;
+            }
+        }
+
+        template<int bPerformErase> void processActiveEdgesTopDown(
+            SweepLineEvent&   rCurrEvent,
+            ListOfEdges&      rActiveEdgeList,
+            VectorOfPolygons& rPolygonPool,
+            B2DPolyPolygon&   rRes )
+        {
+            processActiveEdges<bPerformErase>(
+                rActiveEdgeList. begin(),
+                rActiveEdgeList. end(),
+                rActiveEdgeList,
+                rCurrEvent,
+                rPolygonPool,
+                rRes);
+        }
+
+        template<int bPerformErase> void processActiveEdgesBottomUp(
+            SweepLineEvent&   rCurrEvent,
+            ListOfEdges&      rActiveEdgeList,
+            VectorOfPolygons& rPolygonPool,
+            B2DPolyPolygon&   rRes )
+        {
+            processActiveEdges<bPerformErase>(
+                rActiveEdgeList. rbegin(),
+                rActiveEdgeList. rend(),
+                rActiveEdgeList,
+                rCurrEvent,
+                rPolygonPool,
+                rRes);
+        }
+
+        enum{ NoErase=0, PerformErase=1 };
+
+        void handleStartingEdge( SweepLineEvent&   rCurrEvent,
+                                 ListOfEdges&      rActiveEdgeList,
+                                 VectorOfPolygons& rPolygonPool,
+                                 B2DPolyPolygon&   rRes)
+        {
+            // inject two new active edges for rect
+            createActiveEdgesFromStartEvent( rActiveEdgeList,
+                                             rPolygonPool,
+                                             rCurrEvent );
+
+            if( rCurrEvent.getEdgeDirection() == SweepLineEvent::PROCEED_DOWN )
+                processActiveEdgesTopDown<NoErase>(
+                    rCurrEvent, rActiveEdgeList, rPolygonPool, rRes);
+            else
+                processActiveEdgesBottomUp<NoErase>(
+                    rCurrEvent, rActiveEdgeList, rPolygonPool, rRes);
+        }
+
+        void handleFinishingEdge( SweepLineEvent&   rCurrEvent,
+                                  ListOfEdges&      rActiveEdgeList,
+                                  VectorOfPolygons& rPolygonPool,
+                                  B2DPolyPolygon&   rRes)
+        {
+            if( rCurrEvent.getEdgeDirection() == SweepLineEvent::PROCEED_DOWN )
+                processActiveEdgesTopDown<PerformErase>(
+                    rCurrEvent, rActiveEdgeList, rPolygonPool, rRes);
+            else
+                processActiveEdgesBottomUp<PerformErase>(
+                    rCurrEvent, rActiveEdgeList, rPolygonPool, rRes);
+        }
+
+        void handleSweepLineEvent( SweepLineEvent&   rCurrEvent,
+                                          ListOfEdges&      rActiveEdgeList,
+                                          VectorOfPolygons& rPolygonPool,
+                                          B2DPolyPolygon&   rRes)
+        {
+            if( rCurrEvent.getEdgeType() == SweepLineEvent::STARTING_EDGE )
+                handleStartingEdge(rCurrEvent,rActiveEdgeList,rPolygonPool,rRes);
+            else
+                handleFinishingEdge(rCurrEvent,rActiveEdgeList,rPolygonPool,rRes);
+        }
+    }
+
+    namespace utils
+    {
+        B2DPolyPolygon solveCrossovers(const std::vector<B2DRange>& rRanges,
+                                       const std::vector<B2VectorOrientation>& rOrientations)
+        {
+            // sweep-line algorithm to generate a poly-polygon
+            // from a bunch of rectangles
+            // ===============================================
+
+            // This algorithm uses the well-known sweep line
+            // concept, explained in every good text book about
+            // computational geometry.
+
+            // We start with creating two structures for every
+            // rectangle, one representing the left x coordinate,
+            // one representing the right x coordinate (and both
+            // referencing the original rect). These structs are
+            // sorted with increasing x coordinates.
+
+            // Then, we start processing the resulting list from
+            // the beginning. Every entry in the list defines a
+            // point in time of the line sweeping from left to
+            // right across all rectangles.
+            VectorOfEvents aSweepLineEvents;
+            setupSweepLineEventListFromRanges( aSweepLineEvents,
+                                               rRanges,
+                                               rOrientations );
+
+            B2DPolyPolygon   aRes;
+            VectorOfPolygons aPolygonPool;
+            ListOfEdges      aActiveEdgeList;
+
+            // sometimes not enough, but a usable compromise
+            aPolygonPool.reserve( rRanges.size() );
+
+            for (auto& aSweepLineEvent : aSweepLineEvents)
+                handleSweepLineEvent(aSweepLineEvent, aActiveEdgeList, aPolygonPool, aRes);
+
+            return aRes;
+        }
+    }
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/range/b2xrange.cxx b/basegfx/source/range/b2xrange.cxx
new file mode 100644
index 0000000000..3f04a95af5
--- /dev/null
+++ b/basegfx/source/range/b2xrange.cxx
@@ -0,0 +1,120 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/range/b2irange.hxx>
+
+namespace basegfx
+{
+    namespace
+    {
+        /** Generic implementation of the difference set computation
+
+            @tpl RangeType
+            Type to operate on. Must provide ValueType and TraitsType
+            nested types.
+         */
+        template< class RangeType > void doComputeSetDifference(
+            std::vector< RangeType >& o_rRanges,
+            const RangeType&            a,
+            const RangeType&            b )
+        {
+            o_rRanges.clear();
+
+            // special-casing the empty rect case (this will fail most
+            // of the times below, because of the DBL_MIN/MAX special
+            // values denoting emptiness in the rectangle.
+            if( a.isEmpty() )
+            {
+                o_rRanges.push_back( b );
+                return;
+            }
+            if( b.isEmpty() )
+            {
+                o_rRanges.push_back( a );
+                return;
+            }
+
+            const typename RangeType::ValueType                     ax(a.getMinX());
+            const typename RangeType::ValueType                     ay(a.getMinY());
+            const typename RangeType::TraitsType::DifferenceType    aw(a.getWidth());
+            const typename RangeType::TraitsType::DifferenceType    ah(a.getHeight());
+            const typename RangeType::ValueType                     bx(b.getMinX());
+            const typename RangeType::ValueType                     by(b.getMinY());
+            const typename RangeType::TraitsType::DifferenceType    bw(b.getWidth());
+            const typename RangeType::TraitsType::DifferenceType    bh(b.getHeight());
+
+            const typename RangeType::TraitsType::DifferenceType    h0( (by > ay) ? by - ay : 0 );
+            const typename RangeType::TraitsType::DifferenceType    h3( (by + bh < ay + ah) ? ay + ah - by - bh : 0 );
+            const typename RangeType::TraitsType::DifferenceType    w1( (bx > ax) ? bx - ax : 0 );
+            const typename RangeType::TraitsType::DifferenceType    w2( (ax + aw > bx + bw) ? ax + aw - bx - bw : 0 );
+            const typename RangeType::TraitsType::DifferenceType    h12( (h0 + h3 < ah) ? ah - h0 - h3 : 0 );
+
+            // TODO(E2): Use numeric_cast instead of static_cast here,
+            // need range checks!
+            if (h0 > 0)
+                o_rRanges.push_back(
+                    RangeType(ax,ay,
+                              static_cast<typename RangeType::ValueType>(ax+aw),
+                              static_cast<typename RangeType::ValueType>(ay+h0)) );
+
+            if (w1 > 0 && h12 > 0)
+                o_rRanges.push_back(
+                    RangeType(ax,
+                              static_cast<typename RangeType::ValueType>(ay+h0),
+                              static_cast<typename RangeType::ValueType>(ax+w1),
+                              static_cast<typename RangeType::ValueType>(ay+h0+h12)) );
+
+            if (w2 > 0 && h12 > 0)
+                o_rRanges.push_back(
+                    RangeType(static_cast<typename RangeType::ValueType>(bx+bw),
+                              static_cast<typename RangeType::ValueType>(ay+h0),
+                              static_cast<typename RangeType::ValueType>(bx+bw+w2),
+                              static_cast<typename RangeType::ValueType>(ay+h0+h12)) );
+
+            if (h3 > 0)
+                o_rRanges.push_back(
+                    RangeType(ax,
+                              static_cast<typename RangeType::ValueType>(ay+h0+h12),
+                              static_cast<typename RangeType::ValueType>(ax+aw),
+                              static_cast<typename RangeType::ValueType>(ay+h0+h12+h3)) );
+        }
+    }
+
+    std::vector< B2IRange >& computeSetDifference( std::vector< B2IRange >& o_rResult,
+                                                     const B2IRange&            rFirst,
+                                                     const B2IRange&            rSecond )
+    {
+        doComputeSetDifference( o_rResult, rFirst, rSecond );
+
+        return o_rResult;
+    }
+
+    std::vector< B2DRange >& computeSetDifference( std::vector< B2DRange >& o_rResult,
+                                                     const B2DRange&            rFirst,
+                                                     const B2DRange&            rSecond )
+    {
+        doComputeSetDifference( o_rResult, rFirst, rSecond );
+
+        return o_rResult;
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/range/b3drange.cxx b/basegfx/source/range/b3drange.cxx
new file mode 100644
index 0000000000..89bb98a1e1
--- /dev/null
+++ b/basegfx/source/range/b3drange.cxx
@@ -0,0 +1,64 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/range/b3drange.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+
+namespace basegfx
+{
+    void B3DRange::transform(const B3DHomMatrix& rMatrix)
+    {
+        if(isEmpty() || rMatrix.isIdentity())
+            return;
+
+        const B3DRange aSource(*this);
+        reset();
+        expand(rMatrix * B3DPoint(aSource.getMinX(), aSource.getMinY(), aSource.getMinZ()));
+        expand(rMatrix * B3DPoint(aSource.getMaxX(), aSource.getMinY(), aSource.getMinZ()));
+        expand(rMatrix * B3DPoint(aSource.getMinX(), aSource.getMaxY(), aSource.getMinZ()));
+        expand(rMatrix * B3DPoint(aSource.getMaxX(), aSource.getMaxY(), aSource.getMinZ()));
+        expand(rMatrix * B3DPoint(aSource.getMinX(), aSource.getMinY(), aSource.getMaxZ()));
+        expand(rMatrix * B3DPoint(aSource.getMaxX(), aSource.getMinY(), aSource.getMaxZ()));
+        expand(rMatrix * B3DPoint(aSource.getMinX(), aSource.getMaxY(), aSource.getMaxZ()));
+        expand(rMatrix * B3DPoint(aSource.getMaxX(), aSource.getMaxY(), aSource.getMaxZ()));
+    }
+
+    B3DRange& B3DRange::operator*=( const ::basegfx::B3DHomMatrix& rMat )
+    {
+        transform(rMat);
+        return *this;
+    }
+
+    const B3DRange& B3DRange::getUnitB3DRange()
+    {
+        static const B3DRange aUnitB3DRange(0.0, 0.0, 0.0, 1.0, 1.0, 1.0);
+
+        return aUnitB3DRange;
+    }
+
+    B3DRange operator*( const ::basegfx::B3DHomMatrix& rMat, const B3DRange& rB3DRange )
+    {
+        B3DRange aRes( rB3DRange );
+        aRes *= rMat;
+        return aRes;
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/raster/rasterconvert3d.cxx b/basegfx/source/raster/rasterconvert3d.cxx
new file mode 100644
index 0000000000..e998eb9938
--- /dev/null
+++ b/basegfx/source/raster/rasterconvert3d.cxx
@@ -0,0 +1,337 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/raster/rasterconvert3d.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/polygon/b3dpolygon.hxx>
+#include <basegfx/polygon/b3dpolypolygon.hxx>
+#include <basegfx/point/b3dpoint.hxx>
+
+// implementations of the 3D raster converter
+
+namespace basegfx
+{
+    void RasterConverter3D::addArea(const B3DPolygon& rFill, const B3DHomMatrix* pViewToEye)
+    {
+        const sal_uInt32 nPointCount(rFill.count());
+
+        for(sal_uInt32 a(0); a < nPointCount; a++)
+        {
+            addEdge(rFill, a, (a + 1) % nPointCount, pViewToEye);
+        }
+    }
+
+    void RasterConverter3D::addArea(const B3DPolyPolygon& rFill, const B3DHomMatrix* pViewToEye)
+    {
+        const sal_uInt32 nPolyCount(rFill.count());
+
+        for(sal_uInt32 a(0); a < nPolyCount; a++)
+        {
+            addArea(rFill.getB3DPolygon(a), pViewToEye);
+        }
+    }
+
+    RasterConverter3D::RasterConverter3D()
+    {}
+
+    RasterConverter3D::~RasterConverter3D()
+    {}
+
+    void RasterConverter3D::rasterconvertB3DArea(sal_Int32 nStartLine, sal_Int32 nStopLine)
+    {
+        if(maLineEntries.empty())
+            return;
+
+        OSL_ENSURE(nStopLine >= nStartLine, "nStopLine is bigger than nStartLine (!)");
+
+        // sort global entries by Y, X once. After this, the vector
+        // is seen as frozen. Pointers to its entries will be used in the following code.
+        std::sort(maLineEntries.begin(), maLineEntries.end());
+
+        // local parameters
+        std::vector< RasterConversionLineEntry3D >::iterator aCurrentEntry(maLineEntries.begin());
+        std::vector< RasterConversionLineEntry3D* > aCurrentLine;
+        std::vector< RasterConversionLineEntry3D* > aNextLine;
+        std::vector< RasterConversionLineEntry3D* >::iterator aRasterConversionLineEntry3D;
+
+        // get scanlines first LineNumber as start
+        sal_Int32 nLineNumber(std::max(aCurrentEntry->getY(), nStartLine));
+
+        while((!aCurrentLine.empty() || aCurrentEntry != maLineEntries.end()) && (nLineNumber < nStopLine))
+        {
+            // add all entries which start at current line to current scanline
+            while(aCurrentEntry != maLineEntries.end())
+            {
+                const sal_Int32 nCurrentLineNumber(aCurrentEntry->getY());
+
+                if(nCurrentLineNumber > nLineNumber)
+                {
+                    // line is below current one, done (since array is sorted)
+                    break;
+                }
+                else
+                {
+                    // less or equal. Line is above or at current one. Advance it exactly to
+                    // current line
+                    const sal_uInt32 nStep(nLineNumber - nCurrentLineNumber);
+
+                    if(!nStep || aCurrentEntry->decrementRasterConversionLineEntry3D(nStep))
+                    {
+                        // add when exactly on current line or when increment to it did not
+                        // completely consume it
+                        if(nStep)
+                        {
+                            aCurrentEntry->incrementRasterConversionLineEntry3D(nStep, *this);
+                        }
+
+                        aCurrentLine.push_back(&(*aCurrentEntry));
+                    }
+                }
+
+                ++aCurrentEntry;
+            }
+
+            // sort current scanline using comparator. Only X is used there
+            // since all entries are already in one processed line. This needs to be done
+            // every time since not only new spans may have benn added or old removed,
+            // but incrementing may also have changed the order
+            std::sort(aCurrentLine.begin(), aCurrentLine.end(), lineComparator());
+
+            // process current scanline
+            aRasterConversionLineEntry3D = aCurrentLine.begin();
+            aNextLine.clear();
+            sal_uInt32 nPairCount(0);
+
+            while(aRasterConversionLineEntry3D != aCurrentLine.end())
+            {
+                RasterConversionLineEntry3D& rPrevScanRasterConversionLineEntry3D(**aRasterConversionLineEntry3D++);
+
+                // look for 2nd span
+                if(aRasterConversionLineEntry3D != aCurrentLine.end())
+                {
+                    // work on span from rPrevScanRasterConversionLineEntry3D to aRasterConversionLineEntry3D, fLineNumber is valid
+                    processLineSpan(rPrevScanRasterConversionLineEntry3D, **aRasterConversionLineEntry3D, nLineNumber, nPairCount++);
+                }
+
+                // increment to next line
+                if(rPrevScanRasterConversionLineEntry3D.decrementRasterConversionLineEntry3D(1))
+                {
+                    rPrevScanRasterConversionLineEntry3D.incrementRasterConversionLineEntry3D(1, *this);
+                    aNextLine.push_back(&rPrevScanRasterConversionLineEntry3D);
+                }
+            }
+
+            // copy back next scanline if count has changed
+            if(aNextLine.size() != aCurrentLine.size())
+            {
+                aCurrentLine = aNextLine;
+            }
+
+            // increment fLineNumber
+            nLineNumber++;
+        }
+    }
+
+    void RasterConverter3D::addEdge(const B3DPolygon& rFill, sal_uInt32 a, sal_uInt32 b, const B3DHomMatrix* pViewToEye)
+    {
+        B3DPoint aStart(rFill.getB3DPoint(a));
+        B3DPoint aEnd(rFill.getB3DPoint(b));
+        sal_Int32 nYStart(fround(aStart.getY()));
+        sal_Int32 nYEnd(fround(aEnd.getY()));
+
+        if(nYStart == nYEnd)
+            return;
+
+        if(nYStart > nYEnd)
+        {
+            std::swap(aStart, aEnd);
+            std::swap(nYStart, nYEnd);
+            std::swap(a, b);
+        }
+
+        const sal_uInt32 nYDelta(nYEnd - nYStart);
+        const double fInvYDelta(1.0 / nYDelta);
+        maLineEntries.emplace_back(
+            aStart.getX(), (aEnd.getX() - aStart.getX()) * fInvYDelta,
+            aStart.getZ(), (aEnd.getZ() - aStart.getZ()) * fInvYDelta,
+            nYStart, nYDelta);
+
+        // if extra interpolation data is used, add it to the last created entry
+        RasterConversionLineEntry3D& rEntry = maLineEntries[maLineEntries.size() - 1];
+
+        if(rFill.areBColorsUsed())
+        {
+            rEntry.setColorIndex(addColorInterpolator(rFill.getBColor(a), rFill.getBColor(b), fInvYDelta));
+        }
+
+        if(rFill.areNormalsUsed())
+        {
+            rEntry.setNormalIndex(addNormalInterpolator(rFill.getNormal(a), rFill.getNormal(b), fInvYDelta));
+        }
+
+        if(!rFill.areTextureCoordinatesUsed())
+            return;
+
+        if(pViewToEye)
+        {
+            const double fEyeA(((*pViewToEye) * aStart).getZ());
+            const double fEyeB(((*pViewToEye) * aEnd).getZ());
+
+            rEntry.setInverseTextureIndex(addInverseTextureInterpolator(
+                rFill.getTextureCoordinate(a),
+                rFill.getTextureCoordinate(b),
+                fEyeA, fEyeB, fInvYDelta));
+        }
+        else
+        {
+            rEntry.setTextureIndex(addTextureInterpolator(
+                rFill.getTextureCoordinate(a),
+                rFill.getTextureCoordinate(b),
+                fInvYDelta));
+        }
+    }
+
+    void RasterConverter3D::rasterconvertB3DEdge(const B3DPolygon& rLine, sal_uInt32 nA, sal_uInt32 nB, sal_Int32 nStartLine, sal_Int32 nStopLine, sal_uInt16 nLineWidth)
+    {
+        B3DPoint aStart(rLine.getB3DPoint(nA));
+        B3DPoint aEnd(rLine.getB3DPoint(nB));
+        const double fZBufferLineAdd(0x00ff);
+
+        if(nLineWidth > 1)
+        {
+            // this is not a hairline anymore, in most cases since it's an oversampled
+            // hairline to get e.g. AA for Z-Buffering. Create fill geometry.
+            if(!aStart.equal(aEnd))
+            {
+                reset();
+                maLineEntries.clear();
+
+                B2DVector aVector(aEnd.getX() - aStart.getX(), aEnd.getY() - aStart.getY());
+                aVector.normalize();
+                const B2DVector aPerpend(getPerpendicular(aVector) * ((static_cast<double>(nLineWidth) + 0.5) * 0.5));
+                const double fZStartWithAdd(aStart.getZ() + fZBufferLineAdd);
+                const double fZEndWithAdd(aEnd.getZ() + fZBufferLineAdd);
+
+                B3DPolygon aPolygon;
+                aPolygon.append(B3DPoint(aStart.getX() + aPerpend.getX(), aStart.getY() + aPerpend.getY(), fZStartWithAdd));
+                aPolygon.append(B3DPoint(aEnd.getX() + aPerpend.getX(), aEnd.getY() + aPerpend.getY(), fZEndWithAdd));
+                aPolygon.append(B3DPoint(aEnd.getX() - aPerpend.getX(), aEnd.getY() - aPerpend.getY(), fZEndWithAdd));
+                aPolygon.append(B3DPoint(aStart.getX() - aPerpend.getX(), aStart.getY() - aPerpend.getY(), fZStartWithAdd));
+                aPolygon.setClosed(true);
+
+                addArea(aPolygon, nullptr);
+            }
+        }
+        else
+        {
+            // it's a hairline. Use direct RasterConversionLineEntry creation to
+            // rasterconvert lines as similar to areas as possible to avoid Z-Fighting
+            sal_Int32 nYStart(fround(aStart.getY()));
+            sal_Int32 nYEnd(fround(aEnd.getY()));
+
+            if(nYStart == nYEnd)
+            {
+                // horizontal line, check X
+                const sal_Int32 nXStart(static_cast<sal_Int32>(aStart.getX()));
+                const sal_Int32 nXEnd(static_cast<sal_Int32>(aEnd.getX()));
+
+                if(nXStart != nXEnd)
+                {
+                    reset();
+                    maLineEntries.clear();
+
+                    // horizontal line, create vertical entries. These will be sorted by
+                    // X anyways, so no need to distinguish the case here
+                    maLineEntries.emplace_back(
+                        aStart.getX(), 0.0,
+                        aStart.getZ() + fZBufferLineAdd, 0.0,
+                        nYStart, 1);
+                    maLineEntries.emplace_back(
+                        aEnd.getX(), 0.0,
+                        aEnd.getZ() + fZBufferLineAdd, 0.0,
+                        nYStart, 1);
+                }
+            }
+            else
+            {
+                reset();
+                maLineEntries.clear();
+
+                if(nYStart > nYEnd)
+                {
+                    std::swap(aStart, aEnd);
+                    std::swap(nYStart, nYEnd);
+                }
+
+                const sal_uInt32 nYDelta(static_cast<sal_uInt32>(nYEnd - nYStart));
+                const double fInvYDelta(1.0 / nYDelta);
+
+                // non-horizontal line, create two parallel entries. These will be sorted by
+                // X anyways, so no need to distinguish the case here
+                maLineEntries.emplace_back(
+                    aStart.getX(), (aEnd.getX() - aStart.getX()) * fInvYDelta,
+                    aStart.getZ() + fZBufferLineAdd, (aEnd.getZ() - aStart.getZ()) * fInvYDelta,
+                    nYStart, nYDelta);
+
+                RasterConversionLineEntry3D& rEntry = maLineEntries[maLineEntries.size() - 1];
+
+                // need to choose a X-Distance for the 2nd edge which guarantees all pixels
+                // of the line to be set. This is exactly the X-Increment for one Y-Step.
+                // Same is true for Z, so in both cases, add one increment to them. To also
+                // guarantee one pixel per line, add a minimum of one for X.
+                const double fDistanceX(fabs(rEntry.getX().getInc()) >= 1.0 ? rEntry.getX().getInc() : 1.0);
+
+                maLineEntries.emplace_back(
+                    rEntry.getX().getVal() + fDistanceX, rEntry.getX().getInc(),
+                    rEntry.getZ().getVal() + rEntry.getZ().getInc(), rEntry.getZ().getInc(),
+                    nYStart, nYDelta);
+            }
+        }
+
+        if(!maLineEntries.empty())
+        {
+            rasterconvertB3DArea(nStartLine, nStopLine);
+        }
+    }
+
+    void RasterConverter3D::rasterconvertB3DPolyPolygon(const B3DPolyPolygon& rFill, const B3DHomMatrix* pViewToEye, sal_Int32 nStartLine, sal_Int32 nStopLine)
+    {
+        reset();
+        maLineEntries.clear();
+        addArea(rFill, pViewToEye);
+        rasterconvertB3DArea(nStartLine, nStopLine);
+    }
+
+    void RasterConverter3D::rasterconvertB3DPolygon(const B3DPolygon& rLine, sal_Int32 nStartLine, sal_Int32 nStopLine, sal_uInt16 nLineWidth)
+    {
+        const sal_uInt32 nPointCount(rLine.count());
+
+        if(nPointCount)
+        {
+            const sal_uInt32 nEdgeCount(rLine.isClosed() ? nPointCount : nPointCount - 1);
+
+            for(sal_uInt32 a(0); a < nEdgeCount; a++)
+            {
+                rasterconvertB3DEdge(rLine, a, (a + 1) % nPointCount, nStartLine, nStopLine, nLineWidth);
+            }
+        }
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/b2dclipstate.cxx b/basegfx/source/tools/b2dclipstate.cxx
new file mode 100644
index 0000000000..126235699b
--- /dev/null
+++ b/basegfx/source/tools/b2dclipstate.cxx
@@ -0,0 +1,476 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/utils/b2dclipstate.hxx>
+
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/range/b2dpolyrange.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
+#include <utility>
+
+
+namespace basegfx::utils
+{
+    class ImplB2DClipState
+    {
+    public:
+        enum Operation {UNION, INTERSECT, XOR, SUBTRACT};
+
+        ImplB2DClipState() :
+            mePendingOps(UNION)
+        {}
+
+        explicit ImplB2DClipState( B2DPolyPolygon aPoly ) :
+            maClipPoly(std::move(aPoly)),
+            mePendingOps(UNION)
+        {}
+
+        bool isCleared() const
+        {
+            return !maClipPoly.count()
+                && !maPendingPolygons.count()
+                && !maPendingRanges.count();
+        }
+
+        bool isNullClipPoly() const
+        {
+            return maClipPoly.count() == 1
+                && !maClipPoly.getB2DPolygon(0).count();
+        }
+
+        bool isNull() const
+        {
+            return !maPendingPolygons.count()
+                && !maPendingRanges.count()
+                && isNullClipPoly();
+        }
+
+        void makeNull()
+        {
+            maPendingPolygons.clear();
+            maPendingRanges.clear();
+            maClipPoly.clear();
+            maClipPoly.append(B2DPolygon());
+            mePendingOps = UNION;
+        }
+
+        bool operator==(const ImplB2DClipState& rRHS) const
+        {
+            return maPendingPolygons == rRHS.maPendingPolygons
+                && maPendingRanges == rRHS.maPendingRanges
+                && maClipPoly == rRHS.maClipPoly
+                && mePendingOps == rRHS.mePendingOps;
+        }
+
+        void addRange(const B2DRange& rRange, Operation eOp)
+        {
+            if( rRange.isEmpty() )
+                return;
+
+            commitPendingPolygons();
+            if( mePendingOps != eOp )
+                commitPendingRanges();
+
+            mePendingOps = eOp;
+            maPendingRanges.appendElement(
+                rRange,
+                B2VectorOrientation::Positive);
+        }
+
+        void addPolyPolygon(const B2DPolyPolygon& aPoly, Operation eOp)
+        {
+            commitPendingRanges();
+            if( mePendingOps != eOp )
+                commitPendingPolygons();
+
+            mePendingOps = eOp;
+            maPendingPolygons.append(aPoly);
+        }
+
+        void unionRange(const B2DRange& rRange)
+        {
+            if( isCleared() )
+                return;
+
+            addRange(rRange,UNION);
+        }
+
+        void unionPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+        {
+            if( isCleared() )
+                return;
+
+            addPolyPolygon(rPolyPoly,UNION);
+        }
+
+        void intersectRange(const B2DRange& rRange)
+        {
+            if( isNull() )
+                return;
+
+            addRange(rRange,INTERSECT);
+        }
+
+        void intersectPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+        {
+            if( isNull() )
+                return;
+
+            addPolyPolygon(rPolyPoly,INTERSECT);
+        }
+
+        void subtractRange(const B2DRange& rRange )
+        {
+            if( isNull() )
+                return;
+
+            addRange(rRange,SUBTRACT);
+        }
+
+        void subtractPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+        {
+            if( isNull() )
+                return;
+
+            addPolyPolygon(rPolyPoly,SUBTRACT);
+        }
+
+        void xorRange(const B2DRange& rRange)
+        {
+            addRange(rRange,XOR);
+        }
+
+        void xorPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+        {
+            addPolyPolygon(rPolyPoly,XOR);
+        }
+
+        void transform(const basegfx::B2DHomMatrix& rTranslate)
+        {
+            maPendingRanges.transform(rTranslate);
+            maPendingPolygons.transform(rTranslate);
+            maClipPoly.transform(rTranslate);
+        }
+
+        B2DPolyPolygon const & getClipPoly() const
+        {
+            commitPendingRanges();
+            commitPendingPolygons();
+
+            return maClipPoly;
+        }
+
+    private:
+        void commitPendingPolygons() const
+        {
+            if( !maPendingPolygons.count() )
+                return;
+
+            // assumption: maClipPoly has kept polygons prepared for
+            // clipping; i.e. no neutral polygons & correct
+            // orientation
+            maPendingPolygons = utils::prepareForPolygonOperation(maPendingPolygons);
+            const bool bIsEmpty=isNullClipPoly();
+            const bool bIsCleared=!maClipPoly.count();
+            switch(mePendingOps)
+            {
+                case UNION:
+                    assert( !bIsCleared );
+
+                    if( bIsEmpty )
+                        maClipPoly = maPendingPolygons;
+                    else
+                        maClipPoly = utils::solvePolygonOperationOr(
+                            maClipPoly,
+                            maPendingPolygons);
+                    break;
+                case INTERSECT:
+                    assert( !bIsEmpty );
+
+                    if( bIsCleared )
+                        maClipPoly = maPendingPolygons;
+                    else
+                        maClipPoly = utils::solvePolygonOperationAnd(
+                            maClipPoly,
+                            maPendingPolygons);
+                    break;
+                case XOR:
+                    if( bIsEmpty )
+                        maClipPoly = maPendingPolygons;
+                    else if( bIsCleared )
+                    {
+                        // not representable, strictly speaking,
+                        // using polygons with the common even/odd
+                        // or nonzero winding number fill rule. If
+                        // we'd want to represent it, fill rule
+                        // would need to be "non-negative winding
+                        // number" (and we then would return
+                        // 'holes' here)
+
+                        // going for an ugly hack meanwhile
+                        maClipPoly = utils::solvePolygonOperationXor(
+                            B2DPolyPolygon(
+                                utils::createPolygonFromRect(B2DRange(-1E20,-1E20,1E20,1E20))),
+                            maPendingPolygons);
+                    }
+                    else
+                        maClipPoly = utils::solvePolygonOperationXor(
+                            maClipPoly,
+                            maPendingPolygons);
+                    break;
+                case SUBTRACT:
+                    assert( !bIsEmpty );
+
+                    // first union all pending ones, subtract en bloc then
+                    maPendingPolygons = solveCrossovers(maPendingPolygons);
+                    maPendingPolygons = stripNeutralPolygons(maPendingPolygons);
+                    maPendingPolygons = stripDispensablePolygons(maPendingPolygons);
+
+                    if( bIsCleared )
+                    {
+                        // not representable, strictly speaking,
+                        // using polygons with the common even/odd
+                        // or nonzero winding number fill rule. If
+                        // we'd want to represent it, fill rule
+                        // would need to be "non-negative winding
+                        // number" (and we then would return
+                        // 'holes' here)
+
+                        // going for an ugly hack meanwhile
+                        maClipPoly = utils::solvePolygonOperationDiff(
+                            B2DPolyPolygon(
+                                utils::createPolygonFromRect(B2DRange(-1E20,-1E20,1E20,1E20))),
+                            maPendingPolygons);
+                    }
+                    else
+                        maClipPoly = utils::solvePolygonOperationDiff(
+                            maClipPoly,
+                            maPendingPolygons);
+                    break;
+            }
+
+            maPendingPolygons.clear();
+            mePendingOps = UNION;
+        }
+
+        void commitPendingRanges() const
+        {
+            if( !maPendingRanges.count() )
+                return;
+
+            // use the specialized range clipper for the win
+            B2DPolyPolygon aCollectedRanges;
+            const bool bIsEmpty=isNullClipPoly();
+            const bool bIsCleared=!maClipPoly.count();
+            switch(mePendingOps)
+            {
+                case UNION:
+                    assert( !bIsCleared );
+
+                    aCollectedRanges = maPendingRanges.solveCrossovers();
+                    aCollectedRanges = stripNeutralPolygons(aCollectedRanges);
+                    aCollectedRanges = stripDispensablePolygons(aCollectedRanges);
+                    if( bIsEmpty )
+                        maClipPoly = aCollectedRanges;
+                    else
+                        maClipPoly = utils::solvePolygonOperationOr(
+                            maClipPoly,
+                            aCollectedRanges);
+                    break;
+                case INTERSECT:
+                    assert( !bIsEmpty );
+
+                    aCollectedRanges = maPendingRanges.solveCrossovers();
+                    aCollectedRanges = stripNeutralPolygons(aCollectedRanges);
+                    if( maPendingRanges.count() > 1 )
+                        aCollectedRanges = stripDispensablePolygons(aCollectedRanges, true);
+
+                    if( bIsCleared )
+                        maClipPoly = aCollectedRanges;
+                    else
+                        maClipPoly = utils::solvePolygonOperationAnd(
+                            maClipPoly,
+                            aCollectedRanges);
+                    break;
+                case XOR:
+                    aCollectedRanges = maPendingRanges.solveCrossovers();
+                    aCollectedRanges = stripNeutralPolygons(aCollectedRanges);
+                    aCollectedRanges = correctOrientations(aCollectedRanges);
+
+                    if( bIsEmpty )
+                        maClipPoly = aCollectedRanges;
+                    else if( bIsCleared )
+                    {
+                        // not representable, strictly speaking,
+                        // using polygons with the common even/odd
+                        // or nonzero winding number fill rule. If
+                        // we'd want to represent it, fill rule
+                        // would need to be "non-negative winding
+                        // number" (and we then would return
+                        // 'holes' here)
+
+                        // going for an ugly hack meanwhile
+                        maClipPoly = utils::solvePolygonOperationXor(
+                            B2DPolyPolygon(
+                                utils::createPolygonFromRect(B2DRange(-1E20,-1E20,1E20,1E20))),
+                            aCollectedRanges);
+                    }
+                    else
+                        maClipPoly = utils::solvePolygonOperationXor(
+                            maClipPoly,
+                            aCollectedRanges);
+                    break;
+                case SUBTRACT:
+                    assert( !bIsEmpty );
+
+                    // first union all pending ranges, subtract en bloc then
+                    aCollectedRanges = maPendingRanges.solveCrossovers();
+                    aCollectedRanges = stripNeutralPolygons(aCollectedRanges);
+                    aCollectedRanges = stripDispensablePolygons(aCollectedRanges);
+
+                    if( bIsCleared )
+                    {
+                        // not representable, strictly speaking,
+                        // using polygons with the common even/odd
+                        // or nonzero winding number fill rule. If
+                        // we'd want to represent it, fill rule
+                        // would need to be "non-negative winding
+                        // number" (and we then would return
+                        // 'holes' here)
+
+                        // going for an ugly hack meanwhile
+                        maClipPoly = utils::solvePolygonOperationDiff(
+                            B2DPolyPolygon(
+                                utils::createPolygonFromRect(B2DRange(-1E20,-1E20,1E20,1E20))),
+                            aCollectedRanges);
+                    }
+                    else
+                        maClipPoly = utils::solvePolygonOperationDiff(
+                            maClipPoly,
+                            aCollectedRanges);
+                    break;
+            }
+
+            maPendingRanges.clear();
+            mePendingOps = UNION;
+        }
+
+        mutable B2DPolyPolygon maPendingPolygons;
+        mutable B2DPolyRange   maPendingRanges;
+        mutable B2DPolyPolygon maClipPoly;
+        mutable Operation      mePendingOps;
+    };
+
+    B2DClipState::B2DClipState() = default;
+
+    B2DClipState::~B2DClipState() = default;
+
+    B2DClipState::B2DClipState( const B2DClipState& ) = default;
+
+    B2DClipState::B2DClipState( B2DClipState&& ) = default;
+
+    B2DClipState::B2DClipState( const B2DPolyPolygon& rPolyPoly ) :
+        mpImpl( ImplB2DClipState(rPolyPoly) )
+    {}
+
+    B2DClipState& B2DClipState::operator=( const B2DClipState& ) = default;
+
+    B2DClipState& B2DClipState::operator=( B2DClipState&& ) = default;
+
+    void B2DClipState::makeNull()
+    {
+        mpImpl->makeNull();
+    }
+
+    bool B2DClipState::isCleared() const
+    {
+        return mpImpl->isCleared();
+    }
+
+    bool B2DClipState::operator==(const B2DClipState& rRHS) const
+    {
+        if(mpImpl.same_object(rRHS.mpImpl))
+            return true;
+
+        return ((*mpImpl) == (*rRHS.mpImpl));
+    }
+
+    bool B2DClipState::operator!=(const B2DClipState& rRHS) const
+    {
+        return !(*this == rRHS);
+    }
+
+    void B2DClipState::unionRange(const B2DRange& rRange)
+    {
+        mpImpl->unionRange(rRange);
+    }
+
+    void B2DClipState::unionPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+    {
+        mpImpl->unionPolyPolygon(rPolyPoly);
+    }
+
+    void B2DClipState::intersectRange(const B2DRange& rRange)
+    {
+        mpImpl->intersectRange(rRange);
+    }
+
+    void B2DClipState::intersectPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+    {
+        mpImpl->intersectPolyPolygon(rPolyPoly);
+    }
+
+    void B2DClipState::subtractRange(const B2DRange& rRange)
+    {
+        mpImpl->subtractRange(rRange);
+    }
+
+    void B2DClipState::subtractPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+    {
+        mpImpl->subtractPolyPolygon(rPolyPoly);
+    }
+
+    void B2DClipState::xorRange(const B2DRange& rRange)
+    {
+        mpImpl->xorRange(rRange);
+    }
+
+    void B2DClipState::xorPolyPolygon(const B2DPolyPolygon& rPolyPoly)
+    {
+        mpImpl->xorPolyPolygon(rPolyPoly);
+    }
+
+    B2DPolyPolygon const & B2DClipState::getClipPoly() const
+    {
+        return mpImpl->getClipPoly();
+    }
+
+    void B2DClipState::transform(const basegfx::B2DHomMatrix& rTranslate)
+    {
+        return mpImpl->transform(rTranslate);
+    }
+
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/bgradient.cxx b/basegfx/source/tools/bgradient.cxx
new file mode 100644
index 0000000000..86e1812d21
--- /dev/null
+++ b/basegfx/source/tools/bgradient.cxx
@@ -0,0 +1,997 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+
+#include <basegfx/utils/bgradient.hxx>
+#include <basegfx/utils/gradienttools.hxx>
+#include <com/sun/star/awt/Gradient2.hpp>
+#include <boost/property_tree/json_parser.hpp>
+#include <map>
+
+typedef std::map<OUString, OUString> StringMap;
+
+namespace
+{
+css::awt::GradientStyle lcl_getStyleFromString(std::u16string_view rStyle)
+{
+    if (rStyle == u"LINEAR")
+        return css::awt::GradientStyle_LINEAR;
+    else if (rStyle == u"AXIAL")
+        return css::awt::GradientStyle_AXIAL;
+    else if (rStyle == u"RADIAL")
+        return css::awt::GradientStyle_RADIAL;
+    else if (rStyle == u"ELLIPTICAL")
+        return css::awt::GradientStyle_ELLIPTICAL;
+    else if (rStyle == u"SQUARE")
+        return css::awt::GradientStyle_SQUARE;
+    else if (rStyle == u"RECT")
+        return css::awt::GradientStyle_RECT;
+
+    return css::awt::GradientStyle_LINEAR;
+}
+
+StringMap lcl_jsonToStringMap(std::u16string_view rJSON)
+{
+    StringMap aArgs;
+    if (rJSON.size() && rJSON[0] != '\0')
+    {
+        std::stringstream aStream(std::string(OUStringToOString(rJSON, RTL_TEXTENCODING_ASCII_US)));
+        boost::property_tree::ptree aTree;
+        boost::property_tree::read_json(aStream, aTree);
+
+        for (const auto& rPair : aTree)
+        {
+            aArgs[OUString::fromUtf8(rPair.first)]
+                = OUString::fromUtf8(rPair.second.get_value<std::string>("."));
+        }
+    }
+    return aArgs;
+}
+
+basegfx::BGradient lcl_buildGradientFromStringMap(StringMap& rMap)
+{
+    basegfx::BGradient aGradient(
+        basegfx::BColorStops(ColorToBColorConverter(rMap["startcolor"].toInt32(16)).getBColor(),
+                             ColorToBColorConverter(rMap["endcolor"].toInt32(16)).getBColor()));
+
+    aGradient.SetGradientStyle(lcl_getStyleFromString(rMap["style"]));
+    aGradient.SetAngle(Degree10(rMap["angle"].toInt32()));
+
+    return aGradient;
+}
+}
+
+namespace basegfx
+{
+// constructor with two colors to explicitly create a
+// BColorStops for a single StartColor @0.0 & EndColor @1.0
+BColorStops::BColorStops(const BColor& rStart, const BColor& rEnd)
+{
+    emplace_back(0.0, rStart);
+    emplace_back(1.0, rEnd);
+}
+
+/* Helper to grep the correct ColorStop out of
+        ColorStops and interpolate as needed for given
+        relative value in fPosition in the range of [0.0 .. 1.0].
+        It also takes care of evtl. given RequestedSteps.
+    */
+BColor BColorStops::getInterpolatedBColor(double fPosition, sal_uInt32 nRequestedSteps,
+                                          BColorStopRange& rLastColorStopRange) const
+{
+    // no color at all, done
+    if (empty())
+        return BColor();
+
+    // outside range -> at start
+    const double fMin(front().getStopOffset());
+    if (fPosition < fMin)
+        return front().getStopColor();
+
+    // outside range -> at end
+    const double fMax(back().getStopOffset());
+    if (fPosition > fMax)
+        return back().getStopColor();
+
+    // special case for the 'classic' case with just two colors:
+    // we can optimize that and keep the speed/resources low
+    // by avoiding some calculations and an O(log(N)) array access
+    if (2 == size())
+    {
+        // if same StopOffset use front color
+        if (fTools::equal(fMin, fMax))
+            return front().getStopColor();
+
+        const basegfx::BColor aCStart(front().getStopColor());
+        const basegfx::BColor aCEnd(back().getStopColor());
+
+        // if colors are equal just return one
+        if (aCStart == aCEnd)
+            return aCStart;
+
+        // calculate Steps
+        const sal_uInt32 nSteps(
+            basegfx::utils::calculateNumberOfSteps(nRequestedSteps, aCStart, aCEnd));
+
+        // we need to extend the interpolation to the local
+        // range of ColorStops. Despite having two ColorStops
+        // these are not necessarily at 0.0 and 1.0, so may be
+        // not the classical Start/EndColor (what is allowed)
+        fPosition = (fPosition - fMin) / (fMax - fMin);
+        return basegfx::interpolate(aCStart, aCEnd,
+                                    nSteps > 1 ? floor(fPosition * nSteps) / double(nSteps - 1)
+                                               : fPosition);
+    }
+
+    // check if we need to newly populate the needed interpolation data
+    // or if we can re-use from last time.
+    // If this scope is not entered, we do not need the binary search. It's
+    // only a single buffered entry, and only used when more than three
+    // ColorStops exist, but makes a huge difference compared with accessing
+    // the sorted ColorStop vector each time.
+    // NOTE: with this simple change I get very high hit rates, e.g. rotating
+    //       a donut with gradient test '1' hit rate is at 0.99909440357755486
+    if (rLastColorStopRange.mfOffsetStart == rLastColorStopRange.mfOffsetEnd
+        || fPosition < rLastColorStopRange.mfOffsetStart
+        || fPosition > rLastColorStopRange.mfOffsetEnd)
+    {
+        // access needed spot in sorted array using binary search
+        // NOTE: This *seems* slow(er) when developing compared to just
+        //       looping/accessing, but that's just due to the extensive
+        //       debug test code created by the stl. In a pro version,
+        //       all is good/fast as expected
+        const auto upperBound(std::upper_bound(begin(), end(), BColorStop(fPosition),
+                                               [](const BColorStop& x, const BColorStop& y) {
+                                                   return x.getStopOffset() < y.getStopOffset();
+                                               }));
+
+        // no upper bound, done
+        if (end() == upperBound)
+            return back().getStopColor();
+
+        // lower bound is one entry back, access that
+        const auto lowerBound(upperBound - 1);
+
+        // no lower bound, done
+        if (end() == lowerBound)
+            return back().getStopColor();
+
+        // we have lower and upper bound, get colors and offsets
+        rLastColorStopRange.maColorStart = lowerBound->getStopColor();
+        rLastColorStopRange.maColorEnd = upperBound->getStopColor();
+        rLastColorStopRange.mfOffsetStart = lowerBound->getStopOffset();
+        rLastColorStopRange.mfOffsetEnd = upperBound->getStopOffset();
+    }
+
+    // when there are just two color steps this cannot happen, but when using
+    // a range of colors this *may* be used inside the range to represent
+    // single-colored regions inside a ColorRange. Use that color & done
+    if (rLastColorStopRange.maColorStart == rLastColorStopRange.maColorEnd)
+        return rLastColorStopRange.maColorStart;
+
+    // calculate number of steps and adapted proportional
+    // range for scaler in [0.0 .. 1.0]
+    const double fAdaptedScaler(
+        (fPosition - rLastColorStopRange.mfOffsetStart)
+        / (rLastColorStopRange.mfOffsetEnd - rLastColorStopRange.mfOffsetStart));
+    const sal_uInt32 nSteps(basegfx::utils::calculateNumberOfSteps(
+        nRequestedSteps, rLastColorStopRange.maColorStart, rLastColorStopRange.maColorEnd));
+
+    // interpolate & evtl. apply steps
+    return interpolate(rLastColorStopRange.maColorStart, rLastColorStopRange.maColorEnd,
+                       nSteps > 1 ? floor(fAdaptedScaler * nSteps) / double(nSteps - 1)
+                                  : fAdaptedScaler);
+}
+
+/* Tooling method that allows to replace the StartColor in a
+        vector of ColorStops. A vector in 'ordered state' is expected,
+        so you may use/have used sortAndCorrect.
+        This method is for convenience & backwards compatibility, please
+        think about handling multi-colored gradients directly.
+    */
+void BColorStops::replaceStartColor(const BColor& rStart)
+{
+    BColorStops::iterator a1stNonStartColor(begin());
+
+    // search for highest existing non-StartColor - CAUTION,
+    // there might be none, one or multiple with StopOffset 0.0
+    while (a1stNonStartColor != end()
+           && basegfx::fTools::lessOrEqual(a1stNonStartColor->getStopOffset(), 0.0))
+        a1stNonStartColor++;
+
+    // create new ColorStops by 1st adding new one and then all
+    // non-StartColor entries
+    BColorStops aNewColorStops;
+
+    aNewColorStops.reserve(size() + 1);
+    aNewColorStops.emplace_back(0.0, rStart);
+    aNewColorStops.insert(aNewColorStops.end(), a1stNonStartColor, end());
+
+    // assign & done
+    *this = aNewColorStops;
+}
+
+/* Tooling method that allows to replace the EndColor in a
+        vector of ColorStops. A vector in 'ordered state' is expected,
+        so you may use/have used sortAndCorrectColorStops.
+        This method is for convenience & backwards compatibility, please
+        think about handling multi-colored gradients directly.
+    */
+void BColorStops::replaceEndColor(const BColor& rEnd)
+{
+    // erase all evtl. existing EndColor(s)
+    while (!empty() && basegfx::fTools::moreOrEqual(back().getStopOffset(), 1.0))
+        pop_back();
+
+    // add at the end of existing ColorStops
+    emplace_back(1.0, rEnd);
+}
+
+/* Tooling method to linearly blend the Colors contained in
+        a given ColorStop vector against a given Color using the
+        given intensity values.
+        The intensity values fStartIntensity, fEndIntensity are
+        in the range of [0.0 .. 1.0] and describe how much the
+        blend is supposed to be done at the start color position
+        and the end color position respectively, where 0.0 means
+        to fully use the given BlendColor, 1.0 means to not change
+        the existing color in the ColorStop.
+        Every color entry in the given ColorStop is blended
+        relative to it's StopPosition, interpolating the
+        given intensities with the range [0.0 .. 1.0] to do so.
+    */
+void BColorStops::blendToIntensity(double fStartIntensity, double fEndIntensity,
+                                   const BColor& rBlendColor)
+{
+    // no entries, done
+    if (empty())
+        return;
+
+    // correct intensities (maybe assert when input was wrong)
+    fStartIntensity = std::max(std::min(1.0, fStartIntensity), 0.0);
+    fEndIntensity = std::max(std::min(1.0, fEndIntensity), 0.0);
+
+    // all 100%, no real blend, done
+    if (basegfx::fTools::equal(fStartIntensity, 1.0) && basegfx::fTools::equal(fEndIntensity, 1.0))
+        return;
+
+    // blend relative to StopOffset position
+    for (auto& candidate : *this)
+    {
+        const double fOffset(candidate.getStopOffset());
+        const double fIntensity((fStartIntensity * (1.0 - fOffset)) + (fEndIntensity * fOffset));
+        candidate = basegfx::BColorStop(
+            fOffset, basegfx::interpolate(rBlendColor, candidate.getStopColor(), fIntensity));
+    }
+}
+
+/* Tooling method to guarantee sort and correctness for
+        the given ColorStops vector.
+        A vector fulfilling these conditions is called to be
+        in 'ordered state'.
+
+        At return, the following conditions are guaranteed:
+        - contains no ColorStops with offset < 0.0 (will
+            be removed)
+        - contains no ColorStops with offset > 1.0 (will
+            be removed)
+        - ColorStops with identical offsets are now allowed
+        - will be sorted from lowest offset to highest
+
+        Some more notes:
+        - It can happen that the result is empty
+        - It is allowed to have consecutive entries with
+            the same color, this represents single-color
+            regions inside the gradient
+        - A entry with 0.0 is not required or forced, so
+            no 'StartColor' is technically required
+        - A entry with 1.0 is not required or forced, so
+            no 'EndColor' is technically required
+
+        All this is done in one run (sort + O(N)) without
+        creating a copy of the data in any form
+    */
+void BColorStops::sortAndCorrect()
+{
+    // no content, we are done
+    if (empty())
+        return;
+
+    if (1 == size())
+    {
+        // no gradient at all, but preserve given color
+        // evtl. correct offset to be in valid range [0.0 .. 1.0]
+        // NOTE: This does not move it to 0.0 or 1.0, it *can* still
+        //       be somewhere in-between what is allowed
+        const BColorStop aEntry(front());
+        clear();
+        emplace_back(std::max(0.0, std::min(1.0, aEntry.getStopOffset())), aEntry.getStopColor());
+
+        // done
+        return;
+    }
+
+    // start with sorting the input data. Remember that
+    // this preserves the order of equal entries, where
+    // equal is defined here by offset (see use operator==)
+    std::sort(begin(), end());
+
+    // prepare status values
+    size_t write(0);
+
+    // use the paradigm of a band machine with two heads, read
+    // and write with write <= read all the time. Step over the
+    // data using read and check for valid entry. If valid, decide
+    // how to keep it
+    for (size_t read(0); read < size(); read++)
+    {
+        // get offset of entry at read position
+        double fOff((*this)[read].getStopOffset());
+
+        if (basegfx::fTools::less(fOff, 0.0) && read + 1 < size())
+        {
+            // value < 0.0 and we have a next entry. check for gradient snippet
+            // containing 0.0 resp. StartColor
+            const double fOff2((*this)[read + 1].getStopOffset());
+
+            if (basegfx::fTools::more(fOff2, 0.0))
+            {
+                // read is the start of a gradient snippet containing 0.0. Correct
+                // entry to StartColor, interpolate to correct StartColor
+                (*this)[read]
+                    = BColorStop(0.0, basegfx::interpolate((*this)[read].getStopColor(),
+                                                           (*this)[read + 1].getStopColor(),
+                                                           (0.0 - fOff) / (fOff2 - fOff)));
+
+                // adapt fOff
+                fOff = 0.0;
+            }
+        }
+
+        // step over < 0 values, these are outside and will be removed
+        if (basegfx::fTools::less(fOff, 0.0))
+        {
+            continue;
+        }
+
+        if (basegfx::fTools::less(fOff, 1.0) && read + 1 < size())
+        {
+            // value < 1.0 and we have a next entry. check for gradient snippet
+            // containing 1.0 resp. EndColor
+            const double fOff2((*this)[read + 1].getStopOffset());
+
+            if (basegfx::fTools::more(fOff2, 1.0))
+            {
+                // read is the start of a gradient snippet containing 1.0. Correct
+                // next entry to EndColor, interpolate to correct EndColor
+                (*this)[read + 1]
+                    = BColorStop(1.0, basegfx::interpolate((*this)[read].getStopColor(),
+                                                           (*this)[read + 1].getStopColor(),
+                                                           (1.0 - fOff) / (fOff2 - fOff)));
+
+                // adapt fOff
+                fOff = 1.0;
+            }
+        }
+
+        // step over > 1 values; even break, since all following
+        // entries will also be bigger due to being sorted, so done
+        if (basegfx::fTools::more(fOff, 1.0))
+        {
+            break;
+        }
+
+        // entry is valid value at read position
+        // copy if write target is empty (write at start) or when
+        // write target is different to read in color or offset
+        if (0 == write || !((*this)[read] == (*this)[write - 1]))
+        {
+            if (write != read)
+            {
+                // copy read to write backwards to close gaps
+                (*this)[write] = (*this)[read];
+            }
+
+            // always forward write position
+            write++;
+        }
+    }
+
+    // correct size when length is reduced. write is always at
+    // last used position + 1
+    if (size() > write)
+    {
+        if (0 == write)
+        {
+            // no valid entries at all, but not empty. This can only happen
+            // when all entries are below 0.0 or above 1.0 (else a gradient
+            // snippet spawning over both would have been detected)
+            if (basegfx::fTools::less(back().getStopOffset(), 0.0))
+            {
+                // all outside too low, rescue last due to being closest to content
+                const BColor aBackColor(back().getStopColor());
+                clear();
+                emplace_back(0.0, aBackColor);
+            }
+            else // if (basegfx::fTools::more(front().getStopOffset(), 1.0))
+            {
+                // all outside too high, rescue first due to being closest to content
+                const BColor aFrontColor(front().getStopColor());
+                clear();
+                emplace_back(1.0, aFrontColor);
+            }
+        }
+        else
+        {
+            resize(write);
+        }
+    }
+}
+
+bool BColorStops::checkPenultimate() const
+{
+    // not needed when no ColorStops
+    if (empty())
+        return false;
+
+    // not needed when last ColorStop at the end or outside
+    if (basegfx::fTools::moreOrEqual(back().getStopOffset(), 1.0))
+        return false;
+
+    // get penultimate entry
+    const auto penultimate(rbegin() + 1);
+
+    // if there is none, we need no correction and are done
+    if (penultimate == rend())
+        return false;
+
+    // not needed when the last two ColorStops have different offset, then
+    // a visible range will be processed already
+    if (!basegfx::fTools::equal(back().getStopOffset(), penultimate->getStopOffset()))
+        return false;
+
+    // not needed when the last two ColorStops have the same Color, then the
+    // range before solves the problem
+    if (back().getStopColor() == penultimate->getStopColor())
+        return false;
+
+    return true;
+}
+
+/* Tooling method to check if a ColorStop vector is defined
+        by a single color. It returns true if this is the case.
+        If true is returned, rSingleColor contains that single
+        color for convenience.
+        NOTE: If no ColorStop is defined, a fallback to BColor-default
+                (which is black) and true will be returned
+    */
+bool BColorStops::isSingleColor(BColor& rSingleColor) const
+{
+    if (empty())
+    {
+        rSingleColor = BColor();
+        return true;
+    }
+
+    if (1 == size())
+    {
+        rSingleColor = front().getStopColor();
+        return true;
+    }
+
+    rSingleColor = front().getStopColor();
+
+    for (auto const& rCandidate : *this)
+    {
+        if (rCandidate.getStopColor() != rSingleColor)
+            return false;
+    }
+
+    return true;
+}
+
+/* Tooling method to reverse ColorStops, including offsets.
+        When also mirroring offsets a valid sort keeps valid.
+    */
+void BColorStops::reverseColorStops()
+{
+    // can use std::reverse, but also need to adapt offset(s)
+    std::reverse(begin(), end());
+    for (auto& candidate : *this)
+        candidate = BColorStop(1.0 - candidate.getStopOffset(), candidate.getStopColor());
+}
+
+// createSpaceAtStart creates fOffset space at start by
+// translating/scaling all entries to the right
+void BColorStops::createSpaceAtStart(double fOffset)
+{
+    // nothing to do if empty
+    if (empty())
+        return;
+
+    // correct offset to [0.0 .. 1.0]
+    fOffset = std::max(std::min(1.0, fOffset), 0.0);
+
+    // nothing to do if 0.0 == offset
+    if (basegfx::fTools::equalZero(fOffset))
+        return;
+
+    BColorStops aNewStops;
+
+    for (const auto& candidate : *this)
+    {
+        aNewStops.emplace_back(fOffset + (candidate.getStopOffset() * (1.0 - fOffset)),
+                               candidate.getStopColor());
+    }
+
+    *this = aNewStops;
+}
+
+// removeSpaceAtStart removes fOffset space from start by
+// translating/scaling entries more or equal to fOffset
+// to the left. Entries less than fOffset will be removed
+void BColorStops::removeSpaceAtStart(double fOffset)
+{
+    // nothing to do if empty
+    if (empty())
+        return;
+
+    // correct factor to [0.0 .. 1.0]
+    fOffset = std::max(std::min(1.0, fOffset), 0.0);
+
+    // nothing to do if fOffset == 0.0
+    if (basegfx::fTools::equalZero(fOffset))
+        return;
+
+    BColorStops aNewStops;
+    const double fMul(basegfx::fTools::equal(fOffset, 1.0) ? 1.0 : 1.0 / (1.0 - fOffset));
+
+    for (const auto& candidate : *this)
+    {
+        if (basegfx::fTools::moreOrEqual(candidate.getStopOffset(), fOffset))
+        {
+            aNewStops.emplace_back((candidate.getStopOffset() - fOffset) * fMul,
+                                   candidate.getStopColor());
+        }
+    }
+
+    *this = aNewStops;
+}
+
+// try to detect if an empty/no-color-change area exists
+// at the start and return offset to it. Returns 0.0 if not.
+double BColorStops::detectPossibleOffsetAtStart() const
+{
+    BColor aSingleColor;
+    const bool bSingleColor(isSingleColor(aSingleColor));
+
+    // no useful offset for single color
+    if (bSingleColor)
+        return 0.0;
+
+    // here we know that we have at least two colors, so we have a
+    // color change. Find colors left and right of that first color change
+    BColorStops::const_iterator aColorR(begin());
+    BColorStops::const_iterator aColorL(aColorR++);
+
+    // aColorR would 1st get equal to end(), so no need to also check aColorL
+    // for end(). Loop as long as same color. Since we *have* a color change
+    // not even aColorR can get equal to end() before color inequality, but
+    // keep for safety
+    while (aColorR != end() && aColorL->getStopColor() == aColorR->getStopColor())
+    {
+        aColorL++;
+        aColorR++;
+    }
+
+    // also for safety: access values at aColorL below *only*
+    // if not equal to end(), but can theoretically not happen
+    if (aColorL == end())
+    {
+        return 0.0;
+    }
+
+    // return offset (maybe 0.0 what is OK)
+    return aColorL->getStopOffset();
+}
+
+//  checks whether the color stops are symmetrical in color and offset.
+bool BColorStops::isSymmetrical() const
+{
+    if (empty())
+        return false;
+    if (1 == size())
+        return basegfx::fTools::equal(0.5, front().getStopOffset());
+
+    BColorStops::const_iterator aIter(begin()); // for going forward
+    BColorStops::const_iterator aRIter(end()); // for going backward
+    --aRIter;
+    // We have at least two elements, so aIter <= aRIter fails before iterators no longer point to
+    // an element.
+    while (aIter <= aRIter && aIter->getStopColor().equal(aRIter->getStopColor())
+           && basegfx::fTools::equal(aIter->getStopOffset(), 1.0 - aRIter->getStopOffset()))
+    {
+        ++aIter;
+        --aRIter;
+    }
+    return aIter > aRIter;
+}
+
+void BColorStops::doApplyAxial()
+{
+    // prepare new ColorStops
+    basegfx::BColorStops aNewColorStops;
+
+    // add gradient stops in reverse order, scaled to [0.0 .. 0.5]
+    basegfx::BColorStops::const_reverse_iterator aRevCurrColor(rbegin());
+
+    while (aRevCurrColor != rend())
+    {
+        aNewColorStops.emplace_back((1.0 - aRevCurrColor->getStopOffset()) * 0.5,
+                                    aRevCurrColor->getStopColor());
+        aRevCurrColor++;
+    }
+
+    // prepare non-reverse run
+    basegfx::BColorStops::const_iterator aCurrColor(begin());
+
+    if (basegfx::fTools::equalZero(aCurrColor->getStopOffset()))
+    {
+        // Caution: do not add 1st entry again, that would be double since it was
+        // already added as last element of the inverse run above. But only if
+        // the gradient has a start entry for 0.0 aka StartColor, else it is correct.
+        aCurrColor++;
+    }
+
+    // add gradient stops in non-reverse order, translated and scaled to [0.5 .. 1.0]
+    while (aCurrColor != end())
+    {
+        aNewColorStops.emplace_back((aCurrColor->getStopOffset() * 0.5) + 0.5,
+                                    aCurrColor->getStopColor());
+        aCurrColor++;
+    }
+
+    // apply color stops
+    *this = aNewColorStops;
+}
+
+void BColorStops::doApplySteps(sal_uInt16 nStepCount)
+{
+    // check for zero or invalid steps setting -> done
+    if (0 == nStepCount || nStepCount > 100)
+        return;
+
+    // no change needed if single color
+    BColor aSingleColor;
+    if (isSingleColor(aSingleColor))
+        return;
+
+    // prepare new color stops, get L/R iterators for segments
+    basegfx::BColorStops aNewColorStops;
+    basegfx::BColorStops::const_iterator aColorR(begin());
+    basegfx::BColorStops::const_iterator aColorL(aColorR++);
+
+    while (aColorR != end())
+    {
+        // get start/end color for segment
+        const double fStart(aColorL->getStopOffset());
+        const double fDelta(aColorR->getStopOffset() - fStart);
+
+        if (aNewColorStops.empty() || aNewColorStops.back() != *aColorL)
+        {
+            // add start color, but check if it is already there - which is the
+            // case from the 2nd segment on due to a new segment starting with
+            // the same color as the previous one ended
+            aNewColorStops.push_back(*aColorL);
+        }
+        if (!basegfx::fTools::equalZero(fDelta))
+        {
+            // create in-between steps, always two at the same position to
+            // define a 'hard' color stop. Get start/end color for the segment
+            const basegfx::BColor& rStartColor(aColorL->getStopColor());
+            const basegfx::BColor& rEndColor(aColorR->getStopColor());
+
+            if (rStartColor != rEndColor)
+            {
+                // get relative single-step width
+                // tdf155852 Use same method for the color as in rendering.
+                const double fSingleStep(1.0 / static_cast<double>(nStepCount - 1));
+                const double fOffsetStep(fDelta / static_cast<double>(nStepCount));
+
+                for (sal_uInt16 a(1); a < nStepCount; a++)
+                {
+                    // calculate stop position since being used twice
+                    const double fPosition(fStart + fOffsetStep * static_cast<double>(a));
+
+                    // add end color of previous sub-segment
+                    aNewColorStops.emplace_back(
+                        fPosition, basegfx::interpolate(rStartColor, rEndColor,
+                                                        static_cast<double>(a - 1) * fSingleStep));
+
+                    // add start color of current sub-segment
+                    aNewColorStops.emplace_back(
+                        fPosition, basegfx::interpolate(rStartColor, rEndColor,
+                                                        static_cast<double>(a) * fSingleStep));
+                }
+            }
+        }
+
+        // always add end color of segment
+        aNewColorStops.push_back(*aColorR);
+
+        // next segment
+        aColorL++;
+        aColorR++;
+    }
+
+    // apply the change to color stops
+    *this = aNewColorStops;
+}
+
+std::string BGradient::GradientStyleToString(css::awt::GradientStyle eStyle)
+{
+    switch (eStyle)
+    {
+        case css::awt::GradientStyle::GradientStyle_LINEAR:
+            return "LINEAR";
+
+        case css::awt::GradientStyle::GradientStyle_AXIAL:
+            return "AXIAL";
+
+        case css::awt::GradientStyle::GradientStyle_RADIAL:
+            return "RADIAL";
+
+        case css::awt::GradientStyle::GradientStyle_ELLIPTICAL:
+            return "ELLIPTICAL";
+
+        case css::awt::GradientStyle::GradientStyle_SQUARE:
+            return "SQUARE";
+
+        case css::awt::GradientStyle::GradientStyle_RECT:
+            return "RECT";
+
+        case css::awt::GradientStyle::GradientStyle_MAKE_FIXED_SIZE:
+            return "MAKE_FIXED_SIZE";
+    }
+
+    return "";
+}
+
+BGradient BGradient::fromJSON(std::u16string_view rJSON)
+{
+    StringMap aMap(lcl_jsonToStringMap(rJSON));
+    return lcl_buildGradientFromStringMap(aMap);
+}
+
+BGradient::BGradient()
+    : eStyle(css::awt::GradientStyle_LINEAR)
+    , aColorStops()
+    , nAngle(0)
+    , nBorder(0)
+    , nOfsX(50)
+    , nOfsY(50)
+    , nIntensStart(100)
+    , nIntensEnd(100)
+    , nStepCount(0)
+{
+    aColorStops.emplace_back(0.0, BColor(0.0, 0.0, 0.0)); // COL_BLACK
+    aColorStops.emplace_back(1.0, BColor(1.0, 1.0, 1.0)); // COL_WHITE
+}
+
+BGradient::BGradient(const basegfx::BColorStops& rColorStops, css::awt::GradientStyle eTheStyle,
+                     Degree10 nTheAngle, sal_uInt16 nXOfs, sal_uInt16 nYOfs, sal_uInt16 nTheBorder,
+                     sal_uInt16 nStartIntens, sal_uInt16 nEndIntens, sal_uInt16 nSteps)
+    : eStyle(eTheStyle)
+    , aColorStops(rColorStops)
+    , nAngle(nTheAngle)
+    , nBorder(nTheBorder)
+    , nOfsX(nXOfs)
+    , nOfsY(nYOfs)
+    , nIntensStart(nStartIntens)
+    , nIntensEnd(nEndIntens)
+    , nStepCount(nSteps)
+{
+    SetColorStops(aColorStops);
+}
+
+bool BGradient::operator==(const BGradient& rGradient) const
+{
+    return (eStyle == rGradient.eStyle && aColorStops == rGradient.aColorStops
+            && nAngle == rGradient.nAngle && nBorder == rGradient.nBorder
+            && nOfsX == rGradient.nOfsX && nOfsY == rGradient.nOfsY
+            && nIntensStart == rGradient.nIntensStart && nIntensEnd == rGradient.nIntensEnd
+            && nStepCount == rGradient.nStepCount);
+}
+
+void BGradient::SetColorStops(const basegfx::BColorStops& rSteps)
+{
+    aColorStops = rSteps;
+    aColorStops.sortAndCorrect();
+    if (aColorStops.empty())
+        aColorStops.emplace_back(0.0, basegfx::BColor());
+}
+
+namespace
+{
+OUString AsRGBHexString(const ColorToBColorConverter& rVal)
+{
+    std::stringstream ss;
+    ss << std::hex << std::setfill('0') << std::setw(6) << sal_uInt32(rVal);
+    return OUString::createFromAscii(ss.str());
+}
+}
+
+boost::property_tree::ptree BGradient::dumpAsJSON() const
+{
+    boost::property_tree::ptree aTree;
+
+    aTree.put("style", BGradient::GradientStyleToString(eStyle));
+    const ColorToBColorConverter aStart(GetColorStops().front().getStopColor());
+    aTree.put("startcolor", AsRGBHexString(aStart.GetRGBColor()));
+    const ColorToBColorConverter aEnd(GetColorStops().back().getStopColor());
+    aTree.put("endcolor", AsRGBHexString(aEnd.GetRGBColor()));
+    aTree.put("angle", std::to_string(nAngle.get()));
+    aTree.put("border", std::to_string(nBorder));
+    aTree.put("x", std::to_string(nOfsX));
+    aTree.put("y", std::to_string(nOfsY));
+    aTree.put("intensstart", std::to_string(nIntensStart));
+    aTree.put("intensend", std::to_string(nIntensEnd));
+    aTree.put("stepcount", std::to_string(nStepCount));
+
+    return aTree;
+}
+
+void BGradient::tryToRecreateBorder(basegfx::BColorStops* pAssociatedTransparencyStops)
+{
+    // border already set, do not try to recreate
+    if (0 != GetBorder())
+        return;
+
+    BColor aSingleColor;
+    const bool bSingleColor(GetColorStops().isSingleColor(aSingleColor));
+
+    // no need to recreate with single color
+    if (bSingleColor)
+        return;
+
+    const bool bIsAxial(css::awt::GradientStyle_AXIAL == GetGradientStyle());
+
+    if (bIsAxial)
+    {
+        // for axial due to reverse used gradient work reversed
+        aColorStops.reverseColorStops();
+        if (nullptr != pAssociatedTransparencyStops)
+            pAssociatedTransparencyStops->reverseColorStops();
+    }
+
+    // check if we have space at start of range [0.0 .. 1.0] that
+    // may be interpreted as 'border' -> same color. That may involve
+    // different scenarios, e.g. 1st index > 0.0, but also a non-zero
+    // number of same color entries, or a combination of both
+    const double fOffset(aColorStops.detectPossibleOffsetAtStart());
+
+    if (!basegfx::fTools::equalZero(fOffset))
+    {
+        // we have a border area, indeed re-create
+        aColorStops.removeSpaceAtStart(fOffset);
+        if (nullptr != pAssociatedTransparencyStops)
+            pAssociatedTransparencyStops->removeSpaceAtStart(fOffset);
+
+        // ...and create border value
+        SetBorder(static_cast<sal_uInt16>(std::lround(fOffset * 100.0)));
+    }
+
+    if (bIsAxial)
+    {
+        // take back reverse
+        aColorStops.reverseColorStops();
+        if (nullptr != pAssociatedTransparencyStops)
+            pAssociatedTransparencyStops->reverseColorStops();
+    }
+}
+
+void BGradient::tryToApplyBorder()
+{
+    // no border to apply, done
+    if (0 == GetBorder())
+        return;
+
+    // NOTE: no new start node is added. The new ColorStop
+    //       mechanism does not need entries at 0.0 and 1.0.
+    //       In case this is needed, do that in the caller
+    const double fOffset(GetBorder() * 0.01);
+
+    if (css::awt::GradientStyle_AXIAL == GetGradientStyle())
+    {
+        // for axial due to reverse used gradient work reversed
+        aColorStops.reverseColorStops();
+        aColorStops.createSpaceAtStart(fOffset);
+        aColorStops.reverseColorStops();
+    }
+    else
+    {
+        // apply border to GradientSteps
+        aColorStops.createSpaceAtStart(fOffset);
+    }
+
+    // set changed values
+    SetBorder(0);
+}
+
+void BGradient::tryToApplyStartEndIntensity()
+{
+    // already on default, nothing to apply
+    if (100 == GetStartIntens() && 100 == GetEndIntens())
+        return;
+
+    // apply 'old' blend stuff, blend against black
+    aColorStops.blendToIntensity(GetStartIntens() * 0.01, GetEndIntens() * 0.01,
+                                 BColor()); // COL_BLACK
+
+    // set values to default
+    SetStartIntens(100);
+    SetEndIntens(100);
+}
+
+void BGradient::tryToConvertToAxial()
+{
+    if (css::awt::GradientStyle_LINEAR != GetGradientStyle() || 0 != GetBorder()
+        || GetColorStops().empty())
+        return;
+
+    if (!GetColorStops().isSymmetrical())
+        return;
+
+    SetGradientStyle(css::awt::GradientStyle_AXIAL);
+
+    // Stretch the first half of the color stops to double width
+    // and collect them in a new color stops vector.
+    BColorStops aAxialColorStops;
+    aAxialColorStops.reserve(std::ceil(GetColorStops().size() / 2.0));
+    BColorStops::const_iterator aIter(GetColorStops().begin());
+    while (basegfx::fTools::lessOrEqual(aIter->getStopOffset(), 0.5))
+    {
+        BColorStop aNextStop(std::clamp((*aIter).getStopOffset() * 2.0, 0.0, 1.0),
+                             (*aIter).getStopColor());
+        aAxialColorStops.push_back(aNextStop);
+        ++aIter;
+    }
+    // Axial gradients have outmost color as last color stop.
+    aAxialColorStops.reverseColorStops();
+
+    SetColorStops(aAxialColorStops);
+}
+
+void BGradient::tryToApplyAxial()
+{
+    // only need to do something if css::awt::GradientStyle_AXIAL, else done
+    if (GetGradientStyle() != css::awt::GradientStyle_AXIAL)
+        return;
+
+    // apply the change to color stops
+    aColorStops.doApplyAxial();
+
+    // set style to GradientStyle_LINEAR
+    SetGradientStyle(css::awt::GradientStyle_LINEAR);
+}
+
+void BGradient::tryToApplySteps()
+{
+    // check for zero or invalid steps setting -> done
+    if (0 == GetSteps() || GetSteps() > 100)
+        return;
+
+    // do the action
+    aColorStops.doApplySteps(GetSteps());
+
+    // set value to default
+    SetSteps(0);
+}
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/canvastools.cxx b/basegfx/source/tools/canvastools.cxx
new file mode 100644
index 0000000000..70f4787710
--- /dev/null
+++ b/basegfx/source/tools/canvastools.cxx
@@ -0,0 +1,474 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <com/sun/star/geometry/RealSize2D.hpp>
+#include <com/sun/star/geometry/RealPoint2D.hpp>
+#include <com/sun/star/geometry/RealRectangle2D.hpp>
+#include <com/sun/star/geometry/RealRectangle3D.hpp>
+#include <com/sun/star/geometry/RealBezierSegment2D.hpp>
+#include <com/sun/star/geometry/AffineMatrix2D.hpp>
+#include <com/sun/star/geometry/AffineMatrix3D.hpp>
+#include <com/sun/star/geometry/IntegerSize2D.hpp>
+#include <com/sun/star/geometry/IntegerRectangle2D.hpp>
+#include <com/sun/star/lang/IllegalArgumentException.hpp>
+#include <com/sun/star/rendering/XPolyPolygon2D.hpp>
+#include <com/sun/star/rendering/XGraphicDevice.hpp>
+#include <com/sun/star/awt/Rectangle.hpp>
+#include <basegfx/utils/unopolypolygon.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/vector/b2dsize.hxx>
+#include <basegfx/vector/b2ivector.hxx>
+#include <basegfx/range/b3drange.hxx>
+#include <basegfx/range/b2irange.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/utils/canvastools.hxx>
+
+using namespace ::com::sun::star;
+
+namespace basegfx::unotools
+{
+        namespace
+        {
+            uno::Sequence< geometry::RealBezierSegment2D > bezierSequenceFromB2DPolygon(const ::basegfx::B2DPolygon& rPoly)
+            {
+                const sal_uInt32 nPointCount(rPoly.count());
+                uno::Sequence< geometry::RealBezierSegment2D > outputSequence(nPointCount);
+                geometry::RealBezierSegment2D* pOutput = outputSequence.getArray();
+
+                // fill sequences and imply closed polygon on this implementation layer
+                for(sal_uInt32 a(0); a < nPointCount; a++)
+                {
+                    const basegfx::B2DPoint aStart(rPoly.getB2DPoint(a));
+                    const basegfx::B2DPoint aControlA(rPoly.getNextControlPoint(a));
+                    const basegfx::B2DPoint aControlB(rPoly.getPrevControlPoint((a + 1) % nPointCount));
+
+                    pOutput[a] = geometry::RealBezierSegment2D(
+                        aStart.getX(), aStart.getY(),
+                        aControlA.getX(), aControlA.getY(),
+                        aControlB.getX(), aControlB.getY());
+                }
+
+                return outputSequence;
+            }
+
+            uno::Sequence< geometry::RealPoint2D > pointSequenceFromB2DPolygon( const ::basegfx::B2DPolygon& rPoly )
+            {
+                const sal_uInt32 nNumPoints( rPoly.count() );
+
+                uno::Sequence< geometry::RealPoint2D > outputSequence( nNumPoints );
+                geometry::RealPoint2D* pOutput = outputSequence.getArray();
+
+                // fill sequence from polygon
+                sal_uInt32 i;
+                for( i=0; i<nNumPoints; ++i )
+                {
+                    const ::basegfx::B2DPoint   aPoint( rPoly.getB2DPoint(i) );
+
+                    pOutput[i] = geometry::RealPoint2D( aPoint.getX(),
+                                                        aPoint.getY() );
+                }
+
+                return outputSequence;
+            }
+        }
+
+        uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > > bezierSequenceSequenceFromB2DPolyPolygon( const ::basegfx::B2DPolyPolygon& rPolyPoly )
+        {
+            const sal_uInt32 nNumPolies( rPolyPoly.count() );
+            sal_uInt32 i;
+
+            uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > > outputSequence( nNumPolies );
+            uno::Sequence< geometry::RealBezierSegment2D >* pOutput = outputSequence.getArray();
+
+            for( i=0; i<nNumPolies; ++i )
+            {
+                pOutput[i] = bezierSequenceFromB2DPolygon( rPolyPoly.getB2DPolygon(i) );
+            }
+
+            return outputSequence;
+        }
+
+        uno::Sequence< uno::Sequence< geometry::RealPoint2D > > pointSequenceSequenceFromB2DPolyPolygon( const ::basegfx::B2DPolyPolygon& rPolyPoly  )
+        {
+            const sal_uInt32 nNumPolies( rPolyPoly.count() );
+            sal_uInt32 i;
+
+            uno::Sequence< uno::Sequence< geometry::RealPoint2D > > outputSequence( nNumPolies );
+            uno::Sequence< geometry::RealPoint2D >* pOutput = outputSequence.getArray();
+
+            for( i=0; i<nNumPolies; ++i )
+            {
+                pOutput[i] = pointSequenceFromB2DPolygon( rPolyPoly.getB2DPolygon(i) );
+            }
+
+            return outputSequence;
+        }
+
+        uno::Reference< rendering::XPolyPolygon2D > xPolyPolygonFromB2DPolygon( const uno::Reference< rendering::XGraphicDevice >&  xGraphicDevice,
+                                                                                const ::basegfx::B2DPolygon&                        rPoly    )
+        {
+            uno::Reference< rendering::XPolyPolygon2D > xRes;
+
+            if( !xGraphicDevice.is() )
+                return xRes;
+
+            if( rPoly.areControlPointsUsed() )
+            {
+                uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > > outputSequence{ bezierSequenceFromB2DPolygon( rPoly )};
+
+                xRes = xGraphicDevice->createCompatibleBezierPolyPolygon( outputSequence );
+            }
+            else
+            {
+                uno::Sequence< uno::Sequence< geometry::RealPoint2D > > outputSequence{
+                 pointSequenceFromB2DPolygon( rPoly )};
+
+                xRes = xGraphicDevice->createCompatibleLinePolyPolygon( outputSequence );
+            }
+
+            if( xRes.is() && rPoly.isClosed() )
+                xRes->setClosed( 0, true );
+
+            return xRes;
+        }
+
+        uno::Reference< rendering::XPolyPolygon2D > xPolyPolygonFromB2DPolyPolygon( const uno::Reference< rendering::XGraphicDevice >&  xGraphicDevice,
+                                                                                    const ::basegfx::B2DPolyPolygon&                    rPolyPoly    )
+        {
+            uno::Reference< rendering::XPolyPolygon2D > xRes;
+
+            if( !xGraphicDevice.is() )
+                return xRes;
+
+            const sal_uInt32 nNumPolies( rPolyPoly.count() );
+            sal_uInt32 i;
+
+            if( rPolyPoly.areControlPointsUsed() )
+            {
+                xRes = xGraphicDevice->createCompatibleBezierPolyPolygon(
+                              bezierSequenceSequenceFromB2DPolyPolygon( rPolyPoly ) );
+            }
+            else
+            {
+                xRes = xGraphicDevice->createCompatibleLinePolyPolygon(
+                              pointSequenceSequenceFromB2DPolyPolygon( rPolyPoly ) );
+            }
+
+            for( i=0; i<nNumPolies; ++i )
+            {
+                xRes->setClosed( i, rPolyPoly.getB2DPolygon(i).isClosed() );
+            }
+
+            return xRes;
+        }
+
+        ::basegfx::B2DPolygon polygonFromPoint2DSequence( const uno::Sequence< geometry::RealPoint2D >& points )
+        {
+            const sal_Int32 nCurrSize( points.getLength() );
+
+            ::basegfx::B2DPolygon aPoly;
+
+            for( sal_Int32 nCurrPoint=0; nCurrPoint<nCurrSize; ++nCurrPoint )
+                aPoly.append( b2DPointFromRealPoint2D( points[nCurrPoint] ) );
+
+            return aPoly;
+        }
+
+        ::basegfx::B2DPolyPolygon polyPolygonFromPoint2DSequenceSequence( const uno::Sequence< uno::Sequence< geometry::RealPoint2D > >& points )
+        {
+            ::basegfx::B2DPolyPolygon aRes;
+
+            for( const auto & p : points )
+            {
+                aRes.append( polygonFromPoint2DSequence( p ) );
+            }
+
+            return aRes;
+        }
+
+        ::basegfx::B2DPolygon polygonFromBezier2DSequence( const uno::Sequence< geometry::RealBezierSegment2D >& curves )
+        {
+            const sal_Int32 nSize(curves.getLength());
+            basegfx::B2DPolygon aRetval;
+
+            if(nSize)
+            {
+                // prepare start with providing a start point. Use the first point from
+                // the sequence for this
+                const geometry::RealBezierSegment2D& rFirstSegment(curves[0]); // #i79917# first segment, not last
+                aRetval.append(basegfx::B2DPoint(rFirstSegment.Px, rFirstSegment.Py));
+
+                for(sal_Int32 a(0); a < nSize; a++)
+                {
+                    const geometry::RealBezierSegment2D& rCurrSegment(curves[a]);
+                    const geometry::RealBezierSegment2D& rNextSegment(curves[(a + 1) % nSize]);
+
+                    // append curved edge with the control points and the next point
+                    aRetval.appendBezierSegment(
+                        basegfx::B2DPoint(rCurrSegment.C1x, rCurrSegment.C1y),
+                        basegfx::B2DPoint(rCurrSegment.C2x, rCurrSegment.C2y), // #i79917# Argh! An x for an y!!
+                        basegfx::B2DPoint(rNextSegment.Px, rNextSegment.Py));
+                }
+
+                // rescue the control point and remove the now double-added point
+                aRetval.setPrevControlPoint(0, aRetval.getPrevControlPoint(aRetval.count() - 1));
+                aRetval.remove(aRetval.count() - 1);
+            }
+
+            return aRetval;
+        }
+
+        ::basegfx::B2DPolyPolygon polyPolygonFromBezier2DSequenceSequence( const uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > >& curves )
+        {
+            ::basegfx::B2DPolyPolygon aRes;
+
+            for( const auto & c : curves )
+            {
+                aRes.append( polygonFromBezier2DSequence( c ) );
+            }
+
+            return aRes;
+        }
+
+        ::basegfx::B2DPolyPolygon b2DPolyPolygonFromXPolyPolygon2D( const uno::Reference< rendering::XPolyPolygon2D >& xPoly )
+        {
+            ::basegfx::unotools::UnoPolyPolygon* pPolyImpl =
+                dynamic_cast< ::basegfx::unotools::UnoPolyPolygon* >( xPoly.get() );
+
+            if( pPolyImpl )
+            {
+                return pPolyImpl->getPolyPolygon();
+            }
+            else
+            {
+                // not a known implementation object - try data source
+                // interfaces
+                const sal_Int32 nPolys( xPoly->getNumberOfPolygons() );
+
+                uno::Reference< rendering::XBezierPolyPolygon2D > xBezierPoly(
+                    xPoly,
+                    uno::UNO_QUERY );
+
+                if( xBezierPoly.is() )
+                {
+                    return ::basegfx::unotools::polyPolygonFromBezier2DSequenceSequence(
+                        xBezierPoly->getBezierSegments( 0,
+                                                        nPolys,
+                                                        0,
+                                                        -1 ) );
+                }
+                else
+                {
+                    uno::Reference< rendering::XLinePolyPolygon2D > xLinePoly(
+                        xPoly,
+                        uno::UNO_QUERY );
+
+                    // no implementation class and no data provider
+                    // found - contract violation.
+                    if( !xLinePoly.is() )
+                    {
+                        throw lang::IllegalArgumentException(
+                            "basegfx::unotools::b2DPolyPolygonFromXPolyPolygon2D(): Invalid input"
+                            "poly-polygon, cannot retrieve vertex data",
+                            uno::Reference< uno::XInterface >(),
+                            0 );
+                    }
+
+                    return ::basegfx::unotools::polyPolygonFromPoint2DSequenceSequence(
+                        xLinePoly->getPoints( 0,
+                                              nPolys,
+                                              0,
+                                              -1 ));
+                }
+            }
+        }
+
+        ::basegfx::B2DHomMatrix& homMatrixFromAffineMatrix( ::basegfx::B2DHomMatrix&        output,
+                                                            const geometry::AffineMatrix2D& input )
+        {
+            // ensure last row is [0,0,1] (and optimized away)
+            output.identity();
+
+            output.set(0,0, input.m00);
+            output.set(0,1, input.m01);
+            output.set(0,2, input.m02);
+            output.set(1,0, input.m10);
+            output.set(1,1, input.m11);
+            output.set(1,2, input.m12);
+
+            return output;
+        }
+
+        ::basegfx::B3DHomMatrix homMatrixFromAffineMatrix3D( const ::css::geometry::AffineMatrix3D& input )
+        {
+            ::basegfx::B3DHomMatrix output;
+
+            output.set(0,0, input.m00);
+            output.set(0,1, input.m01);
+            output.set(0,2, input.m02);
+            output.set(0,3, input.m03);
+
+            output.set(1,0, input.m10);
+            output.set(1,1, input.m11);
+            output.set(1,2, input.m12);
+            output.set(1,3, input.m13);
+
+            output.set(2,0, input.m20);
+            output.set(2,1, input.m21);
+            output.set(2,2, input.m22);
+            output.set(2,3, input.m23);
+
+            return output;
+        }
+
+        geometry::AffineMatrix2D& affineMatrixFromHomMatrix( geometry::AffineMatrix2D&      output,
+                                                             const ::basegfx::B2DHomMatrix& input)
+        {
+            output.m00 = input.get(0,0);
+            output.m01 = input.get(0,1);
+            output.m02 = input.get(0,2);
+            output.m10 = input.get(1,0);
+            output.m11 = input.get(1,1);
+            output.m12 = input.get(1,2);
+
+            return output;
+        }
+
+        geometry::AffineMatrix3D& affineMatrixFromHomMatrix3D(
+            geometry::AffineMatrix3D& output,
+            const ::basegfx::B3DHomMatrix&  input)
+        {
+            output.m00 = input.get(0,0);
+            output.m01 = input.get(0,1);
+            output.m02 = input.get(0,2);
+            output.m03 = input.get(0,3);
+
+            output.m10 = input.get(1,0);
+            output.m11 = input.get(1,1);
+            output.m12 = input.get(1,2);
+            output.m13 = input.get(1,3);
+
+            output.m20 = input.get(2,0);
+            output.m21 = input.get(2,1);
+            output.m22 = input.get(2,2);
+            output.m23 = input.get(2,3);
+
+            return output;
+        }
+
+        geometry::RealSize2D size2DFromB2DSize(const ::basegfx::B2DSize& rSize)
+        {
+            return geometry::RealSize2D(rSize.getWidth(), rSize.getHeight());
+        }
+
+        geometry::RealPoint2D point2DFromB2DPoint( const ::basegfx::B2DPoint& rPoint )
+        {
+            return geometry::RealPoint2D( rPoint.getX(),
+                                          rPoint.getY() );
+        }
+
+        geometry::RealRectangle2D rectangle2DFromB2DRectangle( const ::basegfx::B2DRange& rRect )
+        {
+            return geometry::RealRectangle2D( rRect.getMinX(),
+                                              rRect.getMinY(),
+                                              rRect.getMaxX(),
+                                              rRect.getMaxY() );
+        }
+
+        geometry::RealRectangle3D rectangle3DFromB3DRectangle( const ::basegfx::B3DRange& rRect )
+        {
+            return geometry::RealRectangle3D( rRect.getMinX(),
+                                              rRect.getMinY(),
+                                              rRect.getMinZ(),
+                                              rRect.getMaxX(),
+                                              rRect.getMaxY(),
+                                              rRect.getMaxZ());
+        }
+
+        ::basegfx::B2DPoint b2DPointFromRealPoint2D( const geometry::RealPoint2D& rPoint )
+        {
+            return ::basegfx::B2DPoint( rPoint.X,
+                                        rPoint.Y );
+        }
+
+        ::basegfx::B2DRange b2DRectangleFromRealRectangle2D( const geometry::RealRectangle2D& rRect )
+        {
+            return ::basegfx::B2DRange( rRect.X1,
+                                        rRect.Y1,
+                                        rRect.X2,
+                                        rRect.Y2 );
+        }
+
+        ::basegfx::B3DRange b3DRectangleFromRealRectangle3D( const geometry::RealRectangle3D& rRect )
+        {
+            return ::basegfx::B3DRange( rRect.X1,
+                                        rRect.Y1,
+                                        rRect.Z1,
+                                        rRect.X2,
+                                        rRect.Y2,
+                                        rRect.Z2);
+        }
+
+        geometry::IntegerSize2D integerSize2DFromB2ISize( const ::basegfx::B2ISize& rSize )
+        {
+            return geometry::IntegerSize2D( rSize.getWidth(),
+                                            rSize.getHeight() );
+        }
+
+        basegfx::B2ISize b2ISizeFromIntegerSize2D( const geometry::IntegerSize2D& rSize )
+        {
+            return basegfx::B2ISize(rSize.Width, rSize.Height);
+        }
+
+        ::basegfx::B2IRange b2IRectangleFromIntegerRectangle2D( const geometry::IntegerRectangle2D& rRectangle )
+        {
+            return ::basegfx::B2IRange( rRectangle.X1, rRectangle.Y1,
+                                        rRectangle.X2, rRectangle.Y2 );
+        }
+
+        ::basegfx::B2IRange b2IRectangleFromAwtRectangle( const awt::Rectangle& rRect )
+        {
+            return ::basegfx::B2IRange( rRect.X,
+                                        rRect.Y,
+                                        rRect.X + rRect.Width,
+                                        rRect.Y + rRect.Height );
+        }
+
+        ::basegfx::B2IRange b2ISurroundingRangeFromB2DRange( const ::basegfx::B2DRange& rRange )
+        {
+            return ::basegfx::B2IRange( static_cast<sal_Int32>( floor(rRange.getMinX()) ),
+                                        static_cast<sal_Int32>( floor(rRange.getMinY()) ),
+                                        static_cast<sal_Int32>( ceil(rRange.getMaxX()) ),
+                                        static_cast<sal_Int32>( ceil(rRange.getMaxY()) ) );
+        }
+
+        ::basegfx::B2DRange b2DSurroundingIntegerRangeFromB2DRange( const ::basegfx::B2DRange& rRange )
+        {
+            return ::basegfx::B2DRange( floor(rRange.getMinX()),
+                                        floor(rRange.getMinY()),
+                                        ceil(rRange.getMaxX()),
+                                        ceil(rRange.getMaxY()) );
+        }
+
+} // namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/gradienttools.cxx b/basegfx/source/tools/gradienttools.cxx
new file mode 100644
index 0000000000..8f3e8ae83c
--- /dev/null
+++ b/basegfx/source/tools/gradienttools.cxx
@@ -0,0 +1,756 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/utils/gradienttools.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+#include <com/sun/star/awt/Gradient2.hpp>
+#include <osl/endian.h>
+
+#include <algorithm>
+#include <cmath>
+
+namespace basegfx
+{
+    bool ODFGradientInfo::operator==(const ODFGradientInfo& rODFGradientInfo) const
+    {
+        return getTextureTransform() == rODFGradientInfo.getTextureTransform()
+            && getAspectRatio() == rODFGradientInfo.getAspectRatio()
+            && getRequestedSteps() == rODFGradientInfo.getRequestedSteps();
+    }
+
+    const B2DHomMatrix& ODFGradientInfo::getBackTextureTransform() const
+    {
+        if(maBackTextureTransform.isIdentity())
+        {
+            const_cast< ODFGradientInfo* >(this)->maBackTextureTransform = getTextureTransform();
+            const_cast< ODFGradientInfo* >(this)->maBackTextureTransform.invert();
+        }
+
+        return maBackTextureTransform;
+    }
+
+    /** Most of the setup for linear & axial gradient is the same, except
+        for the border treatment. Factored out here.
+    */
+    static ODFGradientInfo init1DGradientInfo(
+        const B2DRange& rTargetRange,
+        sal_uInt32 nSteps,
+        double fBorder,
+        double fAngle,
+        bool bAxial)
+    {
+        B2DHomMatrix aTextureTransform;
+
+        fAngle = -fAngle;
+
+        double fTargetSizeX(rTargetRange.getWidth());
+        double fTargetSizeY(rTargetRange.getHeight());
+        double fTargetOffsetX(rTargetRange.getMinX());
+        double fTargetOffsetY(rTargetRange.getMinY());
+
+        // add object expansion
+        const bool bAngleUsed(!fTools::equalZero(fAngle));
+
+        if(bAngleUsed)
+        {
+            const double fAbsCos(fabs(cos(fAngle)));
+            const double fAbsSin(fabs(sin(fAngle)));
+            const double fNewX(fTargetSizeX * fAbsCos + fTargetSizeY * fAbsSin);
+            const double fNewY(fTargetSizeY * fAbsCos + fTargetSizeX * fAbsSin);
+
+            fTargetOffsetX -= (fNewX - fTargetSizeX) / 2.0;
+            fTargetOffsetY -= (fNewY - fTargetSizeY) / 2.0;
+            fTargetSizeX = fNewX;
+            fTargetSizeY = fNewY;
+        }
+
+        const double fSizeWithoutBorder(1.0 - fBorder);
+
+        if(bAxial)
+        {
+            aTextureTransform.scale(1.0, fSizeWithoutBorder * 0.5);
+            aTextureTransform.translate(0.0, 0.5);
+        }
+        else
+        {
+            if(!fTools::equal(fSizeWithoutBorder, 1.0))
+            {
+                aTextureTransform.scale(1.0, fSizeWithoutBorder);
+                aTextureTransform.translate(0.0, fBorder);
+            }
+        }
+
+        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);
+
+        // add texture rotate after scale to keep perpendicular angles
+        if(bAngleUsed)
+        {
+            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);
+
+            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
+        }
+
+        // add object translate
+        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);
+
+        // prepare aspect for texture
+        const double fAspectRatio(fTools::equalZero(fTargetSizeY) ?  1.0 : fTargetSizeX / fTargetSizeY);
+
+        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
+    }
+
+    /** Most of the setup for radial & ellipsoidal gradient is the same,
+        except for the border treatment. Factored out here.
+    */
+    static ODFGradientInfo initEllipticalGradientInfo(
+        const B2DRange& rTargetRange,
+        const B2DVector& rOffset,
+        sal_uInt32 nSteps,
+        double fBorder,
+        double fAngle,
+        bool bCircular)
+    {
+        B2DHomMatrix aTextureTransform;
+
+        fAngle = -fAngle;
+
+        double fTargetSizeX(rTargetRange.getWidth());
+        double fTargetSizeY(rTargetRange.getHeight());
+        double fTargetOffsetX(rTargetRange.getMinX());
+        double fTargetOffsetY(rTargetRange.getMinY());
+
+        // add object expansion
+        if(bCircular)
+        {
+            const double fOriginalDiag(std::hypot(fTargetSizeX, fTargetSizeY));
+
+            fTargetOffsetX -= (fOriginalDiag - fTargetSizeX) / 2.0;
+            fTargetOffsetY -= (fOriginalDiag - fTargetSizeY) / 2.0;
+            fTargetSizeX = fOriginalDiag;
+            fTargetSizeY = fOriginalDiag;
+        }
+        else
+        {
+            fTargetOffsetX -= ((M_SQRT2 - 1) / 2.0 ) * fTargetSizeX;
+            fTargetOffsetY -= ((M_SQRT2 - 1) / 2.0 ) * fTargetSizeY;
+            fTargetSizeX = M_SQRT2 * fTargetSizeX;
+            fTargetSizeY = M_SQRT2 * fTargetSizeY;
+        }
+
+        const double fHalfBorder((1.0 - fBorder) * 0.5);
+
+        aTextureTransform.scale(fHalfBorder, fHalfBorder);
+        aTextureTransform.translate(0.5, 0.5);
+        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);
+
+        // add texture rotate after scale to keep perpendicular angles
+        if(!bCircular && !fTools::equalZero(fAngle))
+        {
+            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);
+
+            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
+        }
+
+        // add defined offsets after rotation
+        if(!fTools::equal(0.5, rOffset.getX()) || !fTools::equal(0.5, rOffset.getY()))
+        {
+            // use original target size
+            fTargetOffsetX += (rOffset.getX() - 0.5) * rTargetRange.getWidth();
+            fTargetOffsetY += (rOffset.getY() - 0.5) * rTargetRange.getHeight();
+        }
+
+        // add object translate
+        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);
+
+        // prepare aspect for texture
+        const double fAspectRatio(fTargetSizeY == 0.0 ? 1.0 : (fTargetSizeX / fTargetSizeY));
+
+        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
+    }
+
+    /** Setup for rect & square gradient is exactly the same. Factored out
+        here.
+    */
+    static ODFGradientInfo initRectGradientInfo(
+        const B2DRange& rTargetRange,
+        const B2DVector& rOffset,
+        sal_uInt32 nSteps,
+        double fBorder,
+        double fAngle,
+        bool bSquare)
+    {
+        B2DHomMatrix aTextureTransform;
+
+        fAngle = -fAngle;
+
+        double fTargetSizeX(rTargetRange.getWidth());
+        double fTargetSizeY(rTargetRange.getHeight());
+        double fTargetOffsetX(rTargetRange.getMinX());
+        double fTargetOffsetY(rTargetRange.getMinY());
+
+        // add object expansion
+        if(bSquare)
+        {
+            const double fSquareWidth(std::max(fTargetSizeX, fTargetSizeY));
+
+            fTargetOffsetX -= (fSquareWidth - fTargetSizeX) / 2.0;
+            fTargetOffsetY -= (fSquareWidth - fTargetSizeY) / 2.0;
+            fTargetSizeX = fTargetSizeY = fSquareWidth;
+        }
+
+        // add object expansion
+        const bool bAngleUsed(!fTools::equalZero(fAngle));
+
+        if(bAngleUsed)
+        {
+            const double fAbsCos(fabs(cos(fAngle)));
+            const double fAbsSin(fabs(sin(fAngle)));
+            const double fNewX(fTargetSizeX * fAbsCos + fTargetSizeY * fAbsSin);
+            const double fNewY(fTargetSizeY * fAbsCos + fTargetSizeX * fAbsSin);
+
+            fTargetOffsetX -= (fNewX - fTargetSizeX) / 2.0;
+            fTargetOffsetY -= (fNewY - fTargetSizeY) / 2.0;
+            fTargetSizeX = fNewX;
+            fTargetSizeY = fNewY;
+        }
+
+        const double fHalfBorder((1.0 - fBorder) * 0.5);
+
+        aTextureTransform.scale(fHalfBorder, fHalfBorder);
+        aTextureTransform.translate(0.5, 0.5);
+        aTextureTransform.scale(fTargetSizeX, fTargetSizeY);
+
+        // add texture rotate after scale to keep perpendicular angles
+        if(bAngleUsed)
+        {
+            const B2DPoint aCenter(0.5 * fTargetSizeX, 0.5 * fTargetSizeY);
+
+            aTextureTransform *= basegfx::utils::createRotateAroundPoint(aCenter, fAngle);
+        }
+
+        // add defined offsets after rotation
+        if(!fTools::equal(0.5, rOffset.getX()) || !fTools::equal(0.5, rOffset.getY()))
+        {
+            // use original target size
+            fTargetOffsetX += (rOffset.getX() - 0.5) * rTargetRange.getWidth();
+            fTargetOffsetY += (rOffset.getY() - 0.5) * rTargetRange.getHeight();
+        }
+
+        // add object translate
+        aTextureTransform.translate(fTargetOffsetX, fTargetOffsetY);
+
+        // prepare aspect for texture
+        const double fAspectRatio(fTargetSizeY == 0.0 ? 1.0 : (fTargetSizeX / fTargetSizeY));
+
+        return ODFGradientInfo(aTextureTransform, fAspectRatio, nSteps);
+    }
+
+    namespace utils
+    {
+        /* Tooling method to extract data from given BGradient
+           to ColorStops, doing some corrections, partially based
+           on given SingleColor */
+        void prepareColorStops(
+            const basegfx::BGradient& rGradient,
+            BColorStops& rColorStops,
+            BColor& rSingleColor)
+        {
+            if (rGradient.GetColorStops().isSingleColor(rSingleColor))
+            {
+                // when single color, preserve value in rSingleColor
+                // and clear the ColorStops, done.
+                rColorStops.clear();
+                return;
+            }
+
+            const bool bAdaptStartEndIntensity(100 != rGradient.GetStartIntens() || 100 != rGradient.GetEndIntens());
+            const bool bAdaptBorder(0 != rGradient.GetBorder());
+
+            if (!bAdaptStartEndIntensity && !bAdaptBorder)
+            {
+                // copy unchanged ColorStops & done
+                rColorStops = rGradient.GetColorStops();
+                return;
+            }
+
+            // prepare a copy to work on
+            basegfx::BGradient aWorkCopy(rGradient);
+
+            if (bAdaptStartEndIntensity)
+            {
+                aWorkCopy.tryToApplyStartEndIntensity();
+
+                // this can again lead to single color (e.g. both zero, so
+                // all black), so check again for it
+                if (aWorkCopy.GetColorStops().isSingleColor(rSingleColor))
+                {
+                    rColorStops.clear();
+                    return;
+                }
+            }
+
+            if (bAdaptBorder)
+            {
+                aWorkCopy.tryToApplyBorder();
+            }
+
+            // extract ColorStops, that's all we need here
+            rColorStops = aWorkCopy.GetColorStops();
+        }
+
+        /* Tooling method to synchronize the given ColorStops.
+           The intention is that a color GradientStops and an
+           alpha/transparence GradientStops gets synchronized
+           for export. */
+        void synchronizeColorStops(
+            BColorStops& rColorStops,
+            BColorStops& rAlphaStops,
+            const BColor& rSingleColor,
+            const BColor& rSingleAlpha)
+        {
+            if (rColorStops.empty())
+            {
+                if (rAlphaStops.empty())
+                {
+                    // no AlphaStops and no ColorStops
+                    // create two-stop fallbacks for both
+                    rColorStops = BColorStops {
+                        BColorStop(0.0, rSingleColor),
+                        BColorStop(1.0, rSingleColor) };
+                    rAlphaStops = BColorStops {
+                        BColorStop(0.0, rSingleAlpha),
+                        BColorStop(1.0, rSingleAlpha) };
+                }
+                else
+                {
+                    // AlphaStops but no ColorStops
+                    // create fallback synched with existing AlphaStops
+                    for (const auto& cand : rAlphaStops)
+                    {
+                        rColorStops.emplace_back(cand.getStopOffset(), rSingleColor);
+                    }
+                }
+
+                // preparations complete, we are done
+                return;
+            }
+            else if (rAlphaStops.empty())
+            {
+                // ColorStops but no AlphaStops
+                // create fallback AlphaStops synched with existing ColorStops using SingleAlpha
+                for (const auto& cand : rColorStops)
+                {
+                    rAlphaStops.emplace_back(cand.getStopOffset(), rSingleAlpha);
+                }
+
+                // preparations complete, we are done
+                return;
+            }
+
+            // here we have ColorStops and AlphaStops not empty. Check if we need to
+            // synchronize both or if they are already usable/in a synched state so
+            // that they have same count and same StopOffsets
+            bool bNeedToSyncronize(rColorStops.size() != rAlphaStops.size());
+
+            if (!bNeedToSyncronize)
+            {
+                // check for same StopOffsets
+                BColorStops::const_iterator aCurrColor(rColorStops.begin());
+                BColorStops::const_iterator aCurrAlpha(rAlphaStops.begin());
+
+                while (!bNeedToSyncronize &&
+                    aCurrColor != rColorStops.end() &&
+                    aCurrAlpha != rAlphaStops.end())
+                {
+                    if (fTools::equal(aCurrColor->getStopOffset(), aCurrAlpha->getStopOffset()))
+                    {
+                        aCurrColor++;
+                        aCurrAlpha++;
+                    }
+                    else
+                    {
+                        bNeedToSyncronize = true;
+                    }
+                }
+            }
+
+            if (bNeedToSyncronize)
+            {
+                // synchronize sizes & StopOffsets
+                BColorStops::const_iterator aCurrColor(rColorStops.begin());
+                BColorStops::const_iterator aCurrAlpha(rAlphaStops.begin());
+                BColorStops aNewColor;
+                BColorStops aNewAlpha;
+                BColorStops::BColorStopRange aColorStopRange;
+                BColorStops::BColorStopRange aAlphaStopRange;
+                bool bRealChange(false);
+
+                do {
+                    const bool bColor(aCurrColor != rColorStops.end());
+                    const bool bAlpha(aCurrAlpha != rAlphaStops.end());
+
+                    if (bColor && bAlpha)
+                    {
+                        const double fColorOff(aCurrColor->getStopOffset());
+                        const double fAlphaOff(aCurrAlpha->getStopOffset());
+
+                        if (fTools::less(fColorOff, fAlphaOff))
+                        {
+                            // copy color, create alpha
+                            aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
+                            aNewAlpha.emplace_back(fColorOff, rAlphaStops.getInterpolatedBColor(fColorOff, 0, aAlphaStopRange));
+                            bRealChange = true;
+                            aCurrColor++;
+                        }
+                        else if (fTools::more(fColorOff, fAlphaOff))
+                        {
+                            // copy alpha, create color
+                            aNewColor.emplace_back(fAlphaOff, rColorStops.getInterpolatedBColor(fAlphaOff, 0, aColorStopRange));
+                            aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
+                            bRealChange = true;
+                            aCurrAlpha++;
+                        }
+                        else
+                        {
+                            // equal: copy both, advance
+                            aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
+                            aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
+                            aCurrColor++;
+                            aCurrAlpha++;
+                        }
+                    }
+                    else if (bColor)
+                    {
+                        const double fColorOff(aCurrColor->getStopOffset());
+                        aNewAlpha.emplace_back(fColorOff, rAlphaStops.getInterpolatedBColor(fColorOff, 0, aAlphaStopRange));
+                        aNewColor.emplace_back(fColorOff, aCurrColor->getStopColor());
+                        bRealChange = true;
+                        aCurrColor++;
+                    }
+                    else if (bAlpha)
+                    {
+                        const double fAlphaOff(aCurrAlpha->getStopOffset());
+                        aNewColor.emplace_back(fAlphaOff, rColorStops.getInterpolatedBColor(fAlphaOff, 0, aColorStopRange));
+                        aNewAlpha.emplace_back(fAlphaOff, aCurrAlpha->getStopColor());
+                        bRealChange = true;
+                        aCurrAlpha++;
+                    }
+                    else
+                    {
+                        // no more input, break do..while loop
+                        break;
+                    }
+                }
+                while(true);
+
+                if (bRealChange)
+                {
+                    // copy on 'real' change, that means data was added.
+                    // This should always be the cease and should have been
+                    // detected as such above, see bNeedToSyncronize
+                    rColorStops = aNewColor;
+                    rAlphaStops = aNewAlpha; // MCGR: tdf#155537 used wrong result here
+                }
+            }
+        }
+
+        sal_uInt32 calculateNumberOfSteps(
+            sal_uInt32 nRequestedSteps,
+            const BColor& rStart,
+            const BColor& rEnd)
+        {
+            const sal_uInt32 nMaxSteps(sal_uInt32((rStart.getMaximumDistance(rEnd) * 127.5) + 0.5));
+
+            if (0 == nRequestedSteps)
+            {
+                nRequestedSteps = nMaxSteps;
+            }
+
+            if(nRequestedSteps > nMaxSteps)
+            {
+                nRequestedSteps = nMaxSteps;
+            }
+
+            return std::max(sal_uInt32(1), nRequestedSteps);
+        }
+
+        ODFGradientInfo createLinearODFGradientInfo(
+            const B2DRange& rTargetArea,
+            sal_uInt32 nSteps,
+            double fBorder,
+            double fAngle)
+        {
+            return init1DGradientInfo(
+                rTargetArea,
+                nSteps,
+                fBorder,
+                fAngle,
+                false);
+        }
+
+        ODFGradientInfo createAxialODFGradientInfo(
+            const B2DRange& rTargetArea,
+            sal_uInt32 nSteps,
+            double fBorder,
+            double fAngle)
+        {
+            return init1DGradientInfo(
+                rTargetArea,
+                nSteps,
+                fBorder,
+                fAngle,
+                true);
+        }
+
+        ODFGradientInfo createRadialODFGradientInfo(
+            const B2DRange& rTargetArea,
+            const B2DVector& rOffset,
+            sal_uInt32 nSteps,
+            double fBorder)
+        {
+            return initEllipticalGradientInfo(
+                rTargetArea,
+                rOffset,
+                nSteps,
+                fBorder,
+                0.0,
+                true);
+        }
+
+        ODFGradientInfo createEllipticalODFGradientInfo(
+            const B2DRange& rTargetArea,
+            const B2DVector& rOffset,
+            sal_uInt32 nSteps,
+            double fBorder,
+            double fAngle)
+        {
+            return initEllipticalGradientInfo(
+                rTargetArea,
+                rOffset,
+                nSteps,
+                fBorder,
+                fAngle,
+                false);
+        }
+
+        ODFGradientInfo createSquareODFGradientInfo(
+            const B2DRange& rTargetArea,
+            const B2DVector& rOffset,
+            sal_uInt32 nSteps,
+            double fBorder,
+            double fAngle)
+        {
+            return initRectGradientInfo(
+                rTargetArea,
+                rOffset,
+                nSteps,
+                fBorder,
+                fAngle,
+                true);
+        }
+
+        ODFGradientInfo createRectangularODFGradientInfo(
+            const B2DRange& rTargetArea,
+            const B2DVector& rOffset,
+            sal_uInt32 nSteps,
+            double fBorder,
+            double fAngle)
+        {
+            return initRectGradientInfo(
+                rTargetArea,
+                rOffset,
+                nSteps,
+                fBorder,
+                fAngle,
+                false);
+        }
+
+        double getLinearGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+
+            // Ignore X, this is not needed at all for Y-Oriented gradients
+            // if(aCoor.getX() < 0.0 || aCoor.getX() > 1.0)
+            // {
+            //     return 0.0;
+            // }
+
+            if(aCoor.getY() <= 0.0)
+            {
+                return 0.0; // start value for inside
+            }
+
+            if(aCoor.getY() >= 1.0)
+            {
+                return 1.0; // end value for outside
+            }
+
+            return aCoor.getY();
+        }
+
+        double getAxialGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+
+            // Ignore X, this is not needed at all for Y-Oriented gradients
+            //if(aCoor.getX() < 0.0 || aCoor.getX() > 1.0)
+            //{
+            //    return 0.0;
+            //}
+
+            const double fAbsY(fabs(aCoor.getY()));
+
+            if(fAbsY >= 1.0)
+            {
+                return 1.0; // use end value when outside in Y
+            }
+
+            return fAbsY;
+        }
+
+        double getRadialGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+
+            if(aCoor.getX() < -1.0 || aCoor.getX() > 1.0 || aCoor.getY() < -1.0 || aCoor.getY() > 1.0)
+            {
+                return 0.0;
+            }
+
+            return 1.0 - std::hypot(aCoor.getX(), aCoor.getY());
+        }
+
+        double getEllipticalGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+
+            if(aCoor.getX() < -1.0 || aCoor.getX() > 1.0 || aCoor.getY() < -1.0 || aCoor.getY() > 1.0)
+            {
+                return 0.0;
+            }
+
+            double fAspectRatio(rGradInfo.getAspectRatio());
+            double t(1.0);
+
+            // MCGR: Similar to getRectangularGradientAlpha (please
+            // see there) we need to use aspect ratio here. Due to
+            // initEllipticalGradientInfo using M_SQRT2 to make this
+            // gradient look 'nicer' this correction seems not 100%
+            // correct, but is close enough for now
+            if(fAspectRatio > 1.0)
+            {
+                t = 1.0 - std::hypot(aCoor.getX() / fAspectRatio, aCoor.getY());
+            }
+            else if(fAspectRatio > 0.0)
+            {
+                t = 1.0 - std::hypot(aCoor.getX(), aCoor.getY() * fAspectRatio);
+            }
+
+            return t;
+        }
+
+        double getSquareGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+            const double fAbsX(fabs(aCoor.getX()));
+
+            if(fAbsX >= 1.0)
+            {
+                return 0.0;
+            }
+
+            const double fAbsY(fabs(aCoor.getY()));
+
+            if(fAbsY >= 1.0)
+            {
+                return 0.0;
+            }
+
+            return 1.0 - std::max(fAbsX, fAbsY);
+        }
+
+        double getRectangularGradientAlpha(const B2DPoint& rUV, const ODFGradientInfo& rGradInfo)
+        {
+            const B2DPoint aCoor(rGradInfo.getBackTextureTransform() * rUV);
+            double fAbsX(fabs(aCoor.getX()));
+
+            if(fAbsX >= 1.0)
+            {
+                return 0.0;
+            }
+
+            double fAbsY(fabs(aCoor.getY()));
+
+            if(fAbsY >= 1.0)
+            {
+                return 0.0;
+            }
+
+            // MCGR: Visualizations using the texturing method for
+            // displaying gradients (getBackTextureTransform is
+            // involved) show wrong results for GradientElliptical
+            // and GradientRect, this can be best seen when using
+            // less steps, e.g. just four. This thus has influence
+            // on cppcanvas (slideshow) and 3D textures, so needs
+            // to be corrected.
+            // Missing is to use the aspect ratio of the object
+            // in this [-1, -1, 1, 1] unified coordinate space
+            // after getBackTextureTransform is applied. Optically
+            // in the larger direction of the texturing the color
+            // step distances are too big *because* we are in that
+            // unit range now.
+            // To correct that, a kind of 'limo stretching' needs to
+            // be applied, adding space around the center
+            // proportional to the aspect ratio, so the intuitive
+            // idea would be to do
+            //
+            // fAbsX' = ((fAspectRatio - 1) + fAbsX) / fAspectRatio
+            //
+            // which scales from the center. This does not work, and
+            // after some thoughts it's clear why: It's not the
+            // position that needs to be moved (this cannot be
+            // changed), but the position *before* that scale has
+            // to be determined to get the correct, shifted color
+            // for the already 'new' position. Thus, turn around
+            // the expression as
+            //
+            // fAbsX' * fAspectRatio = fAspectRatio - 1 + fAbsX
+            // fAbsX' * fAspectRatio - fAspectRatio + 1 = fAbsX
+            // fAbsX = (fAbsX' - 1) * fAspectRatio + 1
+            //
+            // This works and can even be simply adapted for
+            // fAspectRatio < 1.0 aka vertical is bigger.
+            double fAspectRatio(rGradInfo.getAspectRatio());
+            if(fAspectRatio > 1.0)
+            {
+                fAbsX = ((fAbsX - 1) * fAspectRatio) + 1;
+            }
+            else if(fAspectRatio > 0.0)
+            {
+                fAbsY = ((fAbsY - 1) / fAspectRatio) + 1;
+            }
+
+            return 1.0 - std::max(fAbsX, fAbsY);
+        }
+    } // namespace utils
+} // namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/keystoplerp.cxx b/basegfx/source/tools/keystoplerp.cxx
new file mode 100644
index 0000000000..e5d0d76304
--- /dev/null
+++ b/basegfx/source/tools/keystoplerp.cxx
@@ -0,0 +1,90 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/utils/keystoplerp.hxx>
+#include <com/sun/star/uno/Sequence.hxx>
+#include <osl/diagnose.h>
+
+#include <algorithm>
+
+static void validateInput(const std::vector<double>& rKeyStops)
+{
+#ifdef DBG_UTIL
+    OSL_ENSURE( rKeyStops.size() > 1,
+                "KeyStopLerp::KeyStopLerp(): key stop vector must have two entries or more" );
+
+    // rKeyStops must be sorted in ascending order
+    for( std::size_t i=1, len=rKeyStops.size(); i<len; ++i )
+    {
+        if( rKeyStops[i-1] > rKeyStops[i] )
+            OSL_FAIL( "KeyStopLerp::KeyStopLerp(): time vector is not sorted in ascending order!" );
+    }
+#else
+    (void)rKeyStops;
+#endif
+}
+
+namespace basegfx::utils
+{
+        KeyStopLerp::KeyStopLerp( std::vector<double>&& rKeyStops ) :
+            maKeyStops(std::move(rKeyStops)),
+            mnLastIndex(0)
+        {
+            validateInput(maKeyStops);
+        }
+
+        KeyStopLerp::KeyStopLerp( const ::css::uno::Sequence<double>& rKeyStops ) :
+            maKeyStops(rKeyStops.begin(), rKeyStops.end()),
+            mnLastIndex(0)
+        {
+            validateInput(maKeyStops);
+        }
+
+        KeyStopLerp::ResultType KeyStopLerp::lerp(double fAlpha) const
+        {
+            // cached value still okay?
+            if( maKeyStops.at(mnLastIndex) < fAlpha ||
+                maKeyStops.at(mnLastIndex+1) >= fAlpha )
+            {
+                // nope, find new index
+                mnLastIndex = std::min<std::ptrdiff_t>(
+                    maKeyStops.size()-2,
+                    // range is ensured by max below
+                    std::max<std::ptrdiff_t>(
+                        0,
+                        std::distance( maKeyStops.begin(),
+                                       std::lower_bound( maKeyStops.begin(),
+                                                         maKeyStops.end(),
+                                                         fAlpha )) - 1 ));
+            }
+
+            // lerp between stop and stop+1
+            const double fRawLerp=
+                (fAlpha-maKeyStops.at(mnLastIndex)) /
+                (maKeyStops.at(mnLastIndex+1) - maKeyStops.at(mnLastIndex));
+
+            // clamp to permissible range (input fAlpha might be
+            // everything)
+            return ResultType(
+                mnLastIndex,
+                std::clamp(fRawLerp,0.0,1.0));
+        }
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/numbertools.cxx b/basegfx/source/tools/numbertools.cxx
new file mode 100644
index 0000000000..4248068b7d
--- /dev/null
+++ b/basegfx/source/tools/numbertools.cxx
@@ -0,0 +1,58 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+
+#include <basegfx/utils/tools.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/polygon/b2dpolypolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+
+#include <rtl/strbuf.hxx>
+#include <rtl/math.hxx>
+
+namespace basegfx::utils
+{
+    B2DPolyPolygon number2PolyPolygon(double fValue, sal_Int32 nTotalDigits, sal_Int32 nDecPlaces, bool bLitSegments)
+    {
+        // config here
+        // {
+        const double fSpace=0.2;
+        // }
+        // config here
+
+        OStringBuffer aNum;
+        rtl::math::doubleToStringBuffer(aNum,
+                                         fValue,
+                                         rtl_math_StringFormat_F,
+                                         nDecPlaces, '.',
+                                         nullptr, ',');
+
+        B2DPolyPolygon aRes;
+        B2DHomMatrix aMat;
+        double fCurrX=std::max(nTotalDigits-aNum.getLength(),
+                               sal_Int32(0)) * (1.0+fSpace);
+        for( sal_Int32 i=0; i<aNum.getLength(); ++i )
+        {
+            B2DPolyPolygon aCurr=createSevenSegmentPolyPolygon(aNum[i],
+                                                bLitSegments);
+
+            aMat.identity();
+            aMat.translate(fCurrX,0.0);
+            aCurr.transform(aMat);
+
+            fCurrX += 1.0+fSpace;
+
+            aRes.append(aCurr);
+        }
+
+        return aRes;
+    }
+
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/stringconversiontools.cxx b/basegfx/source/tools/stringconversiontools.cxx
new file mode 100644
index 0000000000..79b6d60466
--- /dev/null
+++ b/basegfx/source/tools/stringconversiontools.cxx
@@ -0,0 +1,158 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <stringconversiontools.hxx>
+#include <rtl/math.hxx>
+
+namespace basegfx::internal
+{
+        void skipSpaces(sal_Int32&      io_rPos,
+                        std::u16string_view rStr,
+                        const sal_Int32 nLen)
+        {
+            while( io_rPos < nLen &&
+                    rStr[io_rPos] == ' ' )
+            {
+                ++io_rPos;
+            }
+        }
+
+        static void skipSpacesAndCommas(sal_Int32&      io_rPos,
+                                 std::u16string_view rStr,
+                                 const sal_Int32 nLen)
+        {
+            while(io_rPos < nLen
+                    && (rStr[io_rPos] == ' ' || rStr[io_rPos] == ','))
+            {
+                ++io_rPos;
+            }
+        }
+
+        static bool getDoubleChar(double&         o_fRetval,
+                           sal_Int32&      io_rPos,
+                           std::u16string_view rStr)
+        {
+            const sal_Int64 nStrSize = rStr.size();
+            sal_Unicode aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+            const sal_Int32 nStartPos = io_rPos;
+
+            // sign
+            if(aChar == '+' || aChar == '-')
+            {
+                aChar = rStr[++io_rPos];
+            }
+
+            // numbers before point
+            while('0' <= aChar && '9' >= aChar)
+            {
+                io_rPos++;
+                aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+            }
+
+            // point
+            if(aChar == '.')
+            {
+                io_rPos++;
+                aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+            }
+
+            // numbers after point
+            while ('0' <= aChar && '9' >= aChar)
+            {
+                io_rPos++;
+                aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+            }
+
+            // 'e'
+            if(aChar == 'e' || aChar == 'E')
+            {
+                io_rPos++;
+                aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+
+                // sign for 'e'
+                if(aChar == '+' || aChar == '-')
+                {
+                    io_rPos++;
+                    aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+                }
+
+                // number for 'e'
+                while('0' <= aChar && '9' >= aChar)
+                {
+                    io_rPos++;
+                    aChar = io_rPos < nStrSize ? rStr[io_rPos] : 0;
+                }
+            }
+
+            const sal_Int32 nLen = io_rPos - nStartPos;
+            if(nLen)
+            {
+                rStr = rStr.substr(nStartPos, nLen);
+                rtl_math_ConversionStatus eStatus;
+                o_fRetval = ::rtl::math::stringToDouble( rStr,
+                                                            '.',
+                                                            ',',
+                                                            &eStatus );
+                return ( eStatus == rtl_math_ConversionStatus_Ok );
+            }
+
+            return false;
+        }
+
+        bool importDoubleAndSpaces(double&         o_fRetval,
+                                   sal_Int32&      io_rPos,
+                                   std::u16string_view rStr,
+                                   const sal_Int32 nLen )
+        {
+            if( !getDoubleChar(o_fRetval, io_rPos, rStr) )
+                return false;
+
+            skipSpacesAndCommas(io_rPos, rStr, nLen);
+
+            return true;
+        }
+
+        bool importFlagAndSpaces(sal_Int32&      o_nRetval,
+                                 sal_Int32&      io_rPos,
+                                 std::u16string_view rStr,
+                                 const sal_Int32 nLen)
+        {
+            sal_Unicode aChar( rStr[io_rPos] );
+
+            if(aChar == '0')
+            {
+                o_nRetval = 0;
+                ++io_rPos;
+            }
+            else if (aChar == '1')
+            {
+                o_nRetval = 1;
+                ++io_rPos;
+            }
+            else
+                return false;
+
+            skipSpacesAndCommas(io_rPos, rStr, nLen);
+
+            return true;
+        }
+
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/systemdependentdata.cxx b/basegfx/source/tools/systemdependentdata.cxx
new file mode 100644
index 0000000000..0d64d9982c
--- /dev/null
+++ b/basegfx/source/tools/systemdependentdata.cxx
@@ -0,0 +1,166 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+
+#include <basegfx/utils/systemdependentdata.hxx>
+#include <config_fuzzers.h>
+#include <math.h>
+
+namespace basegfx
+{
+    SystemDependentDataManager::SystemDependentDataManager()
+    {
+    }
+
+    SystemDependentDataManager::~SystemDependentDataManager()
+    {
+    }
+} // namespace basegfx
+
+namespace basegfx
+{
+    SystemDependentData::SystemDependentData(
+        SystemDependentDataManager& rSystemDependentDataManager)
+    :   mrSystemDependentDataManager(rSystemDependentDataManager),
+        mnCalculatedCycles(0)
+    {
+    }
+
+    SystemDependentData::~SystemDependentData()
+    {
+    }
+
+    sal_uInt32 SystemDependentData::calculateCombinedHoldCyclesInSeconds() const
+    {
+#if ENABLE_FUZZERS
+        return 0;
+#endif
+
+        if(0 == mnCalculatedCycles)
+        {
+            const sal_Int64 nBytes(estimateUsageInBytes());
+
+            // tdf#129845 as indicator for no need to buffer trivial data, stay at and
+            // return zero. As border, use 450 bytes. For polygons, this means to buffer
+            // starting with ca. 50 points (GDIPLUS uses 9 bytes per coordinate). For
+            // Bitmap data this means to more or less always buffer (as it was before).
+            // For the future, a more sophisticated differentiation may be added
+            if(nBytes > 450)
+            {
+                // HoldCyclesInSeconds
+                const sal_uInt32 nSeconds = 60;
+
+                // default is Seconds (minimal is one)
+                sal_uInt32 nResult(0 == nSeconds ? 1 : nSeconds);
+
+                if(0 != nBytes)
+                {
+                    // use sqrt to get some curved shape. With a default of 60s we get
+                    // a single second at 3600 byte. To get close to 10mb, multiply by
+                    // a corresponding scaling factor
+                    const double fScaleToMB(3600.0 / (1024.0 * 1024.0 * 10.0));
+
+                    // also use a multiplier to move the start point higher
+                    const double fMultiplierSeconds(10.0);
+
+                    // calculate
+                    nResult = static_cast<sal_uInt32>((fMultiplierSeconds * nSeconds) / sqrt(nBytes * fScaleToMB));
+
+                    // minimal value is 1
+                    if(nResult < 1)
+                    {
+                        nResult = 1;
+                    }
+
+                    // maximal value is nSeconds
+                    if(nResult > nSeconds)
+                    {
+                        nResult = nSeconds;
+                    }
+                }
+
+                // set locally (once, on-demand created, non-zero)
+                const_cast<SystemDependentData*>(this)->mnCalculatedCycles = nResult;
+            }
+        }
+
+        return mnCalculatedCycles;
+    }
+
+    sal_Int64 SystemDependentData::estimateUsageInBytes() const
+    {
+        // default implementation has no idea
+        return 0;
+    }
+} // namespace basegfx
+
+namespace basegfx
+{
+    SystemDependentDataHolder::SystemDependentDataHolder()
+    {
+    }
+
+    SystemDependentDataHolder::~SystemDependentDataHolder()
+    {
+        for(const auto& candidate : maSystemDependentReferences)
+        {
+            basegfx::SystemDependentData_SharedPtr aData(candidate.second.lock());
+
+            if(aData)
+            {
+                aData->getSystemDependentDataManager().endUsage(aData);
+            }
+        }
+    }
+
+    void SystemDependentDataHolder::addOrReplaceSystemDependentData(basegfx::SystemDependentData_SharedPtr& rData)
+    {
+        const size_t hash_code(typeid(*rData).hash_code());
+        auto result(maSystemDependentReferences.find(hash_code));
+
+        if(result != maSystemDependentReferences.end())
+        {
+            basegfx::SystemDependentData_SharedPtr aData(result->second.lock());
+
+            if(aData)
+            {
+                aData->getSystemDependentDataManager().endUsage(aData);
+            }
+
+            maSystemDependentReferences.erase(result);
+            result = maSystemDependentReferences.end();
+        }
+
+        maSystemDependentReferences[hash_code] = rData;
+        rData->getSystemDependentDataManager().startUsage(rData);
+    }
+
+    SystemDependentData_SharedPtr SystemDependentDataHolder::getSystemDependentData(size_t hash_code) const
+    {
+        basegfx::SystemDependentData_SharedPtr aRetval;
+        auto result(maSystemDependentReferences.find(hash_code));
+
+        if(result != maSystemDependentReferences.end())
+        {
+            aRetval = result->second.lock();
+
+            if(aRetval)
+            {
+                aRetval->getSystemDependentDataManager().touchUsage(aRetval);
+            }
+            else
+            {
+                const_cast< SystemDependentDataHolder* >(this)->maSystemDependentReferences.erase(result);
+            }
+        }
+
+        return aRetval;
+    }
+} // namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/tools.cxx b/basegfx/source/tools/tools.cxx
new file mode 100644
index 0000000000..4a7f2c962a
--- /dev/null
+++ b/basegfx/source/tools/tools.cxx
@@ -0,0 +1,111 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/utils/tools.hxx>
+#include <basegfx/range/b2drange.hxx>
+
+#include <algorithm>
+
+namespace basegfx::utils
+{
+        namespace
+        {
+            double distance( const double&                   nX,
+                                    const double&                   nY,
+                                    const ::basegfx::B2DVector&     rNormal,
+                                    const double&                   nC )
+            {
+                return nX*rNormal.getX() + nY*rNormal.getY() - nC;
+            }
+
+            void moveLineOutsideRect( ::basegfx::B2DPoint&          io_rStart,
+                                      ::basegfx::B2DPoint&          io_rEnd,
+                                      const ::basegfx::B2DVector&   rMoveDirection,
+                                      const ::basegfx::B2DRange&    rFitTarget      )
+            {
+                // calc c for normal line form equation n x - c = 0
+                const double nC( rMoveDirection.scalar( io_rStart ) );
+
+                // calc maximum orthogonal distance for all four bound
+                // rect corners to the line
+                const double nMaxDistance( std::max(
+                                               0.0,
+                                               std::max(
+                                                   distance(rFitTarget.getMinX(),
+                                                            rFitTarget.getMinY(),
+                                                            rMoveDirection,
+                                                            nC),
+                                                   std::max(
+                                                       distance(rFitTarget.getMinX(),
+                                                                rFitTarget.getMaxY(),
+                                                                rMoveDirection,
+                                                                nC),
+                                                       std::max(
+                                                           distance(rFitTarget.getMaxX(),
+                                                                    rFitTarget.getMinY(),
+                                                                    rMoveDirection,
+                                                                    nC),
+                                                           distance(rFitTarget.getMaxX(),
+                                                                    rFitTarget.getMaxY(),
+                                                                    rMoveDirection,
+                                                                    nC) ) ) ) ) );
+
+                // now move line points, such that the bound rect
+                // points are all either 'on' or on the negative side
+                // of the half-plane
+                io_rStart += nMaxDistance*rMoveDirection;
+                io_rEnd   += nMaxDistance*rMoveDirection;
+            }
+        }
+
+        void infiniteLineFromParallelogram( ::basegfx::B2DPoint&        io_rLeftTop,
+                                            ::basegfx::B2DPoint&        io_rLeftBottom,
+                                            ::basegfx::B2DPoint&        io_rRightTop,
+                                            ::basegfx::B2DPoint&        io_rRightBottom,
+                                            const ::basegfx::B2DRange&  rFitTarget  )
+        {
+            // For the top and bottom border line of the
+            // parallelogram, we determine the distance to all four
+            // corner points of the bound rect (tl, tr, bl, br). When
+            // using the unit normal form for lines (n x - c = 0), and
+            // choosing n to point 'outwards' the parallelogram, then
+            // all bound rect corner points having positive distance
+            // to the line lie outside the extended gradient rect, and
+            // thus, the corresponding border line must be moved the
+            // maximum distance outwards.
+
+            // don't use the top and bottom border line direction, and
+            // calculate the normal from them. Instead, use the
+            // vertical lines (lt - lb or rt - rb), as they more
+            // faithfully represent the direction of the
+            // to-be-generated infinite line
+            ::basegfx::B2DVector aDirectionVertical( io_rLeftTop - io_rLeftBottom );
+            aDirectionVertical.normalize();
+
+            const ::basegfx::B2DVector aNormalTop( aDirectionVertical );
+            const ::basegfx::B2DVector aNormalBottom( -aDirectionVertical );
+
+            // now extend parallelogram, such that the bound rect
+            // point are included
+            moveLineOutsideRect( io_rLeftTop, io_rRightTop, aNormalTop, rFitTarget );
+            moveLineOutsideRect( io_rLeftBottom, io_rRightBottom, aNormalBottom, rFitTarget );
+        }
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/unopolypolygon.cxx b/basegfx/source/tools/unopolypolygon.cxx
new file mode 100644
index 0000000000..41f1497319
--- /dev/null
+++ b/basegfx/source/tools/unopolypolygon.cxx
@@ -0,0 +1,446 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <com/sun/star/lang/IllegalArgumentException.hpp>
+
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/range/b2drange.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/utils/canvastools.hxx>
+#include <basegfx/polygon/b2dpolygon.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/utils/unopolypolygon.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+#include <cppuhelper/supportsservice.hxx>
+#include <utility>
+
+using namespace ::com::sun::star;
+
+namespace basegfx::unotools
+{
+    UnoPolyPolygon::UnoPolyPolygon( B2DPolyPolygon aPolyPoly ) :
+        maPolyPoly(std::move( aPolyPoly )),
+        meFillRule( rendering::FillRule_EVEN_ODD )
+    {
+    }
+
+    void SAL_CALL UnoPolyPolygon::addPolyPolygon(
+        const geometry::RealPoint2D&                        position,
+        const uno::Reference< rendering::XPolyPolygon2D >&  polyPolygon )
+    {
+        std::unique_lock const guard( m_aMutex );
+        modifying();
+
+        // TODO(F1): Correctly fulfill the UNO API
+        // specification. This will probably result in a vector of
+        // poly-polygons to be stored in this object.
+
+        const sal_Int32 nPolys( polyPolygon->getNumberOfPolygons() );
+
+        if( !polyPolygon.is() || !nPolys )
+        {
+            // invalid or empty polygon - nothing to do.
+            return;
+        }
+
+        B2DPolyPolygon        aSrcPoly;
+        const UnoPolyPolygon* pSrc( dynamic_cast< UnoPolyPolygon* >(polyPolygon.get()) );
+
+        // try to extract polygon data from interface. First,
+        // check whether it's the same implementation object,
+        // which we can tunnel then.
+        if( pSrc )
+        {
+            aSrcPoly = pSrc->getPolyPolygon();
+        }
+        else
+        {
+            // not a known implementation object - try data source
+            // interfaces
+            uno::Reference< rendering::XBezierPolyPolygon2D > xBezierPoly(
+                polyPolygon,
+                uno::UNO_QUERY );
+
+            if( xBezierPoly.is() )
+            {
+                aSrcPoly = unotools::polyPolygonFromBezier2DSequenceSequence(
+                    xBezierPoly->getBezierSegments( 0,
+                                                    nPolys,
+                                                    0,
+                                                    -1 ) );
+            }
+            else
+            {
+                uno::Reference< rendering::XLinePolyPolygon2D > xLinePoly(
+                    polyPolygon,
+                    uno::UNO_QUERY );
+
+                // no implementation class and no data provider
+                // found - contract violation.
+                if( !xLinePoly.is() )
+                    throw lang::IllegalArgumentException(
+                        "UnoPolyPolygon::addPolyPolygon(): Invalid input "
+                        "poly-polygon, cannot retrieve vertex data",
+                        getXWeak(), 1);
+
+                aSrcPoly = unotools::polyPolygonFromPoint2DSequenceSequence(
+                    xLinePoly->getPoints( 0,
+                                          nPolys,
+                                          0,
+                                          -1 ) );
+            }
+        }
+
+        const B2DRange  aBounds( utils::getRange( aSrcPoly ) );
+        const B2DVector     aOffset( unotools::b2DPointFromRealPoint2D( position ) -
+                                             aBounds.getMinimum() );
+
+        if( !aOffset.equalZero() )
+        {
+            const B2DHomMatrix aTranslate(utils::createTranslateB2DHomMatrix(aOffset));
+            aSrcPoly.transform( aTranslate );
+        }
+
+        maPolyPoly.append( aSrcPoly );
+    }
+
+    sal_Int32 SAL_CALL UnoPolyPolygon::getNumberOfPolygons()
+    {
+        std::unique_lock const guard( m_aMutex );
+        return maPolyPoly.count();
+    }
+
+    sal_Int32 SAL_CALL UnoPolyPolygon::getNumberOfPolygonPoints(
+        sal_Int32 polygon )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( polygon );
+
+        return maPolyPoly.getB2DPolygon(polygon).count();
+    }
+
+    rendering::FillRule SAL_CALL UnoPolyPolygon::getFillRule()
+    {
+        std::unique_lock const guard( m_aMutex );
+        return meFillRule;
+    }
+
+    void SAL_CALL UnoPolyPolygon::setFillRule(
+        rendering::FillRule fillRule )
+    {
+        std::unique_lock const guard( m_aMutex );
+        modifying();
+
+        meFillRule = fillRule;
+    }
+
+    sal_Bool SAL_CALL UnoPolyPolygon::isClosed(
+        sal_Int32 index )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( index );
+
+        return maPolyPoly.getB2DPolygon(index).isClosed();
+    }
+
+    void SAL_CALL UnoPolyPolygon::setClosed(
+        sal_Int32 index,
+        sal_Bool closedState )
+    {
+        std::unique_lock const guard( m_aMutex );
+        modifying();
+
+        if( index == -1 )
+        {
+            // set all
+            maPolyPoly.setClosed( closedState );
+        }
+        else
+        {
+            checkIndex( index );
+
+            // fetch referenced polygon, change state
+            B2DPolygon aTmp( maPolyPoly.getB2DPolygon(index) );
+            aTmp.setClosed( closedState );
+
+            // set back to container
+            maPolyPoly.setB2DPolygon( index, aTmp );
+        }
+    }
+
+    uno::Sequence< uno::Sequence< geometry::RealPoint2D > > SAL_CALL UnoPolyPolygon::getPoints(
+        sal_Int32 nPolygonIndex,
+        sal_Int32 nNumberOfPolygons,
+        sal_Int32 nPointIndex,
+        sal_Int32 nNumberOfPoints )
+    {
+        return unotools::pointSequenceSequenceFromB2DPolyPolygon(
+            getSubsetPolyPolygon( nPolygonIndex,
+                                  nNumberOfPolygons,
+                                  nPointIndex,
+                                  nNumberOfPoints ) );
+    }
+
+    void SAL_CALL UnoPolyPolygon::setPoints(
+        const uno::Sequence< uno::Sequence< geometry::RealPoint2D > >& points,
+        sal_Int32 nPolygonIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        modifying();
+
+        const B2DPolyPolygon& rNewPolyPoly(
+            unotools::polyPolygonFromPoint2DSequenceSequence( points ) );
+
+        if( nPolygonIndex == -1 )
+        {
+            maPolyPoly = rNewPolyPoly;
+        }
+        else
+        {
+            checkIndex( nPolygonIndex );
+
+            maPolyPoly.insert( nPolygonIndex, rNewPolyPoly );
+        }
+    }
+
+    geometry::RealPoint2D SAL_CALL UnoPolyPolygon::getPoint(
+        sal_Int32 nPolygonIndex,
+        sal_Int32 nPointIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( nPolygonIndex );
+
+        const B2DPolygon& rPoly( maPolyPoly.getB2DPolygon( nPolygonIndex ) );
+
+        if( nPointIndex < 0 || o3tl::make_unsigned(nPointIndex) >= rPoly.count() )
+            throw lang::IndexOutOfBoundsException();
+
+        return unotools::point2DFromB2DPoint( rPoly.getB2DPoint( nPointIndex ) );
+    }
+
+    void SAL_CALL UnoPolyPolygon::setPoint(
+        const geometry::RealPoint2D& point,
+        sal_Int32 nPolygonIndex,
+        sal_Int32 nPointIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( nPolygonIndex );
+        modifying();
+
+        B2DPolygon aPoly( maPolyPoly.getB2DPolygon( nPolygonIndex ) );
+
+        if( nPointIndex < 0 || o3tl::make_unsigned(nPointIndex) >= aPoly.count() )
+            throw lang::IndexOutOfBoundsException();
+
+        aPoly.setB2DPoint( nPointIndex,
+                           unotools::b2DPointFromRealPoint2D( point ) );
+        maPolyPoly.setB2DPolygon( nPolygonIndex, aPoly );
+    }
+
+    uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > > SAL_CALL UnoPolyPolygon::getBezierSegments(
+        sal_Int32 nPolygonIndex,
+        sal_Int32 nNumberOfPolygons,
+        sal_Int32 nPointIndex,
+        sal_Int32 nNumberOfPoints )
+    {
+        return unotools::bezierSequenceSequenceFromB2DPolyPolygon(
+            getSubsetPolyPolygon( nPolygonIndex,
+                                  nNumberOfPolygons,
+                                  nPointIndex,
+                                  nNumberOfPoints ) );
+    }
+
+    void SAL_CALL UnoPolyPolygon::setBezierSegments(
+        const uno::Sequence< uno::Sequence< geometry::RealBezierSegment2D > >&  points,
+        sal_Int32                                                               nPolygonIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        modifying();
+        const B2DPolyPolygon& rNewPolyPoly(
+            unotools::polyPolygonFromBezier2DSequenceSequence( points ) );
+
+        if( nPolygonIndex == -1 )
+        {
+            maPolyPoly = rNewPolyPoly;
+        }
+        else
+        {
+            checkIndex( nPolygonIndex );
+
+            maPolyPoly.insert( nPolygonIndex, rNewPolyPoly );
+        }
+    }
+
+    geometry::RealBezierSegment2D SAL_CALL UnoPolyPolygon::getBezierSegment( sal_Int32 nPolygonIndex,
+                                                                             sal_Int32 nPointIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( nPolygonIndex );
+
+        const B2DPolygon& rPoly( maPolyPoly.getB2DPolygon( nPolygonIndex ) );
+        const sal_uInt32  nPointCount(rPoly.count());
+
+        if( nPointIndex < 0 || o3tl::make_unsigned(nPointIndex) >= nPointCount )
+            throw lang::IndexOutOfBoundsException();
+
+        const B2DPoint& rPt( rPoly.getB2DPoint( nPointIndex ) );
+        const B2DPoint& rCtrl0( rPoly.getNextControlPoint(nPointIndex) );
+        const B2DPoint& rCtrl1( rPoly.getPrevControlPoint((nPointIndex + 1) % nPointCount) );
+
+        return geometry::RealBezierSegment2D( rPt.getX(),
+                                              rPt.getY(),
+                                              rCtrl0.getX(),
+                                              rCtrl0.getY(),
+                                              rCtrl1.getX(),
+                                              rCtrl1.getY() );
+    }
+
+    void SAL_CALL UnoPolyPolygon::setBezierSegment( const geometry::RealBezierSegment2D& segment,
+                                                         sal_Int32                       nPolygonIndex,
+                                                         sal_Int32                       nPointIndex )
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( nPolygonIndex );
+        modifying();
+
+        B2DPolygon aPoly( maPolyPoly.getB2DPolygon( nPolygonIndex ) );
+        const sal_uInt32 nPointCount(aPoly.count());
+
+        if( nPointIndex < 0 || o3tl::make_unsigned(nPointIndex) >= nPointCount )
+            throw lang::IndexOutOfBoundsException();
+
+        aPoly.setB2DPoint( nPointIndex,
+                           B2DPoint( segment.Px,
+                                     segment.Py ) );
+        aPoly.setNextControlPoint(nPointIndex,
+                                  B2DPoint(segment.C1x, segment.C1y));
+        aPoly.setPrevControlPoint((nPointIndex + 1) % nPointCount,
+                                  B2DPoint(segment.C2x, segment.C2y));
+
+        maPolyPoly.setB2DPolygon( nPolygonIndex, aPoly );
+    }
+
+    B2DPolyPolygon UnoPolyPolygon::getSubsetPolyPolygon(
+        sal_Int32 nPolygonIndex,
+        sal_Int32 nNumberOfPolygons,
+        sal_Int32 nPointIndex,
+        sal_Int32 nNumberOfPoints ) const
+    {
+        std::unique_lock const guard( m_aMutex );
+        checkIndex( nPolygonIndex );
+
+        const sal_Int32 nPolyCount( maPolyPoly.count() );
+
+        // check for "full polygon" case
+        if( !nPolygonIndex &&
+            !nPointIndex &&
+            nNumberOfPolygons == nPolyCount &&
+            nNumberOfPoints == -1 )
+        {
+            return maPolyPoly;
+        }
+
+        B2DPolyPolygon aSubsetPoly;
+
+        // create temporary polygon (as an extract from maPoly,
+        // which contains the requested subset)
+        for( sal_Int32 i=nPolygonIndex; i<nNumberOfPolygons; ++i )
+        {
+            checkIndex(i);
+
+            const B2DPolygon& rCurrPoly( maPolyPoly.getB2DPolygon(i) );
+
+            sal_Int32 nFirstPoint(0);
+            sal_Int32 nLastPoint(nPolyCount-1);
+
+            if( nPointIndex && i==nPolygonIndex )
+            {
+                // very first polygon - respect nPointIndex, if
+                // not zero
+
+                // empty polygon - impossible to specify _any_
+                // legal value except 0 here!
+                if( !nPolyCount)
+                    throw lang::IndexOutOfBoundsException();
+
+                nFirstPoint = nPointIndex;
+            }
+
+            if( i==nNumberOfPolygons-1 && nNumberOfPoints != -1 )
+            {
+                // very last polygon - respect nNumberOfPoints
+
+                // empty polygon - impossible to specify _any_
+                // legal value except -1 here!
+                if( !nPolyCount )
+                    throw lang::IndexOutOfBoundsException();
+
+                nLastPoint = nFirstPoint+nNumberOfPoints;
+            }
+
+            if( !nPolyCount )
+            {
+                // empty polygon - index checks already performed
+                // above, now simply append empty polygon
+                aSubsetPoly.append( rCurrPoly );
+            }
+            else
+            {
+                if( nFirstPoint < 0 || nFirstPoint >= nPolyCount )
+                    throw lang::IndexOutOfBoundsException();
+
+                if( nLastPoint < 0 || nLastPoint >= nPolyCount )
+                    throw lang::IndexOutOfBoundsException();
+
+                B2DPolygon aTmp;
+                for( sal_Int32 j=nFirstPoint; j<nLastPoint; ++j )
+                    aTmp.append( rCurrPoly.getB2DPoint(j) );
+
+                aSubsetPoly.append( aTmp );
+            }
+        }
+
+        return aSubsetPoly;
+    }
+
+    OUString SAL_CALL UnoPolyPolygon::getImplementationName()
+    {
+        return "gfx::internal::UnoPolyPolygon";
+    }
+
+    sal_Bool SAL_CALL UnoPolyPolygon::supportsService( const OUString& ServiceName )
+    {
+        return cppu::supportsService(this, ServiceName);
+    }
+
+    uno::Sequence< OUString > SAL_CALL UnoPolyPolygon::getSupportedServiceNames()
+    {
+        return { "com.sun.star.rendering.PolyPolygon2D" };
+    }
+
+    B2DPolyPolygon UnoPolyPolygon::getPolyPolygon() const
+    {
+        std::unique_lock const guard( m_aMutex );
+
+        return maPolyPoly;
+    }
+
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tools/zoomtools.cxx b/basegfx/source/tools/zoomtools.cxx
new file mode 100644
index 0000000000..dd4c7a6cbb
--- /dev/null
+++ b/basegfx/source/tools/zoomtools.cxx
@@ -0,0 +1,113 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+
+#include <basegfx/utils/zoomtools.hxx>
+
+namespace basegfx::zoomtools
+{
+
+/** 2^(1/6) as the default step
+
+    This ensures (unless the rounding is used) that 6 steps lead
+    to double / half zoom level.
+*/
+const double ZOOM_FACTOR = 1.12246205;
+
+/**
+* Round a value against a specified multiple. Values below half
+* of the multiple are rounded down and all others are rounded up.
+*
+* @param nCurrent current value
+* @param nMultiple multiple against which the current value is rounded
+*/
+static sal_uInt16 roundMultiple(sal_uInt16 nCurrent, int nMultiple)
+{
+    // round zoom to a multiple of nMultiple
+    return (( nCurrent + nMultiple / 2 ) - ( nCurrent + nMultiple / 2 ) % nMultiple);
+}
+
+/**
+* Convert geometric progression results into more common values by
+* rounding them against certain multiples depending on the size.
+* Beginning with 50 the multiple is 5, with 100, 10, and so on.
+*
+* @param nCurrent current zoom factor
+*/
+static sal_uInt16 roundZoom(double nCurrent)
+{
+    // convert nCurrent properly to int
+    sal_uInt16 nNew = nCurrent + 0.5;
+
+    // round to more common numbers above 50
+    if (nNew > 1000) {
+        nNew = roundMultiple(nNew, 100);
+    } else if ( nNew > 500 ) {
+        nNew = roundMultiple(nNew, 50);
+    } else if ( nNew > 100 ) {
+        nNew = roundMultiple(nNew, 10);
+    } else if ( nNew > 50 ) {
+        nNew = roundMultiple(nNew, 5);
+    }
+
+    return nNew;
+}
+
+/**
+* Make sure that a certain step isn't skipped during the zooming
+* progress.
+*
+* @param nCurrent current zoom factor
+* @param nPrevious previous zoom factor
+* @param nStep step which shouldn't be skipped
+*/
+static sal_uInt16 enforceStep(sal_uInt16 nCurrent, sal_uInt16 nPrevious, unsigned int nStep)
+{
+    if ((( nCurrent > nStep ) && ( nPrevious < nStep ))
+    || (( nCurrent < nStep ) && ( nPrevious > nStep )))
+        return nStep;
+    else
+        return nCurrent;
+}
+
+/**
+* Increasing the zoom level.
+*
+* @param nCurrent current zoom factor
+*/
+sal_uInt16 zoomIn(sal_uInt16 nCurrent)
+{
+    sal_uInt16 nNew = roundZoom( nCurrent * ZOOM_FACTOR );
+    // make sure some values are not skipped
+    nNew = enforceStep(nNew, nCurrent, 200);
+    nNew = enforceStep(nNew, nCurrent, 100);
+    nNew = enforceStep(nNew, nCurrent, 75);
+    nNew = enforceStep(nNew, nCurrent, 50);
+    nNew = enforceStep(nNew, nCurrent, 25);
+    return nNew;
+}
+
+/**
+* Decreasing the zoom level.
+*
+* @param nCurrent current zoom factor
+*/
+sal_uInt16 zoomOut(sal_uInt16 nCurrent)
+{
+    sal_uInt16 nNew = roundZoom( nCurrent / ZOOM_FACTOR );
+    // make sure some values are not skipped
+    nNew = enforceStep(nNew, nCurrent, 200);
+    nNew = enforceStep(nNew, nCurrent, 100);
+    nNew = enforceStep(nNew, nCurrent, 75);
+    nNew = enforceStep(nNew, nCurrent, 50);
+    nNew = enforceStep(nNew, nCurrent, 25);
+    return nNew;
+}
+} // namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tuple/b2dtuple.cxx b/basegfx/source/tuple/b2dtuple.cxx
new file mode 100644
index 0000000000..18a93f8d73
--- /dev/null
+++ b/basegfx/source/tuple/b2dtuple.cxx
@@ -0,0 +1,43 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/tuple/b2dtuple.hxx>
+#include <basegfx/tuple/b2ituple.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    const B2DTuple& B2DTuple::getEmptyTuple()
+    {
+        static B2DTuple const singleton;
+        return singleton;
+    }
+
+    B2DTuple::B2DTuple(const B2ITuple& rTup)
+        : Tuple2D(rTup.getX(), rTup.getY())
+    {}
+
+    B2ITuple fround(const B2DTuple& rTup)
+    {
+        return B2ITuple(fround(rTup.getX()), fround(rTup.getY()));
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/tuple/b3dtuple.cxx b/basegfx/source/tuple/b3dtuple.cxx
new file mode 100644
index 0000000000..73e9fd042a
--- /dev/null
+++ b/basegfx/source/tuple/b3dtuple.cxx
@@ -0,0 +1,37 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/tuple/b3dtuple.hxx>
+#include <basegfx/tuple/b3ituple.hxx>
+
+namespace basegfx
+{
+    const B3DTuple& B3DTuple::getEmptyTuple()
+    {
+        static B3DTuple const singleton;
+        return singleton;
+    }
+
+    B3ITuple fround(const B3DTuple& rTup)
+    {
+        return B3ITuple(fround(rTup.getX()), fround(rTup.getY()), fround(rTup.getZ()));
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/vector/b2dvector.cxx b/basegfx/source/vector/b2dvector.cxx
new file mode 100644
index 0000000000..85ec6ca811
--- /dev/null
+++ b/basegfx/source/vector/b2dvector.cxx
@@ -0,0 +1,184 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    B2DVector& B2DVector::normalize()
+    {
+        double fLen(scalar(*this));
+
+        if(fTools::equalZero(fLen))
+        {
+            mnX = 0.0;
+            mnY = 0.0;
+        }
+        else
+        {
+            const double fOne(1.0);
+
+            if(!fTools::equal(fOne, fLen))
+            {
+                fLen = sqrt(fLen);
+
+                if(!fTools::equalZero(fLen))
+                {
+                    mnX /= fLen;
+                    mnY /= fLen;
+                }
+            }
+        }
+
+        return *this;
+    }
+
+    double B2DVector::getLength() const
+    {
+        if(fTools::equalZero(mnX))
+        {
+            return fabs(mnY);
+        }
+        else if(fTools::equalZero(mnY))
+        {
+            return fabs(mnX);
+        }
+
+        return hypot( mnX, mnY );
+    }
+
+    double B2DVector::angle( const B2DVector& rVec ) const
+    {
+        return atan2(mnX * rVec.getY() - mnY * rVec.getX(),
+            mnX * rVec.getX() + mnY * rVec.getY());
+    }
+
+    const B2DVector& B2DVector::getEmptyVector()
+    {
+        return static_cast<const B2DVector&>( B2DTuple::getEmptyTuple() );
+    }
+
+    B2DVector& B2DVector::operator*=( const B2DHomMatrix& rMat )
+    {
+        const double fTempX( rMat.get(0,0)*mnX +
+                            rMat.get(0,1)*mnY );
+        const double fTempY( rMat.get(1,0)*mnX +
+                            rMat.get(1,1)*mnY );
+        mnX = fTempX;
+        mnY = fTempY;
+
+        return *this;
+    }
+
+    B2DVector& B2DVector::setLength(double fLen)
+    {
+        double fLenNow(scalar(*this));
+
+        if(!fTools::equalZero(fLenNow))
+        {
+            const double fOne(1.0);
+
+            if(!fTools::equal(fOne, fLenNow))
+            {
+                fLen /= sqrt(fLenNow);
+            }
+
+            mnX *= fLen;
+            mnY *= fLen;
+        }
+
+        return *this;
+    }
+
+    bool areParallel( const B2DVector& rVecA, const B2DVector& rVecB )
+    {
+        const double fValA(rVecA.getX() * rVecB.getY());
+        const double fValB(rVecA.getY() * rVecB.getX());
+
+        return fTools::equal(fValA, fValB);
+    }
+
+    B2VectorOrientation getOrientation( const B2DVector& rVecA, const B2DVector& rVecB )
+    {
+        double fVal(rVecA.getX() * rVecB.getY() - rVecA.getY() * rVecB.getX());
+
+        if(fTools::equalZero(fVal))
+        {
+            return B2VectorOrientation::Neutral;
+        }
+
+        if(fVal > 0.0)
+        {
+            return B2VectorOrientation::Positive;
+        }
+        else
+        {
+            return B2VectorOrientation::Negative;
+        }
+    }
+
+    B2DVector getPerpendicular( const B2DVector& rNormalizedVec )
+    {
+        B2DVector aPerpendicular(-rNormalizedVec.getY(), rNormalizedVec.getX());
+        return aPerpendicular;
+    }
+
+    B2DVector getNormalizedPerpendicular( const B2DVector& rVec )
+    {
+        B2DVector aPerpendicular(rVec);
+        aPerpendicular.normalize();
+        const double aTemp(-aPerpendicular.getY());
+        aPerpendicular.setY(aPerpendicular.getX());
+        aPerpendicular.setX(aTemp);
+        return aPerpendicular;
+    }
+
+    B2DVector operator*( const B2DHomMatrix& rMat, const B2DVector& rVec )
+    {
+        B2DVector aRes( rVec );
+        aRes *= rMat;
+        return aRes;
+    }
+
+    B2VectorContinuity getContinuity(const B2DVector& rBackVector, const B2DVector& rForwardVector )
+    {
+        if(rBackVector.equalZero() || rForwardVector.equalZero())
+        {
+            return B2VectorContinuity::NONE;
+        }
+
+        if(fTools::equal(rBackVector.getX(), -rForwardVector.getX()) && fTools::equal(rBackVector.getY(), -rForwardVector.getY()))
+        {
+            // same direction and same length -> C2
+            return B2VectorContinuity::C2;
+        }
+
+        if(areParallel(rBackVector, rForwardVector) && rBackVector.scalar(rForwardVector) < 0.0)
+        {
+            // parallel and opposite direction -> C1
+            return B2VectorContinuity::C1;
+        }
+
+        return B2VectorContinuity::NONE;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/vector/b2ivector.cxx b/basegfx/source/vector/b2ivector.cxx
new file mode 100644
index 0000000000..5b45871a39
--- /dev/null
+++ b/basegfx/source/vector/b2ivector.cxx
@@ -0,0 +1,65 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/vector/b2ivector.hxx>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/numeric/ftools.hxx>
+
+namespace basegfx
+{
+    B2IVector& B2IVector::operator=( const ::basegfx::B2ITuple& rVec )
+    {
+        mnX = rVec.getX();
+        mnY = rVec.getY();
+        return *this;
+    }
+
+    B2IVector& B2IVector::operator*=( const B2DHomMatrix& rMat )
+    {
+        mnX = fround( rMat.get(0,0)*mnX +
+                      rMat.get(0,1)*mnY );
+        mnY = fround( rMat.get(1,0)*mnX +
+                      rMat.get(1,1)*mnY );
+
+        return *this;
+    }
+
+    B2IVector& B2IVector::setLength(double fLen)
+    {
+        double fLenNow(scalar(*this));
+
+        if(!::basegfx::fTools::equalZero(fLenNow))
+        {
+            const double fOne(1.0);
+
+            if(!::basegfx::fTools::equal(fOne, fLenNow))
+            {
+                fLen /= sqrt(fLenNow);
+            }
+
+            mnX = fround( mnX*fLen );
+            mnY = fround( mnY*fLen );
+        }
+
+        return *this;
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/vector/b3dvector.cxx b/basegfx/source/vector/b3dvector.cxx
new file mode 100644
index 0000000000..89bc33c2bd
--- /dev/null
+++ b/basegfx/source/vector/b3dvector.cxx
@@ -0,0 +1,86 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <basegfx/vector/b3dvector.hxx>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+
+namespace basegfx
+{
+    B3DVector& B3DVector::normalize()
+    {
+        double fLen(scalar(*this));
+
+        if(!::basegfx::fTools::equalZero(fLen))
+        {
+            const double fOne(1.0);
+
+            if(!::basegfx::fTools::equal(fOne, fLen))
+            {
+                fLen = sqrt(fLen);
+
+                mnX /= fLen;
+                mnY /= fLen;
+                mnZ /= fLen;
+            }
+        }
+
+        return *this;
+    }
+
+    B3DVector B3DVector::getPerpendicular(const B3DVector& rNormalizedVec) const
+    {
+        B3DVector aNew = cross(*this, rNormalizedVec);
+        aNew.normalize();
+        return aNew;
+    }
+
+    B3DVector& B3DVector::operator*=( const ::basegfx::B3DHomMatrix& rMat )
+    {
+        const double fTempX( rMat.get(0,0)*mnX + rMat.get(0,1)*mnY + rMat.get(0,2)*mnZ );
+        const double fTempY( rMat.get(1,0)*mnX + rMat.get(1,1)*mnY + rMat.get(1,2)*mnZ );
+        const double fTempZ( rMat.get(2,0)*mnX + rMat.get(2,1)*mnY + rMat.get(2,2)*mnZ );
+        mnX = fTempX;
+        mnY = fTempY;
+        mnZ = fTempZ;
+
+        return *this;
+    }
+
+    B3DVector operator*( const ::basegfx::B3DHomMatrix& rMat, const B3DVector& rVec )
+    {
+        B3DVector aRes( rVec );
+        aRes *= rMat;
+        return aRes;
+    }
+
+    bool areParallel( const B3DVector& rVecA, const B3DVector& rVecB )
+    {
+        // i think fastest is to compare relations, need no square or division
+        if(!fTools::equal(rVecA.getX() * rVecB.getY(), rVecA.getY() * rVecB.getX()))
+            return false;
+
+        if(!fTools::equal(rVecA.getX() * rVecB.getZ(), rVecA.getZ() * rVecB.getX()))
+            return false;
+
+        return fTools::equal(rVecA.getY() * rVecB.getZ(), rVecA.getZ() * rVecB.getY());
+    }
+
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/workbench/Makefile b/basegfx/source/workbench/Makefile
new file mode 100644
index 0000000000..6218141da1
--- /dev/null
+++ b/basegfx/source/workbench/Makefile
@@ -0,0 +1,23 @@
+#
+# This file is part of the LibreOffice project.
+#
+# This Source Code Form is subject to the terms of the Mozilla Public
+# License, v. 2.0. If a copy of the MPL was not distributed with this
+# file, You can obtain one at http://mozilla.org/MPL/2.0/.
+#
+# This file incorporates work covered by the following license notice:
+#
+#   Licensed to the Apache Software Foundation (ASF) under one or more
+#   contributor license agreements. See the NOTICE file distributed
+#   with this work for additional information regarding copyright
+#   ownership. The ASF licenses this file to you under the Apache
+#   License, Version 2.0 (the "License"); you may not use this file
+#   except in compliance with the License. You may obtain a copy of
+#   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+#
+
+prog : bezierclip.cxx convexhull.cxx
+	g++ -I. -Wall -g bezierclip.cxx convexhull.cxx -o bezierclip
+
+.cxx.o:
+	g++ -c $(LOCALDEFINES) $(CCFLAGS) $<
diff --git a/basegfx/source/workbench/bezierclip.cxx b/basegfx/source/workbench/bezierclip.cxx
new file mode 100644
index 0000000000..676f239efd
--- /dev/null
+++ b/basegfx/source/workbench/bezierclip.cxx
@@ -0,0 +1,2006 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <iostream>
+#include <cassert>
+#include <algorithm>
+#include <iterator>
+#include <vector>
+#include <utility>
+
+#include <math.h>
+
+#include <bezierclip.hxx>
+#include <gauss.hxx>
+
+// what to test
+#define WITH_ASSERTIONS
+//#define WITH_CONVEXHULL_TEST
+//#define WITH_MULTISUBDIVIDE_TEST
+//#define WITH_FATLINE_TEST
+//#define WITH_CALCFOCUS_TEST
+//#define WITH_SAFEPARAMBASE_TEST
+//#define WITH_SAFEPARAMS_TEST
+//#define WITH_SAFEPARAM_DETAILED_TEST
+//#define WITH_SAFEFOCUSPARAM_CALCFOCUS
+//#define WITH_SAFEFOCUSPARAM_TEST
+//#define WITH_SAFEFOCUSPARAM_DETAILED_TEST
+#define WITH_BEZIERCLIP_TEST
+
+/* Implementation of the so-called 'Fat-Line Bezier Clipping Algorithm' by Sederberg et al.
+ *
+ * Actual reference is: T. W. Sederberg and T Nishita: Curve
+ * intersection using Bezier clipping. In Computer Aided Design, 22
+ * (9), 1990, pp. 538--549
+ */
+
+/* Misc helper
+ * ===========
+ */
+int fallFac( int n, int k )
+{
+#ifdef WITH_ASSERTIONS
+    assert(n>=k); // "For factorials, n must be greater or equal k"
+    assert(n>=0); // "For factorials, n must be positive"
+    assert(k>=0); // "For factorials, k must be positive"
+#endif
+
+    int res( 1 );
+
+    while( k-- && n ) res *= n--;
+
+    return res;
+}
+
+int fac( int n )
+{
+    return fallFac(n, n);
+}
+
+/* Bezier fat line clipping part
+ * =============================
+ */
+
+void Impl_calcFatLine( FatLine& line, const Bezier& c )
+{
+    // Prepare normalized implicit line
+    // ================================
+
+    // calculate vector orthogonal to p1-p4:
+    line.a = -(c.p0.y - c.p3.y);
+    line.b = (c.p0.x - c.p3.x);
+
+    // normalize
+    const double len(std::hypot(line.a, line.b));
+    if( !tolZero(len) )
+    {
+        line.a /= len;
+        line.b /= len;
+    }
+
+    line.c = -(line.a*c.p0.x + line.b*c.p0.y);
+
+    // Determine bounding fat line from it
+    // ===================================
+
+    // calc control point distances
+    const double dP2( calcLineDistance(line.a, line.b, line.c, c.p1.x, c.p1.y ) );
+    const double dP3( calcLineDistance(line.a, line.b, line.c, c.p2.x, c.p2.y ) );
+
+    // calc approximate bounding lines to curve (tight bounds are
+    // possible here, but more expensive to calculate and thus not
+    // worth the overhead)
+    if( dP2 * dP3 > 0.0 )
+    {
+        line.dMin = 3.0/4.0 * std::min(0.0, std::min(dP2, dP3));
+        line.dMax = 3.0/4.0 * std::max(0.0, std::max(dP2, dP3));
+    }
+    else
+    {
+        line.dMin = 4.0/9.0 * std::min(0.0, std::min(dP2, dP3));
+        line.dMax = 4.0/9.0 * std::max(0.0, std::max(dP2, dP3));
+    }
+}
+
+void Impl_calcBounds( Point2D&          leftTop,
+                      Point2D&          rightBottom,
+                      const Bezier&     c1          )
+{
+    leftTop.x = std::min( c1.p0.x, std::min( c1.p1.x, std::min( c1.p2.x, c1.p3.x ) ) );
+    leftTop.y = std::min( c1.p0.y, std::min( c1.p1.y, std::min( c1.p2.y, c1.p3.y ) ) );
+    rightBottom.x = std::max( c1.p0.x, std::max( c1.p1.x, std::max( c1.p2.x, c1.p3.x ) ) );
+    rightBottom.y = std::max( c1.p0.y, std::max( c1.p1.y, std::max( c1.p2.y, c1.p3.y ) ) );
+}
+
+bool Impl_doBBoxIntersect( const Bezier& c1,
+                           const Bezier& c2 )
+{
+    // calc rectangular boxes from c1 and c2
+    Point2D lt1;
+    Point2D rb1;
+    Point2D lt2;
+    Point2D rb2;
+
+    Impl_calcBounds( lt1, rb1, c1 );
+    Impl_calcBounds( lt2, rb2, c2 );
+
+    if( std::min(rb1.x, rb2.x) < std::max(lt1.x, lt2.x) ||
+        std::min(rb1.y, rb2.y) < std::max(lt1.y, lt2.y) )
+    {
+        return false;
+    }
+    else
+    {
+        return true;
+    }
+}
+
+/* calculates two t's for the given bernstein control polygon: the first is
+ * the intersection of the min value line with the convex hull from
+ * the left, the second is the intersection of the max value line with
+ * the convex hull from the right.
+ */
+bool Impl_calcSafeParams( double&           t1,
+                          double&           t2,
+                          const Polygon2D&  rPoly,
+                          double            lowerYBound,
+                          double            upperYBound )
+{
+    // need the convex hull of the control polygon, as this is
+    // guaranteed to completely bound the curve
+    Polygon2D convHull( convexHull(rPoly) );
+
+    // init min and max buffers
+    t1 = 0.0 ;
+    double currLowerT( 1.0 );
+
+    t2 = 1.0;
+    double currHigherT( 0.0 );
+
+    if( convHull.size() <= 1 )
+        return false; // only one point? Then we're done with clipping
+
+    /* now, clip against lower and higher bounds */
+    Point2D p0;
+    Point2D p1;
+
+    bool bIntersection( false );
+
+    for( Polygon2D::size_type i=0; i<convHull.size(); ++i )
+    {
+        // have to check against convHull.size() segments, as the
+        // convex hull is, by definition, closed. Thus, for the
+        // last point, we take the first point as partner.
+        if( i+1 == convHull.size() )
+        {
+            // close the polygon
+            p0 = convHull[i];
+            p1 = convHull[0];
+        }
+        else
+        {
+            p0 = convHull[i];
+            p1 = convHull[i+1];
+        }
+
+        // is the segment in question within or crossing the
+        // horizontal band spanned by lowerYBound and upperYBound? If
+        // not, we've got no intersection. If yes, we maybe don't have
+        // an intersection, but we've got to update the permissible
+        // range, nevertheless. This is because inside lying segments
+        // leads to full range forbidden.
+        if( (tolLessEqual(p0.y, upperYBound) || tolLessEqual(p1.y, upperYBound)) &&
+            (tolGreaterEqual(p0.y, lowerYBound) || tolGreaterEqual(p1.y, lowerYBound)) )
+        {
+            // calc intersection of convex hull segment with
+            // one of the horizontal bounds lines
+            // to optimize a bit, r_x is calculated only in else case
+            const double r_y( p1.y - p0.y );
+
+            if( tolZero(r_y) )
+            {
+                // r_y is virtually zero, thus we've got a horizontal
+                // line. Now check whether we maybe coincide with lower or
+                // upper horizontal bound line.
+                if( tolEqual(p0.y, lowerYBound) ||
+                    tolEqual(p0.y, upperYBound) )
+                {
+                    // yes, simulate intersection then
+                    currLowerT = std::min(currLowerT, std::min(p0.x, p1.x));
+                    currHigherT = std::max(currHigherT, std::max(p0.x, p1.x));
+                }
+            }
+            else
+            {
+                // check against lower and higher bounds
+                // =====================================
+                const double r_x( p1.x - p0.x );
+
+                // calc intersection with horizontal dMin line
+                const double currTLow( (lowerYBound - p0.y) * r_x / r_y + p0.x );
+
+                // calc intersection with horizontal dMax line
+                const double currTHigh( (upperYBound - p0.y) * r_x / r_y + p0.x );
+
+                currLowerT = std::min(currLowerT, std::min(currTLow, currTHigh));
+                currHigherT = std::max(currHigherT, std::max(currTLow, currTHigh));
+            }
+
+            // set flag that at least one segment is contained or
+            // intersects given horizontal band.
+            bIntersection = true;
+        }
+    }
+
+#ifndef WITH_SAFEPARAMBASE_TEST
+    // limit intersections found to permissible t parameter range
+    t1 = std::max(0.0, currLowerT);
+    t2 = std::min(1.0, currHigherT);
+#endif
+
+    return bIntersection;
+}
+
+/* calculates two t's for the given bernstein polynomial: the first is
+ * the intersection of the min value line with the convex hull from
+ * the left, the second is the intersection of the max value line with
+ * the convex hull from the right.
+ *
+ * The polynomial coefficients c0 to c3 given to this method
+ * must correspond to t values of 0, 1/3, 2/3 and 1, respectively.
+ */
+bool Impl_calcSafeParams_clip( double&          t1,
+                               double&          t2,
+                               const FatLine&   bounds,
+                               double           c0,
+                               double           c1,
+                               double           c2,
+                               double           c3 )
+{
+    /* first of all, determine convex hull of c0-c3 */
+    Polygon2D poly(4);
+    poly[0] = Point2D(0,        c0);
+    poly[1] = Point2D(1.0/3.0,  c1);
+    poly[2] = Point2D(2.0/3.0,  c2);
+    poly[3] = Point2D(1,        c3);
+
+#ifndef WITH_SAFEPARAM_DETAILED_TEST
+
+    return Impl_calcSafeParams( t1, t2, poly, bounds.dMin, bounds.dMax );
+
+#else
+    bool bRet( Impl_calcSafeParams( t1, t2, poly, bounds.dMin, bounds.dMax ) );
+
+    Polygon2D convHull( convexHull( poly ) );
+
+    std::cout << "# convex hull testing" << std::endl
+         << "plot [t=0:1] ";
+    std::cout << " bez("
+         << poly[0].x << ","
+         << poly[1].x << ","
+         << poly[2].x << ","
+         << poly[3].x << ",t),bez("
+         << poly[0].y << ","
+         << poly[1].y << ","
+         << poly[2].y << ","
+         << poly[3].y << ",t), "
+         << "t, " << bounds.dMin << ", "
+         << "t, " << bounds.dMax << ", "
+         << t1 << ", t, "
+         << t2 << ", t, "
+         << "'-' using ($1):($2) title \"control polygon\" with lp, "
+         << "'-' using ($1):($2) title \"convex hull\" with lp" << std::endl;
+
+    unsigned int k;
+    for( k=0; k<poly.size(); ++k )
+    {
+        std::cout << poly[k].x << " " << poly[k].y << std::endl;
+    }
+    std::cout << poly[0].x << " " << poly[0].y << std::endl;
+    std::cout << "e" << std::endl;
+
+    for( k=0; k<convHull.size(); ++k )
+    {
+        std::cout << convHull[k].x << " " << convHull[k].y << std::endl;
+    }
+    std::cout << convHull[0].x << " " << convHull[0].y << std::endl;
+    std::cout << "e" << std::endl;
+
+    return bRet;
+#endif
+}
+
+void Impl_deCasteljauAt( Bezier&        part1,
+                         Bezier&        part2,
+                         const Bezier&  input,
+                         double         t        )
+{
+    // deCasteljau bezier arc, scheme is:
+
+    // First row is    C_0^n,C_1^n,...,C_n^n
+    // Second row is         P_1^n,...,P_n^n
+    // etc.
+    // with P_k^r = (1 - x_s)P_{k-1}^{r-1} + x_s P_k{r-1}
+
+    // this results in:
+
+    // P1  P2  P3  P4
+    // L1  P2  P3  R4
+    //     L2  H   R3
+    //         L3  R2
+    //             L4/R1
+    if( tolZero(t) )
+    {
+        // t is zero -> part2 is input curve, part1 is empty (input.p0, that is)
+        part1.p0.x = part1.p1.x = part1.p2.x = part1.p3.x = input.p0.x;
+        part1.p0.y = part1.p1.y = part1.p2.y = part1.p3.y = input.p0.y;
+        part2 = input;
+    }
+    else if( tolEqual(t, 1.0) )
+    {
+        // t is one -> part1 is input curve, part2 is empty (input.p3, that is)
+        part1 = input;
+        part2.p0.x = part2.p1.x = part2.p2.x = part2.p3.x = input.p3.x;
+        part2.p0.y = part2.p1.y = part2.p2.y = part2.p3.y = input.p3.y;
+    }
+    else
+    {
+        part1.p0.x = input.p0.x;                                    part1.p0.y = input.p0.y;
+        part1.p1.x = (1.0 - t)*part1.p0.x + t*input.p1.x;           part1.p1.y = (1.0 - t)*part1.p0.y + t*input.p1.y;
+        const double Hx ( (1.0 - t)*input.p1.x + t*input.p2.x ),    Hy ( (1.0 - t)*input.p1.y + t*input.p2.y );
+        part1.p2.x = (1.0 - t)*part1.p1.x + t*Hx;                   part1.p2.y = (1.0 - t)*part1.p1.y + t*Hy;
+        part2.p3.x = input.p3.x;                                    part2.p3.y = input.p3.y;
+        part2.p2.x = (1.0 - t)*input.p2.x + t*input.p3.x;           part2.p2.y = (1.0 - t)*input.p2.y + t*input.p3.y;
+        part2.p1.x = (1.0 - t)*Hx + t*part2.p2.x;                   part2.p1.y = (1.0 - t)*Hy + t*part2.p2.y;
+        part2.p0.x = (1.0 - t)*part1.p2.x + t*part2.p1.x;           part2.p0.y = (1.0 - t)*part1.p2.y + t*part2.p1.y;
+        part1.p3.x = part2.p0.x;                                    part1.p3.y = part2.p0.y;
+    }
+}
+
+void printCurvesWithSafeRange( const Bezier& c1, const Bezier& c2, double t1_c1, double t2_c1,
+                               const Bezier& c2_part, const FatLine& bounds_c2 )
+{
+    static int offset = 0;
+
+    std::cout << "# safe param range testing" << std::endl
+         << "plot [t=0.0:1.0] ";
+
+    // clip safe ranges off c1
+    Bezier c1_part1;
+    Bezier c1_part2;
+    Bezier c1_part3;
+
+    // subdivide at t1_c1
+    Impl_deCasteljauAt( c1_part1, c1_part2, c1, t1_c1 );
+    // subdivide at t2_c1
+    Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, t2_c1 );
+
+    // output remaining segment (c1_part1)
+
+    std::cout << "bez("
+         << c1.p0.x+offset << ","
+         << c1.p1.x+offset << ","
+         << c1.p2.x+offset << ","
+         << c1.p3.x+offset << ",t),bez("
+         << c1.p0.y << ","
+         << c1.p1.y << ","
+         << c1.p2.y << ","
+         << c1.p3.y << ",t), bez("
+         << c2.p0.x+offset << ","
+         << c2.p1.x+offset << ","
+         << c2.p2.x+offset << ","
+         << c2.p3.x+offset << ",t),bez("
+         << c2.p0.y << ","
+         << c2.p1.y << ","
+         << c2.p2.y << ","
+         << c2.p3.y << ",t), "
+#if 1
+         << "bez("
+         << c1_part1.p0.x+offset << ","
+         << c1_part1.p1.x+offset << ","
+         << c1_part1.p2.x+offset << ","
+         << c1_part1.p3.x+offset << ",t),bez("
+         << c1_part1.p0.y << ","
+         << c1_part1.p1.y << ","
+         << c1_part1.p2.y << ","
+         << c1_part1.p3.y << ",t), "
+#endif
+#if 1
+         << "bez("
+         << c2_part.p0.x+offset << ","
+         << c2_part.p1.x+offset << ","
+         << c2_part.p2.x+offset << ","
+         << c2_part.p3.x+offset << ",t),bez("
+         << c2_part.p0.y << ","
+         << c2_part.p1.y << ","
+         << c2_part.p2.y << ","
+         << c2_part.p3.y << ",t), "
+#endif
+         << "linex("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c << ",t)+" << offset << ", liney("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c << ",t) title \"fat line (center)\", linex("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c-bounds_c2.dMin << ",t)+" << offset << ", liney("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c-bounds_c2.dMin << ",t) title \"fat line (min) \", linex("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c-bounds_c2.dMax << ",t)+" << offset << ", liney("
+         << bounds_c2.a << ","
+         << bounds_c2.b << ","
+         << bounds_c2.c-bounds_c2.dMax << ",t) title \"fat line (max) \"" << std::endl;
+
+    offset += 1;
+}
+
+void printResultWithFinalCurves( const Bezier& c1, const Bezier& c1_part,
+                                 const Bezier& c2, const Bezier& c2_part,
+                                 double t1_c1, double t2_c1 )
+{
+    static int offset = 0;
+
+    std::cout << "# final result" << std::endl
+         << "plot [t=0.0:1.0] ";
+
+    std::cout << "bez("
+         << c1.p0.x+offset << ","
+         << c1.p1.x+offset << ","
+         << c1.p2.x+offset << ","
+         << c1.p3.x+offset << ",t),bez("
+         << c1.p0.y << ","
+         << c1.p1.y << ","
+         << c1.p2.y << ","
+         << c1.p3.y << ",t), bez("
+         << c1_part.p0.x+offset << ","
+         << c1_part.p1.x+offset << ","
+         << c1_part.p2.x+offset << ","
+         << c1_part.p3.x+offset << ",t),bez("
+         << c1_part.p0.y << ","
+         << c1_part.p1.y << ","
+         << c1_part.p2.y << ","
+         << c1_part.p3.y << ",t), "
+         << " pointmarkx(bez("
+         << c1.p0.x+offset << ","
+         << c1.p1.x+offset << ","
+         << c1.p2.x+offset << ","
+         << c1.p3.x+offset << ","
+         << t1_c1 << "),t), "
+         << " pointmarky(bez("
+         << c1.p0.y << ","
+         << c1.p1.y << ","
+         << c1.p2.y << ","
+         << c1.p3.y << ","
+         << t1_c1 << "),t), "
+         << " pointmarkx(bez("
+         << c1.p0.x+offset << ","
+         << c1.p1.x+offset << ","
+         << c1.p2.x+offset << ","
+         << c1.p3.x+offset << ","
+         << t2_c1 << "),t), "
+         << " pointmarky(bez("
+         << c1.p0.y << ","
+         << c1.p1.y << ","
+         << c1.p2.y << ","
+         << c1.p3.y << ","
+         << t2_c1 << "),t), "
+
+         << "bez("
+         << c2.p0.x+offset << ","
+         << c2.p1.x+offset << ","
+         << c2.p2.x+offset << ","
+         << c2.p3.x+offset << ",t),bez("
+         << c2.p0.y << ","
+         << c2.p1.y << ","
+         << c2.p2.y << ","
+         << c2.p3.y << ",t), "
+         << "bez("
+         << c2_part.p0.x+offset << ","
+         << c2_part.p1.x+offset << ","
+         << c2_part.p2.x+offset << ","
+         << c2_part.p3.x+offset << ",t),bez("
+         << c2_part.p0.y << ","
+         << c2_part.p1.y << ","
+         << c2_part.p2.y << ","
+         << c2_part.p3.y << ",t)" << std::endl;
+
+    offset += 1;
+}
+
+/** determine parameter ranges [0,t1) and (t2,1] on c1, where c1 is guaranteed to lie outside c2.
+      Returns false, if the two curves don't even intersect.
+
+    @param t1
+    Range [0,t1) on c1 is guaranteed to lie outside c2
+
+    @param t2
+    Range (t2,1] on c1 is guaranteed to lie outside c2
+
+    @param c1_orig
+    Original curve c1
+
+    @param c1_part
+    Subdivided current part of c1
+
+    @param c2_orig
+    Original curve c2
+
+    @param c2_part
+    Subdivided current part of c2
+ */
+bool Impl_calcClipRange( double&        t1,
+                         double&        t2,
+                         const Bezier&  c1_orig,
+                         const Bezier&  c1_part,
+                         const Bezier&  c2_orig,
+                         const Bezier&  c2_part )
+{
+    // TODO: Maybe also check fat line orthogonal to P0P3, having P0
+    //       and P3 as the extremal points
+
+    if( Impl_doBBoxIntersect(c1_part, c2_part) )
+    {
+        // Calculate fat lines around c1
+        FatLine bounds_c2;
+
+        // must use the subdivided version of c2, since the fat line
+        // algorithm works implicitly with the convex hull bounding
+        // box.
+        Impl_calcFatLine(bounds_c2, c2_part);
+
+        // determine clip positions on c2. Can use original c1 (which
+        // is necessary anyway, to get the t's on the original curve),
+        // since the distance calculations work directly in the
+        // Bernstein polynomial parameter domain.
+        if( Impl_calcSafeParams_clip( t1, t2, bounds_c2,
+                                      calcLineDistance( bounds_c2.a,
+                                                        bounds_c2.b,
+                                                        bounds_c2.c,
+                                                        c1_orig.p0.x,
+                                                        c1_orig.p0.y    ),
+                                      calcLineDistance( bounds_c2.a,
+                                                        bounds_c2.b,
+                                                        bounds_c2.c,
+                                                        c1_orig.p1.x,
+                                                        c1_orig.p1.y    ),
+                                      calcLineDistance( bounds_c2.a,
+                                                        bounds_c2.b,
+                                                        bounds_c2.c,
+                                                        c1_orig.p2.x,
+                                                        c1_orig.p2.y    ),
+                                      calcLineDistance( bounds_c2.a,
+                                                        bounds_c2.b,
+                                                        bounds_c2.c,
+                                                        c1_orig.p3.x,
+                                                        c1_orig.p3.y    ) ) )
+        {
+            //printCurvesWithSafeRange(c1_orig, c2_orig, t1, t2, c2_part, bounds_c2);
+
+            // they do intersect
+            return true;
+        }
+    }
+
+    // they don't intersect: nothing to do
+    return false;
+}
+
+/* Tangent intersection part
+ * =========================
+ */
+
+void Impl_calcFocus( Bezier& res, const Bezier& c )
+{
+    // arbitrary small value, for now
+    // TODO: find meaningful value
+    const double minPivotValue( 1.0e-20 );
+
+    Point2D::value_type fMatrix[6];
+    Point2D::value_type fRes[2];
+
+    // calc new curve from hodograph, c and linear blend
+
+    // Coefficients for derivative of c are (C_i=n(C_{i+1} - C_i)):
+
+    // 3(P1 - P0), 3(P2 - P1), 3(P3 - P2) (bezier curve of degree 2)
+
+    // The hodograph is then (bezier curve of 2nd degree is P0(1-t)^2 + 2P1(1-t)t + P2t^2):
+
+    // 3(P1 - P0)(1-t)^2 + 6(P2 - P1)(1-t)t + 3(P3 - P2)t^2
+
+    // rotate by 90 degrees: x=-y, y=x and you get the normal vector function N(t):
+
+    // x(t) = -(3(P1.y - P0.y)(1-t)^2 + 6(P2.y - P1.y)(1-t)t + 3(P3.y - P2.y)t^2)
+    // y(t) =   3(P1.x - P0.x)(1-t)^2 + 6(P2.x - P1.x)(1-t)t + 3(P3.x - P2.x)t^2
+
+    // Now, the focus curve is defined to be F(t)=P(t) + c(t)N(t),
+    // where P(t) is the original curve, and c(t)=c0(1-t) + c1 t
+
+    // This results in the following expression for F(t):
+
+    // x(t) =  P0.x (1-t)^3 + 3 P1.x (1-t)^2t + 3 P2.x (1.t)t^2 + P3.x t^3 -
+    //          (c0(1-t) + c1 t)(3(P1.y - P0.y)(1-t)^2 + 6(P2.y - P1.y)(1-t)t + 3(P3.y - P2.y)t^2)
+
+    // y(t) =  P0.y (1-t)^3 + 3 P1.y (1-t)^2t + 3 P2.y (1.t)t^2 + P3.y t^3 +
+    //          (c0(1-t) + c1 t)(3(P1.x - P0.x)(1-t)^2 + 6(P2.x - P1.x)(1-t)t + 3(P3.x - P2.x)t^2)
+
+    // As a heuristic, we set F(0)=F(1) (thus, the curve is closed and _tends_ to be small):
+
+    // For F(0), the following results:
+
+    // x(0) = P0.x - c0 3(P1.y - P0.y)
+    // y(0) = P0.y + c0 3(P1.x - P0.x)
+
+    // For F(1), the following results:
+
+    // x(1) = P3.x - c1 3(P3.y - P2.y)
+    // y(1) = P3.y + c1 3(P3.x - P2.x)
+
+    // Reorder, collect and substitute into F(0)=F(1):
+
+    // P0.x - c0 3(P1.y - P0.y) = P3.x - c1 3(P3.y - P2.y)
+    // P0.y + c0 3(P1.x - P0.x) = P3.y + c1 3(P3.x - P2.x)
+
+    // which yields
+
+    // (P0.y - P1.y)c0 + (P3.y - P2.y)c1 = (P3.x - P0.x)/3
+    // (P1.x - P0.x)c0 + (P2.x - P3.x)c1 = (P3.y - P0.y)/3
+
+    // so, this is what we calculate here (determine c0 and c1):
+    fMatrix[0] = c.p1.x - c.p0.x;
+    fMatrix[1] = c.p2.x - c.p3.x;
+    fMatrix[2] = (c.p3.y - c.p0.y)/3.0;
+    fMatrix[3] = c.p0.y - c.p1.y;
+    fMatrix[4] = c.p3.y - c.p2.y;
+    fMatrix[5] = (c.p3.x - c.p0.x)/3.0;
+
+    // TODO: determine meaningful value for
+    if( !solve(fMatrix, 2, 3, fRes, minPivotValue) )
+    {
+        // TODO: generate meaningful values here
+        // singular or nearly singular system -- use arbitrary
+        // values for res
+        fRes[0] = 0.0;
+        fRes[1] = 1.0;
+
+        std::cerr << "Matrix singular!" << std::endl;
+    }
+
+    // now, the reordered and per-coefficient collected focus curve is
+    // the following third degree bezier curve F(t):
+
+    // x(t) =  P0.x (1-t)^3 + 3 P1.x (1-t)^2t + 3 P2.x (1.t)t^2 + P3.x t^3 -
+    //          (c0(1-t) + c1 t)(3(P1.y - P0.y)(1-t)^2 + 6(P2.y - P1.y)(1-t)t + 3(P3.y - P2.y)t^2)
+    //      =  P0.x (1-t)^3 + 3 P1.x (1-t)^2t + 3 P2.x (1.t)t^2 + P3.x t^3 -
+    //         (3c0P1.y(1-t)^3 - 3c0P0.y(1-t)^3 + 6c0P2.y(1-t)^2t - 6c0P1.y(1-t)^2t +
+    //          3c0P3.y(1-t)t^2 - 3c0P2.y(1-t)t^2 +
+    //          3c1P1.y(1-t)^2t - 3c1P0.y(1-t)^2t + 6c1P2.y(1-t)t^2 - 6c1P1.y(1-t)t^2 +
+    //          3c1P3.yt^3 - 3c1P2.yt^3)
+    //      =  (P0.x - 3 c0 P1.y + 3 c0 P0.y)(1-t)^3 +
+    //         3(P1.x - c1 P1.y + c1 P0.y - 2 c0 P2.y + 2 c0 P1.y)(1-t)^2t +
+    //         3(P2.x - 2 c1 P2.y + 2 c1 P1.y - c0 P3.y + c0 P2.y)(1-t)t^2 +
+    //         (P3.x - 3 c1 P3.y + 3 c1 P2.y)t^3
+    //      =  (P0.x - 3 c0(P1.y - P0.y))(1-t)^3 +
+    //         3(P1.x - c1(P1.y - P0.y) - 2c0(P2.y - P1.y))(1-t)^2t +
+    //         3(P2.x - 2 c1(P2.y - P1.y) - c0(P3.y - P2.y))(1-t)t^2 +
+    //         (P3.x - 3 c1(P3.y - P2.y))t^3
+
+    // y(t) =  P0.y (1-t)^3 + 3 P1.y (1-t)^2t + 3 P2.y (1-t)t^2 + P3.y t^3 +
+    //          (c0(1-t) + c1 t)(3(P1.x - P0.x)(1-t)^2 + 6(P2.x - P1.x)(1-t)t + 3(P3.x - P2.x)t^2)
+    //      =  P0.y (1-t)^3 + 3 P1.y (1-t)^2t + 3 P2.y (1-t)t^2 + P3.y t^3 +
+    //         3c0(P1.x - P0.x)(1-t)^3 + 6c0(P2.x - P1.x)(1-t)^2t + 3c0(P3.x - P2.x)(1-t)t^2 +
+    //         3c1(P1.x - P0.x)(1-t)^2t + 6c1(P2.x - P1.x)(1-t)t^2 + 3c1(P3.x - P2.x)t^3
+    //      =  (P0.y + 3 c0 (P1.x - P0.x))(1-t)^3 +
+    //         3(P1.y + 2 c0 (P2.x - P1.x) + c1 (P1.x - P0.x))(1-t)^2t +
+    //         3(P2.y + c0 (P3.x - P2.x) + 2 c1 (P2.x - P1.x))(1-t)t^2 +
+    //         (P3.y + 3 c1 (P3.x - P2.x))t^3
+
+    // Therefore, the coefficients F0 to F3 of the focus curve are:
+
+    // F0.x = (P0.x - 3 c0(P1.y - P0.y))                    F0.y = (P0.y + 3 c0 (P1.x - P0.x))
+    // F1.x = (P1.x - c1(P1.y - P0.y) - 2c0(P2.y - P1.y))   F1.y = (P1.y + 2 c0 (P2.x - P1.x) + c1 (P1.x - P0.x))
+    // F2.x = (P2.x - 2 c1(P2.y - P1.y) - c0(P3.y - P2.y))  F2.y = (P2.y + c0 (P3.x - P2.x) + 2 c1 (P2.x - P1.x))
+    // F3.x = (P3.x - 3 c1(P3.y - P2.y))                    F3.y = (P3.y + 3 c1 (P3.x - P2.x))
+
+    res.p0.x = c.p0.x - 3*fRes[0]*(c.p1.y - c.p0.y);
+    res.p1.x = c.p1.x - fRes[1]*(c.p1.y - c.p0.y) - 2*fRes[0]*(c.p2.y - c.p1.y);
+    res.p2.x = c.p2.x - 2*fRes[1]*(c.p2.y - c.p1.y) - fRes[0]*(c.p3.y - c.p2.y);
+    res.p3.x = c.p3.x - 3*fRes[1]*(c.p3.y - c.p2.y);
+
+    res.p0.y = c.p0.y + 3*fRes[0]*(c.p1.x - c.p0.x);
+    res.p1.y = c.p1.y + 2*fRes[0]*(c.p2.x - c.p1.x) + fRes[1]*(c.p1.x - c.p0.x);
+    res.p2.y = c.p2.y + fRes[0]*(c.p3.x - c.p2.x) + 2*fRes[1]*(c.p2.x - c.p1.x);
+    res.p3.y = c.p3.y + 3*fRes[1]*(c.p3.x - c.p2.x);
+}
+
+bool Impl_calcSafeParams_focus( double&         t1,
+                                double&         t2,
+                                const Bezier&   curve,
+                                const Bezier&   focus )
+{
+    // now, we want to determine which normals of the original curve
+    // P(t) intersect with the focus curve F(t). The condition for
+    // this statement is P'(t)(P(t) - F) = 0, i.e. hodograph P'(t) and
+    // line through P(t) and F are perpendicular.
+    // If you expand this equation, you end up with something like
+
+    // (\sum_{i=0}^n (P_i - F)B_i^n(t))^T (\sum_{j=0}^{n-1} n(P_{j+1} - P_j)B_j^{n-1}(t))
+
+    // Multiplying that out (as the scalar product is linear, we can
+    // extract some terms) yields:
+
+    // (P_i - F)^T n(P_{j+1} - P_j) B_i^n(t)B_j^{n-1}(t) + ...
+
+    // If we combine the B_i^n(t)B_j^{n-1}(t) product, we arrive at a
+    // Bernstein polynomial of degree 2n-1, as
+
+    // \binom{n}{i}(1-t)^{n-i}t^i) \binom{n-1}{j}(1-t)^{n-1-j}t^j) =
+    // \binom{n}{i}\binom{n-1}{j}(1-t)^{2n-1-i-j}t^{i+j}
+
+    // Thus, with the defining equation for a 2n-1 degree Bernstein
+    // polynomial
+
+    // \sum_{i=0}^{2n-1} d_i B_i^{2n-1}(t)
+
+    // the d_i are calculated as follows:
+
+    // d_i = \sum_{j+k=i, j\in\{0,...,n\}, k\in\{0,...,n-1\}} \frac{\binom{n}{j}\binom{n-1}{k}}{\binom{2n-1}{i}} n (P_{k+1} - P_k)^T(P_j - F)
+
+    // Okay, but F is now not a single point, but itself a curve
+    // F(u). Thus, for every value of u, we get a different 2n-1
+    // bezier curve from the above equation. Therefore, we have a
+    // tensor product bezier patch, with the following defining
+    // equation:
+
+    // d(t,u) = \sum_{i=0}^{2n-1} \sum_{j=0}^m B_i^{2n-1}(t) B_j^{m}(u) d_{ij}, where
+    // d_{ij} = \sum_{k+l=i, l\in\{0,...,n\}, k\in\{0,...,n-1\}} \frac{\binom{n}{l}\binom{n-1}{k}}{\binom{2n-1}{i}} n (P_{k+1} - P_k)^T(P_l - F_j)
+
+    // as above, only that now F is one of the focus' control points.
+
+    // Note the difference in the binomial coefficients to the
+    // reference paper, these formulas most probably contained a typo.
+
+    // To determine, where D(t,u) is _not_ zero (these are the parts
+    // of the curve that don't share normals with the focus and can
+    // thus be safely clipped away), we project D(u,t) onto the
+    // (d(t,u), t) plane, determine the convex hull there and proceed
+    // as for the curve intersection part (projection is orthogonal to
+    // u axis, thus simply throw away u coordinate).
+
+    // \fallfac are so-called falling factorials (see Concrete
+    // Mathematics, p. 47 for a definition).
+
+    // now, for tensor product bezier curves, the convex hull property
+    // holds, too. Thus, we simply project the control points (t_{ij},
+    // u_{ij}, d_{ij}) onto the (t,d) plane and calculate the
+    // intersections of the convex hull with the t axis, as for the
+    // bezier clipping case.
+
+    // calc polygon of control points (t_{ij}, d_{ij}):
+
+    const int n( 3 ); // cubic bezier curves, as a matter of fact
+    const int i_card( 2*n );
+    const int j_card( n + 1 );
+    const int k_max( n-1 );
+    Polygon2D controlPolygon( i_card*j_card ); // vector of (t_{ij}, d_{ij}) in row-major order
+
+    int i, j, k, l; // variable notation from formulas above and Sederberg article
+    Point2D::value_type d;
+    for( i=0; i<i_card; ++i )
+    {
+        for( j=0; j<j_card; ++j )
+        {
+            // calc single d_{ij} sum:
+            for( d=0.0, k=std::max(0,i-n); k<=k_max && k<=i; ++k )
+            {
+                l = i - k; // invariant: k + l = i
+                assert(k>=0 && k<=n-1); // k \in {0,...,n-1}
+                assert(l>=0 && l<=n);   // l \in {0,...,n}
+
+                // TODO: find, document and assert proper limits for n and int's max_val.
+                // This becomes important should anybody wants to use
+                // this code for higher-than-cubic beziers
+                d += static_cast<double>(fallFac(n,l)*fallFac(n-1,k)*fac(i)) /
+                    static_cast<double>(fac(l)*fac(k) * fallFac(2*n-1,i)) * n *
+                    ( (curve[k+1].x - curve[k].x)*(curve[l].x - focus[j].x) +   // dot product here
+                      (curve[k+1].y - curve[k].y)*(curve[l].y - focus[j].y) );
+            }
+
+            // Note that the t_{ij} values are evenly spaced on the
+            // [0,1] interval, thus t_{ij}=i/(2n-1)
+            controlPolygon[ i*j_card + j ] = Point2D( i/(2.0*n-1.0), d );
+        }
+    }
+
+#ifndef WITH_SAFEFOCUSPARAM_DETAILED_TEST
+
+    // calc safe parameter range, to determine [0,t1] and [t2,1] where
+    // no zero crossing is guaranteed.
+    return Impl_calcSafeParams( t1, t2, controlPolygon, 0.0, 0.0 );
+
+#else
+    bool bRet( Impl_calcSafeParams( t1, t2, controlPolygon, 0.0, 0.0 ) );
+
+    Polygon2D convHull( convexHull( controlPolygon ) );
+
+    std::cout << "# convex hull testing (focus)" << std::endl
+         << "plot [t=0:1] ";
+    std::cout << "'-' using ($1):($2) title \"control polygon\" with lp, "
+         << "'-' using ($1):($2) title \"convex hull\" with lp" << std::endl;
+
+    unsigned int count;
+    for( count=0; count<controlPolygon.size(); ++count )
+    {
+        std::cout << controlPolygon[count].x << " " << controlPolygon[count].y << std::endl;
+    }
+    std::cout << controlPolygon[0].x << " " << controlPolygon[0].y << std::endl;
+    std::cout << "e" << std::endl;
+
+    for( count=0; count<convHull.size(); ++count )
+    {
+        std::cout << convHull[count].x << " " << convHull[count].y << std::endl;
+    }
+    std::cout << convHull[0].x << " " << convHull[0].y << std::endl;
+    std::cout << "e" << std::endl;
+
+    return bRet;
+#endif
+}
+
+/** Calc all values t_i on c1, for which safeRanges functor does not
+    give a safe range on c1 and c2.
+
+    This method is the workhorse of the bezier clipping. Because c1
+    and c2 must be alternatingly tested against each other (first
+    determine safe parameter interval on c1 with regard to c2, then
+    the other way around), we call this method recursively with c1 and
+    c2 swapped.
+
+    @param result
+    Output iterator where the final t values are added to. If curves
+    don't intersect, nothing is added.
+
+    @param delta
+    Maximal allowed distance to true critical point (measured in the
+    original curve's coordinate system)
+
+    @param safeRangeFunctor
+    Functor object, that must provide the following operator():
+    bool safeRangeFunctor( double& t1,
+                           double& t2,
+                           const Bezier& c1_orig,
+                           const Bezier& c1_part,
+                           const Bezier& c2_orig,
+                           const Bezier& c2_part );
+    This functor must calculate the safe ranges [0,t1] and [t2,1] on
+    c1_orig, where c1_orig is 'safe' from c2_part. If the whole
+    c1_orig is safe, false must be returned, true otherwise.
+ */
+template <class Functor> void Impl_applySafeRanges_rec( std::back_insert_iterator< std::vector< std::pair<double, double> > >&    result,
+                                                        double                                                                          delta,
+                                                        const Functor&                                                                  safeRangeFunctor,
+                                                        int                                                                             recursionLevel,
+                                                        const Bezier&                                                                   c1_orig,
+                                                        const Bezier&                                                                   c1_part,
+                                                        double                                                                          last_t1_c1,
+                                                        double                                                                          last_t2_c1,
+                                                        const Bezier&                                                                   c2_orig,
+                                                        const Bezier&                                                                   c2_part,
+                                                        double                                                                          last_t1_c2,
+                                                        double                                                                          last_t2_c2  )
+{
+    // check end condition
+    // ===================
+
+    // TODO: tidy up recursion handling. maybe put everything in a
+    // struct and swap that here at method entry
+
+    // TODO: Implement limit on recursion depth. Should that limit be
+    // reached, chances are that we're on a higher-order tangency. For
+    // this case, AW proposed to take the middle of the current
+    // interval, and to correct both curve's tangents at that new
+    // endpoint to be equal. That virtually generates a first-order
+    // tangency, and justifies to return a single intersection
+    // point. Otherwise, inside/outside test might fail here.
+
+    for( int i=0; i<recursionLevel; ++i ) std::cerr << " ";
+    if( recursionLevel % 2 )
+    {
+        std::cerr << std::endl << "level: " << recursionLevel
+             << " t: "
+             << last_t1_c2 + (last_t2_c2 - last_t1_c2)/2.0
+             << ", c1: " << last_t1_c2 << " " << last_t2_c2
+             << ", c2: " << last_t1_c1 << " " << last_t2_c1
+             << std::endl;
+    }
+    else
+    {
+        std::cerr << std::endl << "level: " << recursionLevel
+             << " t: "
+             << last_t1_c1 + (last_t2_c1 - last_t1_c1)/2.0
+             << ", c1: " << last_t1_c1 << " " << last_t2_c1
+             << ", c2: " << last_t1_c2 << " " << last_t2_c2
+             << std::endl;
+    }
+
+    // refine solution
+    // ===============
+
+    double t1_c1, t2_c1;
+
+    // Note: we first perform the clipping and only test for precision
+    // sufficiency afterwards, since we want to exploit the fact that
+    // Impl_calcClipRange returns false if the curves don't
+    // intersect. We would have to check that separately for the end
+    // condition, otherwise.
+
+    // determine safe range on c1_orig
+    if( safeRangeFunctor( t1_c1, t2_c1, c1_orig, c1_part, c2_orig, c2_part ) )
+    {
+        // now, t1 and t2 are calculated on the original curve
+        // (but against a fat line calculated from the subdivided
+        // c2, namely c2_part). If the [t1,t2] range is outside
+        // our current [last_t1,last_t2] range, we're done in this
+        // branch - the curves no longer intersect.
+        if( tolLessEqual(t1_c1, last_t2_c1) && tolGreaterEqual(t2_c1, last_t1_c1) )
+        {
+            // As noted above, t1 and t2 are calculated on the
+            // original curve, but against a fat line
+            // calculated from the subdivided c2, namely
+            // c2_part. Our domain to work on is
+            // [last_t1,last_t2], on the other hand, so values
+            // of [t1,t2] outside that range are irrelevant
+            // here. Clip range appropriately.
+            t1_c1 = std::max(t1_c1, last_t1_c1);
+            t2_c1 = std::min(t2_c1, last_t2_c1);
+
+            // TODO: respect delta
+            // for now, end condition is just a fixed threshold on the t's
+
+            // check end condition
+            // ===================
+
+#if 1
+            if( fabs(last_t2_c1 - last_t1_c1) < 0.0001 &&
+                fabs(last_t2_c2 - last_t1_c2) < 0.0001  )
+#else
+            if( fabs(last_t2_c1 - last_t1_c1) < 0.01 &&
+                fabs(last_t2_c2 - last_t1_c2) < 0.01    )
+#endif
+            {
+                // done. Add to result
+                if( recursionLevel % 2 )
+                {
+                    // uneven level: have to swap the t's, since curves are swapped, too
+                    *result++ = std::make_pair( last_t1_c2 + (last_t2_c2 - last_t1_c2)/2.0,
+                                                  last_t1_c1 + (last_t2_c1 - last_t1_c1)/2.0 );
+                }
+                else
+                {
+                    *result++ = std::make_pair( last_t1_c1 + (last_t2_c1 - last_t1_c1)/2.0,
+                                                  last_t1_c2 + (last_t2_c2 - last_t1_c2)/2.0 );
+                }
+
+#if 0
+                //printResultWithFinalCurves( c1_orig, c1_part, c2_orig, c2_part, last_t1_c1, last_t2_c1 );
+                printResultWithFinalCurves( c1_orig, c1_part, c2_orig, c2_part, t1_c1, t2_c1 );
+#else
+                // calc focus curve of c2
+                Bezier focus;
+                Impl_calcFocus(focus, c2_part); // need to use subdivided c2
+
+                safeRangeFunctor( t1_c1, t2_c1, c1_orig, c1_part, c2_orig, c2_part );
+
+                //printResultWithFinalCurves( c1_orig, c1_part, c2_orig, focus, t1_c1, t2_c1 );
+                printResultWithFinalCurves( c1_orig, c1_part, c2_orig, focus, last_t1_c1, last_t2_c1 );
+#endif
+            }
+            else
+            {
+                // heuristic: if parameter range is not reduced by at least
+                // 20%, subdivide longest curve, and clip shortest against
+                // both parts of longest
+//                if( (last_t2_c1 - last_t1_c1 - t2_c1 + t1_c1) / (last_t2_c1 - last_t1_c1) < 0.2 )
+                if( false )
+                {
+                    // subdivide and descend
+                    // =====================
+
+                    Bezier part1;
+                    Bezier part2;
+
+                    double intervalMiddle;
+
+                    if( last_t2_c1 - last_t1_c1 > last_t2_c2 - last_t1_c2 )
+                    {
+                        // subdivide c1
+                        // ============
+
+                        intervalMiddle = last_t1_c1 + (last_t2_c1 - last_t1_c1)/2.0;
+
+                        // subdivide at the middle of the interval (as
+                        // we're not subdividing on the original
+                        // curve, this simply amounts to subdivision
+                        // at 0.5)
+                        Impl_deCasteljauAt( part1, part2, c1_part, 0.5 );
+
+                        // and descend recursively with swapped curves
+                        Impl_applySafeRanges_rec( result, delta, safeRangeFunctor, recursionLevel+1,
+                                                  c2_orig, c2_part, last_t1_c2, last_t2_c2,
+                                                  c1_orig, part1, last_t1_c1, intervalMiddle );
+
+                        Impl_applySafeRanges_rec( result, delta, safeRangeFunctor, recursionLevel+1,
+                                                  c2_orig, c2_part, last_t1_c2, last_t2_c2,
+                                                  c1_orig, part2, intervalMiddle, last_t2_c1 );
+                    }
+                    else
+                    {
+                        // subdivide c2
+                        // ============
+
+                        intervalMiddle = last_t1_c2 + (last_t2_c2 - last_t1_c2)/2.0;
+
+                        // subdivide at the middle of the interval (as
+                        // we're not subdividing on the original
+                        // curve, this simply amounts to subdivision
+                        // at 0.5)
+                        Impl_deCasteljauAt( part1, part2, c2_part, 0.5 );
+
+                        // and descend recursively with swapped curves
+                        Impl_applySafeRanges_rec( result, delta, safeRangeFunctor, recursionLevel+1,
+                                                  c2_orig, part1, last_t1_c2, intervalMiddle,
+                                                  c1_orig, c1_part, last_t1_c1, last_t2_c1 );
+
+                        Impl_applySafeRanges_rec( result, delta, safeRangeFunctor, recursionLevel+1,
+                                                  c2_orig, part2, intervalMiddle, last_t2_c2,
+                                                  c1_orig, c1_part, last_t1_c1, last_t2_c1 );
+                    }
+                }
+                else
+                {
+                    // apply calculated clip
+                    // =====================
+
+                    // clip safe ranges off c1_orig
+                    Bezier c1_part1;
+                    Bezier c1_part2;
+                    Bezier c1_part3;
+
+                    // subdivide at t1_c1
+                    Impl_deCasteljauAt( c1_part1, c1_part2, c1_orig, t1_c1 );
+
+                    // subdivide at t2_c1. As we're working on
+                    // c1_part2 now, we have to adapt t2_c1 since
+                    // we're no longer in the original parameter
+                    // interval. This is based on the following
+                    // assumption: t2_new = (t2-t1)/(1-t1), which
+                    // relates the t2 value into the new parameter
+                    // range [0,1] of c1_part2.
+                    Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, (t2_c1-t1_c1)/(1.0-t1_c1) );
+
+                    // descend with swapped curves and c1_part1 as the
+                    // remaining (middle) segment
+                    Impl_applySafeRanges_rec( result, delta, safeRangeFunctor, recursionLevel+1,
+                                              c2_orig, c2_part, last_t1_c2, last_t2_c2,
+                                              c1_orig, c1_part1, t1_c1, t2_c1 );
+                }
+            }
+        }
+    }
+}
+
+struct ClipBezierFunctor
+{
+    bool operator()( double& t1_c1,
+                     double& t2_c1,
+                     const Bezier& c1_orig,
+                     const Bezier& c1_part,
+                     const Bezier& c2_orig,
+                     const Bezier& c2_part ) const
+    {
+        return Impl_calcClipRange( t1_c1, t2_c1, c1_orig, c1_part, c2_orig, c2_part );
+    }
+};
+
+struct BezierTangencyFunctor
+{
+    bool operator()( double& t1_c1,
+                     double& t2_c1,
+                     const Bezier& c1_orig,
+                     const Bezier& c1_part,
+                     const Bezier& c2_orig,
+                     const Bezier& c2_part ) const
+    {
+        // calc focus curve of c2
+        Bezier focus;
+        Impl_calcFocus(focus, c2_part); // need to use subdivided c2
+                                        // here, as the whole curve is
+                                        // used for focus calculation
+
+        // determine safe range on c1_orig
+        bool bRet( Impl_calcSafeParams_focus( t1_c1, t2_c1,
+                                              c1_orig, // use orig curve here, need t's on original curve
+                                              focus ) );
+
+        std::cerr << "range: " << t2_c1 - t1_c1 << ", ret: " << bRet << std::endl;
+
+        return bRet;
+    }
+};
+
+/** Perform a bezier clip (curve against curve)
+
+    @param result
+    Output iterator where the final t values are added to. This
+    iterator will remain empty, if there are no intersections.
+
+    @param delta
+    Maximal allowed distance to true intersection (measured in the
+    original curve's coordinate system)
+ */
+void clipBezier( std::back_insert_iterator< std::vector< std::pair<double, double> > >&   result,
+                 double                                                                         delta,
+                 const Bezier&                                                                  c1,
+                 const Bezier&                                                                  c2        )
+{
+#if 0
+    // first of all, determine list of collinear normals. Collinear
+    // normals typically separate two intersections, thus, subdivide
+    // at all collinear normal's t values beforehand. This will cater
+    // for tangent intersections, where two or more intersections are
+    // infinitesimally close together.
+
+    // TODO: evaluate effects of higher-than-second-order
+    // tangencies. Sederberg et al. state that collinear normal
+    // algorithm then degrades quickly.
+
+    std::vector< std::pair<double,double> > results;
+    std::back_insert_iterator< std::vector< std::pair<double, double> > > ii(results);
+
+    Impl_calcCollinearNormals( ii, delta, 0, c1, c1, 0.0, 1.0, c2, c2, 0.0, 1.0 );
+
+    // As Sederberg's collinear normal theorem is only sufficient, not
+    // necessary for two intersections left and right, we've to test
+    // all segments generated by the collinear normal algorithm
+    // against each other. In other words, if the two curves are both
+    // divided in a left and a right part, the collinear normal
+    // theorem does _not_ state that the left part of curve 1 does not
+    // e.g. intersect with the right part of curve 2.
+
+    // divide c1 and c2 at collinear normal intersection points
+    std::vector< Bezier > c1_segments( results.size()+1 );
+    std::vector< Bezier > c2_segments( results.size()+1 );
+    Bezier c1_remainder( c1 );
+    Bezier c2_remainder( c2 );
+    unsigned int i;
+    for( i=0; i<results.size(); ++i )
+    {
+        Bezier c1_part2;
+        Impl_deCasteljauAt( c1_segments[i], c1_part2, c1_remainder, results[i].first );
+        c1_remainder = c1_part2;
+
+        Bezier c2_part2;
+        Impl_deCasteljauAt( c2_segments[i], c2_part2, c2_remainder, results[i].second );
+        c2_remainder = c2_part2;
+    }
+    c1_segments[i] = c1_remainder;
+    c2_segments[i] = c2_remainder;
+
+    // now, c1/c2_segments contain all segments, then
+    // clip every resulting segment against every other
+    unsigned int c1_curr, c2_curr;
+    for( c1_curr=0; c1_curr<c1_segments.size(); ++c1_curr )
+    {
+        for( c2_curr=0; c2_curr<c2_segments.size(); ++c2_curr )
+        {
+            if( c1_curr != c2_curr )
+            {
+                Impl_clipBezier_rec(result, delta, 0,
+                                    c1_segments[c1_curr], c1_segments[c1_curr],
+                                    0.0, 1.0,
+                                    c2_segments[c2_curr], c2_segments[c2_curr],
+                                    0.0, 1.0);
+            }
+        }
+    }
+#else
+    Impl_applySafeRanges_rec( result, delta, BezierTangencyFunctor(), 0, c1, c1, 0.0, 1.0, c2, c2, 0.0, 1.0 );
+    //Impl_applySafeRanges_rec( result, delta, ClipBezierFunctor(), 0, c1, c1, 0.0, 1.0, c2, c2, 0.0, 1.0 );
+#endif
+    // that's it, boys'n'girls!
+}
+
+int main(int argc, const char *argv[])
+{
+    double curr_Offset( 0 );
+    unsigned int i,j,k;
+
+    Bezier someCurves[] =
+        {
+//            {Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0),Point2D(1.0,0.0)},
+//            {Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0),Point2D(1.0,0.5)},
+//            {Point2D(1.0,0.0),Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0)}
+//            {Point2D(0.25+1,0.5),Point2D(0.25+1,0.708333),Point2D(0.423611+1,0.916667),Point2D(0.770833+1,0.980324)},
+//            {Point2D(0.0+1,0.0),Point2D(0.0+1,1.0),Point2D(1.0+1,1.0),Point2D(1.0+1,0.5)}
+
+// tangency1
+//            {Point2D(0.627124+1,0.828427),Point2D(0.763048+1,0.828507),Point2D(0.885547+1,0.77312),Point2D(0.950692+1,0.67325)},
+//            {Point2D(0.0,1.0),Point2D(0.1,1.0),Point2D(0.4,1.0),Point2D(0.5,1.0)}
+
+//            {Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0),Point2D(1.0,0.5)},
+//            {Point2D(0.60114,0.933091),Point2D(0.69461,0.969419),Point2D(0.80676,0.992976),Point2D(0.93756,0.998663)}
+//            {Point2D(1.0,0.0),Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0)},
+//            {Point2D(0.62712,0.828427),Point2D(0.76305,0.828507),Point2D(0.88555,0.77312),Point2D(0.95069,0.67325)}
+
+// clipping1
+//            {Point2D(0.0,0.0),Point2D(0.0,3.5),Point2D(1.0,-2.5),Point2D(1.0,1.0)},
+//            {Point2D(0.0,1.0),Point2D(3.5,1.0),Point2D(-2.5,0.0),Point2D(1.0,0.0)}
+
+// tangency2
+//            {Point2D(0.0,1.0),Point2D(3.5,1.0),Point2D(-2.5,0.0),Point2D(1.0,0.0)},
+//            {Point2D(15.3621,0.00986464),Point2D(15.3683,0.0109389),Point2D(15.3682,0.0109315),Point2D(15.3621,0.00986464)}
+
+// tangency3
+//            {Point2D(1.0,0.0),Point2D(0.0,0.0),Point2D(0.0,1.0),Point2D(1.0,1.0)},
+//            {Point2D(-0.5,0.0),Point2D(0.5,0.0),Point2D(0.5,1.0),Point2D(-0.5,1.0)}
+
+// tangency4
+//            {Point2D(-0.5,0.0),Point2D(0.5,0.0),Point2D(0.5,1.0),Point2D(-0.5,1.0)},
+//            {Point2D(0.26,0.4),Point2D(0.25,0.5),Point2D(0.25,0.5),Point2D(0.26,0.6)}
+
+// tangency5
+//            {Point2D(0.0,0.0),Point2D(0.0,3.5),Point2D(1.0,-2.5),Point2D(1.0,1.0)},
+//            {Point2D(15.3621,0.00986464),Point2D(15.3683,0.0109389),Point2D(15.3682,0.0109315),Point2D(15.3621,0.00986464)}
+
+// tangency6
+//            {Point2D(0.0,0.0),Point2D(0.0,3.5),Point2D(1.0,-2.5),Point2D(1.0,1.0)},
+//            {Point2D(15.3621,10.00986464),Point2D(15.3683,10.0109389),Point2D(15.3682,10.0109315),Point2D(15.3621,10.00986464)}
+
+// tangency7
+//            {Point2D(2.505,0.0),Point2D(2.505+4.915,4.300),Point2D(2.505+3.213,10.019),Point2D(2.505-2.505,10.255)},
+//            {Point2D(15.3621,10.00986464),Point2D(15.3683,10.0109389),Point2D(15.3682,10.0109315),Point2D(15.3621,10.00986464)}
+
+// tangency Sederberg example
+            {Point2D(2.505,0.0),Point2D(2.505+4.915,4.300),Point2D(2.505+3.213,10.019),Point2D(2.505-2.505,10.255)},
+            {Point2D(5.33+9.311,0.0),Point2D(5.33+9.311-13.279,4.205),Point2D(5.33+9.311-10.681,9.119),Point2D(5.33+9.311-2.603,10.254)}
+
+// clipping2
+//            {Point2D(-0.5,0.0),Point2D(0.5,0.0),Point2D(0.5,1.0),Point2D(-0.5,1.0)},
+//            {Point2D(0.2575,0.4),Point2D(0.2475,0.5),Point2D(0.2475,0.5),Point2D(0.2575,0.6)}
+
+//            {Point2D(0.0,0.1),Point2D(0.2,3.5),Point2D(1.0,-2.5),Point2D(1.1,1.2)},
+//            {Point2D(0.0,1.0),Point2D(3.5,0.9),Point2D(-2.5,0.1),Point2D(1.1,0.2)}
+//            {Point2D(0.0,0.1),Point2D(0.2,3.0),Point2D(1.0,-2.0),Point2D(1.1,1.2)},
+//            {Point2D(0.627124+1,0.828427),Point2D(0.763048+1,0.828507),Point2D(0.885547+1,0.77312),Point2D(0.950692+1,0.67325)}
+//            {Point2D(0.0,1.0),Point2D(3.0,0.9),Point2D(-2.0,0.1),Point2D(1.1,0.2)}
+//            {Point2D(0.0,4.0),Point2D(0.1,5.0),Point2D(0.9,5.0),Point2D(1.0,4.0)},
+//            {Point2D(0.0,0.0),Point2D(0.1,0.5),Point2D(0.9,0.5),Point2D(1.0,0.0)},
+//            {Point2D(0.0,0.1),Point2D(0.1,1.5),Point2D(0.9,1.5),Point2D(1.0,0.1)},
+//            {Point2D(0.0,-4.0),Point2D(0.1,-5.0),Point2D(0.9,-5.0),Point2D(1.0,-4.0)}
+        };
+
+    // output gnuplot setup
+    std::cout << "#!/usr/bin/gnuplot -persist" << std::endl
+         << "#" << std::endl
+         << "# automatically generated by bezierclip, don't change!" << std::endl
+         << "#" << std::endl
+         << "set parametric" << std::endl
+         << "bez(p,q,r,s,t) = p*(1-t)**3+q*3*(1-t)**2*t+r*3*(1-t)*t**2+s*t**3" << std::endl
+         << "bezd(p,q,r,s,t) = 3*(q-p)*(1-t)**2+6*(r-q)*(1-t)*t+3*(s-r)*t**2" << std::endl
+         << "pointmarkx(c,t) = c-0.03*t" << std::endl
+         << "pointmarky(c,t) = c+0.03*t" << std::endl
+         << "linex(a,b,c,t) = a*-c + t*-b" << std::endl
+         << "liney(a,b,c,t) = b*-c + t*a" << std::endl << std::endl
+         << "# end of setup" << std::endl << std::endl;
+
+#ifdef WITH_CONVEXHULL_TEST
+    // test convex hull algorithm
+    const double convHull_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# convex hull testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Polygon2D aTestPoly(4);
+        aTestPoly[0] = someCurves[i].p0;
+        aTestPoly[1] = someCurves[i].p1;
+        aTestPoly[2] = someCurves[i].p2;
+        aTestPoly[3] = someCurves[i].p3;
+
+        aTestPoly[0].x += convHull_xOffset;
+        aTestPoly[1].x += convHull_xOffset;
+        aTestPoly[2].x += convHull_xOffset;
+        aTestPoly[3].x += convHull_xOffset;
+
+        std::cout << " bez("
+             << aTestPoly[0].x << ","
+             << aTestPoly[1].x << ","
+             << aTestPoly[2].x << ","
+             << aTestPoly[3].x << ",t),bez("
+             << aTestPoly[0].y << ","
+             << aTestPoly[1].y << ","
+             << aTestPoly[2].y << ","
+             << aTestPoly[3].y << ",t), '-' using ($1):($2) title \"convex hull " << i << "\" with lp";
+
+        if( i+1<sizeof(someCurves)/sizeof(Bezier) )
+            std::cout << ",\\" << std::endl;
+        else
+            std::cout << std::endl;
+    }
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Polygon2D aTestPoly(4);
+        aTestPoly[0] = someCurves[i].p0;
+        aTestPoly[1] = someCurves[i].p1;
+        aTestPoly[2] = someCurves[i].p2;
+        aTestPoly[3] = someCurves[i].p3;
+
+        aTestPoly[0].x += convHull_xOffset;
+        aTestPoly[1].x += convHull_xOffset;
+        aTestPoly[2].x += convHull_xOffset;
+        aTestPoly[3].x += convHull_xOffset;
+
+        Polygon2D convHull( convexHull(aTestPoly) );
+
+        for( k=0; k<convHull.size(); ++k )
+        {
+            std::cout << convHull[k].x << " " << convHull[k].y << std::endl;
+        }
+        std::cout << convHull[0].x << " " << convHull[0].y << std::endl;
+        std::cout << "e" << std::endl;
+    }
+#endif
+
+#ifdef WITH_MULTISUBDIVIDE_TEST
+    // test convex hull algorithm
+    const double multiSubdivide_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# multi subdivide testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Bezier c( someCurves[i] );
+        Bezier c1_part1;
+        Bezier c1_part2;
+        Bezier c1_part3;
+
+        c.p0.x += multiSubdivide_xOffset;
+        c.p1.x += multiSubdivide_xOffset;
+        c.p2.x += multiSubdivide_xOffset;
+        c.p3.x += multiSubdivide_xOffset;
+
+        const double t1( 0.1+i/(3.0*sizeof(someCurves)/sizeof(Bezier)) );
+        const double t2( 0.9-i/(3.0*sizeof(someCurves)/sizeof(Bezier)) );
+
+        // subdivide at t1
+        Impl_deCasteljauAt( c1_part1, c1_part2, c, t1 );
+
+        // subdivide at t2_c1. As we're working on
+        // c1_part2 now, we have to adapt t2_c1 since
+        // we're no longer in the original parameter
+        // interval. This is based on the following
+        // assumption: t2_new = (t2-t1)/(1-t1), which
+        // relates the t2 value into the new parameter
+        // range [0,1] of c1_part2.
+        Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, (t2-t1)/(1.0-t1) );
+
+        // subdivide at t2
+        Impl_deCasteljauAt( c1_part3, c1_part2, c, t2 );
+
+        std::cout << " bez("
+             << c1_part1.p0.x << ","
+             << c1_part1.p1.x << ","
+             << c1_part1.p2.x << ","
+             << c1_part1.p3.x << ",t), bez("
+             << c1_part1.p0.y+0.01 << ","
+             << c1_part1.p1.y+0.01 << ","
+             << c1_part1.p2.y+0.01 << ","
+             << c1_part1.p3.y+0.01 << ",t) title \"middle " << i << "\", "
+             << " bez("
+             << c1_part2.p0.x << ","
+             << c1_part2.p1.x << ","
+             << c1_part2.p2.x << ","
+             << c1_part2.p3.x << ",t), bez("
+             << c1_part2.p0.y << ","
+             << c1_part2.p1.y << ","
+             << c1_part2.p2.y << ","
+             << c1_part2.p3.y << ",t) title \"right " << i << "\", "
+             << " bez("
+             << c1_part3.p0.x << ","
+             << c1_part3.p1.x << ","
+             << c1_part3.p2.x << ","
+             << c1_part3.p3.x << ",t), bez("
+             << c1_part3.p0.y << ","
+             << c1_part3.p1.y << ","
+             << c1_part3.p2.y << ","
+             << c1_part3.p3.y << ",t) title \"left " << i << "\"";
+
+        if( i+1<sizeof(someCurves)/sizeof(Bezier) )
+            std::cout << ",\\" << std::endl;
+        else
+            std::cout << std::endl;
+    }
+#endif
+
+#ifdef WITH_FATLINE_TEST
+    // test fatline algorithm
+    const double fatLine_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# fat line testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Bezier c( someCurves[i] );
+
+        c.p0.x += fatLine_xOffset;
+        c.p1.x += fatLine_xOffset;
+        c.p2.x += fatLine_xOffset;
+        c.p3.x += fatLine_xOffset;
+
+        FatLine line;
+
+        Impl_calcFatLine(line, c);
+
+        std::cout << " bez("
+             << c.p0.x << ","
+             << c.p1.x << ","
+             << c.p2.x << ","
+             << c.p3.x << ",t), bez("
+             << c.p0.y << ","
+             << c.p1.y << ","
+             << c.p2.y << ","
+             << c.p3.y << ",t) title \"bezier " << i << "\", linex("
+             << line.a << ","
+             << line.b << ","
+             << line.c << ",t), liney("
+             << line.a << ","
+             << line.b << ","
+             << line.c << ",t) title \"fat line (center) on " << i << "\", linex("
+             << line.a << ","
+             << line.b << ","
+             << line.c-line.dMin << ",t), liney("
+             << line.a << ","
+             << line.b << ","
+             << line.c-line.dMin << ",t) title \"fat line (min) on " << i << "\", linex("
+             << line.a << ","
+             << line.b << ","
+             << line.c-line.dMax << ",t), liney("
+             << line.a << ","
+             << line.b << ","
+             << line.c-line.dMax << ",t) title \"fat line (max) on " << i << "\"";
+
+        if( i+1<sizeof(someCurves)/sizeof(Bezier) )
+            std::cout << ",\\" << std::endl;
+        else
+            std::cout << std::endl;
+    }
+#endif
+
+#ifdef WITH_CALCFOCUS_TEST
+    // test focus curve algorithm
+    const double focus_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# focus line testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Bezier c( someCurves[i] );
+
+        c.p0.x += focus_xOffset;
+        c.p1.x += focus_xOffset;
+        c.p2.x += focus_xOffset;
+        c.p3.x += focus_xOffset;
+
+        // calc focus curve
+        Bezier focus;
+        Impl_calcFocus(focus, c);
+
+        std::cout << " bez("
+             << c.p0.x << ","
+             << c.p1.x << ","
+             << c.p2.x << ","
+             << c.p3.x << ",t), bez("
+             << c.p0.y << ","
+             << c.p1.y << ","
+             << c.p2.y << ","
+             << c.p3.y << ",t) title \"bezier " << i << "\", bez("
+             << focus.p0.x << ","
+             << focus.p1.x << ","
+             << focus.p2.x << ","
+             << focus.p3.x << ",t), bez("
+             << focus.p0.y << ","
+             << focus.p1.y << ","
+             << focus.p2.y << ","
+             << focus.p3.y << ",t) title \"focus " << i << "\"";
+
+        if( i+1<sizeof(someCurves)/sizeof(Bezier) )
+            std::cout << ",\\" << std::endl;
+        else
+            std::cout << std::endl;
+    }
+#endif
+
+#ifdef WITH_SAFEPARAMBASE_TEST
+    // test safe params base method
+    double safeParamsBase_xOffset( curr_Offset );
+    std::cout << "# safe param base method testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Bezier c( someCurves[i] );
+
+        c.p0.x += safeParamsBase_xOffset;
+        c.p1.x += safeParamsBase_xOffset;
+        c.p2.x += safeParamsBase_xOffset;
+        c.p3.x += safeParamsBase_xOffset;
+
+        Polygon2D poly(4);
+        poly[0] = c.p0;
+        poly[1] = c.p1;
+        poly[2] = c.p2;
+        poly[3] = c.p3;
+
+        double t1, t2;
+
+        bool bRet( Impl_calcSafeParams( t1, t2, poly, 0, 1 ) );
+
+        Polygon2D convHull( convexHull( poly ) );
+
+        std::cout << " bez("
+             << poly[0].x << ","
+             << poly[1].x << ","
+             << poly[2].x << ","
+             << poly[3].x << ",t),bez("
+             << poly[0].y << ","
+             << poly[1].y << ","
+             << poly[2].y << ","
+             << poly[3].y << ",t), "
+             << "t+" << safeParamsBase_xOffset << ", 0, "
+             << "t+" << safeParamsBase_xOffset << ", 1, ";
+        if( bRet )
+        {
+            std::cout << t1+safeParamsBase_xOffset << ", t, "
+                 << t2+safeParamsBase_xOffset << ", t, ";
+        }
+        std::cout << "'-' using ($1):($2) title \"control polygon\" with lp, "
+             << "'-' using ($1):($2) title \"convex hull\" with lp";
+
+        if( i+1<sizeof(someCurves)/sizeof(Bezier) )
+            std::cout << ",\\" << std::endl;
+        else
+            std::cout << std::endl;
+
+        safeParamsBase_xOffset += 2;
+    }
+
+    safeParamsBase_xOffset = curr_Offset;
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        Bezier c( someCurves[i] );
+
+        c.p0.x += safeParamsBase_xOffset;
+        c.p1.x += safeParamsBase_xOffset;
+        c.p2.x += safeParamsBase_xOffset;
+        c.p3.x += safeParamsBase_xOffset;
+
+        Polygon2D poly(4);
+        poly[0] = c.p0;
+        poly[1] = c.p1;
+        poly[2] = c.p2;
+        poly[3] = c.p3;
+
+        double t1, t2;
+
+        Impl_calcSafeParams( t1, t2, poly, 0, 1 );
+
+        Polygon2D convHull( convexHull( poly ) );
+
+        unsigned int k;
+        for( k=0; k<poly.size(); ++k )
+        {
+            std::cout << poly[k].x << " " << poly[k].y << std::endl;
+        }
+        std::cout << poly[0].x << " " << poly[0].y << std::endl;
+        std::cout << "e" << std::endl;
+
+        for( k=0; k<convHull.size(); ++k )
+        {
+            std::cout << convHull[k].x << " " << convHull[k].y << std::endl;
+        }
+        std::cout << convHull[0].x << " " << convHull[0].y << std::endl;
+        std::cout << "e" << std::endl;
+
+        safeParamsBase_xOffset += 2;
+    }
+    curr_Offset += 20;
+#endif
+
+#ifdef WITH_SAFEPARAMS_TEST
+    // test safe parameter range algorithm
+    const double safeParams_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# safe param range testing" << std::endl
+         << "plot [t=0.0:1.0] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        for( j=i+1; j<sizeof(someCurves)/sizeof(Bezier); ++j )
+        {
+            Bezier c1( someCurves[i] );
+            Bezier c2( someCurves[j] );
+
+            c1.p0.x += safeParams_xOffset;
+            c1.p1.x += safeParams_xOffset;
+            c1.p2.x += safeParams_xOffset;
+            c1.p3.x += safeParams_xOffset;
+            c2.p0.x += safeParams_xOffset;
+            c2.p1.x += safeParams_xOffset;
+            c2.p2.x += safeParams_xOffset;
+            c2.p3.x += safeParams_xOffset;
+
+            double t1, t2;
+
+            if( Impl_calcClipRange(t1, t2, c1, c1, c2, c2) )
+            {
+                // clip safe ranges off c1
+                Bezier c1_part1;
+                Bezier c1_part2;
+                Bezier c1_part3;
+
+                // subdivide at t1_c1
+                Impl_deCasteljauAt( c1_part1, c1_part2, c1, t1 );
+                // subdivide at t2_c1
+                Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, (t2-t1)/(1.0-t1) );
+
+                // output remaining segment (c1_part1)
+
+                std::cout << " bez("
+                     << c1.p0.x << ","
+                     << c1.p1.x << ","
+                     << c1.p2.x << ","
+                     << c1.p3.x << ",t),bez("
+                     << c1.p0.y << ","
+                     << c1.p1.y << ","
+                     << c1.p2.y << ","
+                     << c1.p3.y << ",t), bez("
+                     << c2.p0.x << ","
+                     << c2.p1.x << ","
+                     << c2.p2.x << ","
+                     << c2.p3.x << ",t),bez("
+                     << c2.p0.y << ","
+                     << c2.p1.y << ","
+                     << c2.p2.y << ","
+                     << c2.p3.y << ",t), bez("
+                     << c1_part1.p0.x << ","
+                     << c1_part1.p1.x << ","
+                     << c1_part1.p2.x << ","
+                     << c1_part1.p3.x << ",t),bez("
+                     << c1_part1.p0.y << ","
+                     << c1_part1.p1.y << ","
+                     << c1_part1.p2.y << ","
+                     << c1_part1.p3.y << ",t)";
+
+                if( i+2<sizeof(someCurves)/sizeof(Bezier) )
+                    std::cout << ",\\" << std::endl;
+                else
+                    std::cout << std::endl;
+            }
+        }
+    }
+#endif
+
+#ifdef WITH_SAFEPARAM_DETAILED_TEST
+    // test safe parameter range algorithm
+    const double safeParams2_xOffset( curr_Offset );
+    curr_Offset += 20;
+    if( sizeof(someCurves)/sizeof(Bezier) > 1 )
+    {
+        Bezier c1( someCurves[0] );
+        Bezier c2( someCurves[1] );
+
+        c1.p0.x += safeParams2_xOffset;
+        c1.p1.x += safeParams2_xOffset;
+        c1.p2.x += safeParams2_xOffset;
+        c1.p3.x += safeParams2_xOffset;
+        c2.p0.x += safeParams2_xOffset;
+        c2.p1.x += safeParams2_xOffset;
+        c2.p2.x += safeParams2_xOffset;
+        c2.p3.x += safeParams2_xOffset;
+
+        double t1, t2;
+
+        // output happens here
+        Impl_calcClipRange(t1, t2, c1, c1, c2, c2);
+    }
+#endif
+
+#ifdef WITH_SAFEFOCUSPARAM_TEST
+    // test safe parameter range from focus algorithm
+    const double safeParamsFocus_xOffset( curr_Offset );
+    curr_Offset += 20;
+    std::cout << "# safe param range from focus testing" << std::endl
+         << "plot [t=0.0:1.0] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        for( j=i+1; j<sizeof(someCurves)/sizeof(Bezier); ++j )
+        {
+            Bezier c1( someCurves[i] );
+            Bezier c2( someCurves[j] );
+
+            c1.p0.x += safeParamsFocus_xOffset;
+            c1.p1.x += safeParamsFocus_xOffset;
+            c1.p2.x += safeParamsFocus_xOffset;
+            c1.p3.x += safeParamsFocus_xOffset;
+            c2.p0.x += safeParamsFocus_xOffset;
+            c2.p1.x += safeParamsFocus_xOffset;
+            c2.p2.x += safeParamsFocus_xOffset;
+            c2.p3.x += safeParamsFocus_xOffset;
+
+            double t1, t2;
+
+            Bezier focus;
+#ifdef WITH_SAFEFOCUSPARAM_CALCFOCUS
+#if 0
+            {
+                // clip safe ranges off c1_orig
+                Bezier c1_part1;
+                Bezier c1_part2;
+                Bezier c1_part3;
+
+                // subdivide at t1_c1
+                Impl_deCasteljauAt( c1_part1, c1_part2, c2, 0.30204 );
+
+                // subdivide at t2_c1. As we're working on
+                // c1_part2 now, we have to adapt t2_c1 since
+                // we're no longer in the original parameter
+                // interval. This is based on the following
+                // assumption: t2_new = (t2-t1)/(1-t1), which
+                // relates the t2 value into the new parameter
+                // range [0,1] of c1_part2.
+                Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, (0.57151-0.30204)/(1.0-0.30204) );
+
+                c2 = c1_part1;
+                Impl_calcFocus( focus, c2 );
+            }
+#else
+            Impl_calcFocus( focus, c2 );
+#endif
+#else
+            focus = c2;
+#endif
+            // determine safe range on c1
+            bool bRet( Impl_calcSafeParams_focus( t1, t2,
+                                                  c1, focus ) );
+
+            std::cerr << "t1: " << t1 << ", t2: " << t2 << std::endl;
+
+            // clip safe ranges off c1
+            Bezier c1_part1;
+            Bezier c1_part2;
+            Bezier c1_part3;
+
+            // subdivide at t1_c1
+            Impl_deCasteljauAt( c1_part1, c1_part2, c1, t1 );
+            // subdivide at t2_c1
+            Impl_deCasteljauAt( c1_part1, c1_part3, c1_part2, (t2-t1)/(1.0-t1) );
+
+            // output remaining segment (c1_part1)
+
+            std::cout << " bez("
+                 << c1.p0.x << ","
+                 << c1.p1.x << ","
+                 << c1.p2.x << ","
+                 << c1.p3.x << ",t),bez("
+                 << c1.p0.y << ","
+                 << c1.p1.y << ","
+                 << c1.p2.y << ","
+                 << c1.p3.y << ",t) title \"c1\", "
+#ifdef WITH_SAFEFOCUSPARAM_CALCFOCUS
+                 << "bez("
+                 << c2.p0.x << ","
+                 << c2.p1.x << ","
+                 << c2.p2.x << ","
+                 << c2.p3.x << ",t),bez("
+                 << c2.p0.y << ","
+                 << c2.p1.y << ","
+                 << c2.p2.y << ","
+                 << c2.p3.y << ",t) title \"c2\", "
+                 << "bez("
+                 << focus.p0.x << ","
+                 << focus.p1.x << ","
+                 << focus.p2.x << ","
+                 << focus.p3.x << ",t),bez("
+                 << focus.p0.y << ","
+                 << focus.p1.y << ","
+                 << focus.p2.y << ","
+                 << focus.p3.y << ",t) title \"focus\"";
+#else
+                 << "bez("
+                 << c2.p0.x << ","
+                 << c2.p1.x << ","
+                 << c2.p2.x << ","
+                 << c2.p3.x << ",t),bez("
+                 << c2.p0.y << ","
+                 << c2.p1.y << ","
+                 << c2.p2.y << ","
+                 << c2.p3.y << ",t) title \"focus\"";
+#endif
+            if( bRet )
+            {
+                std::cout << ", bez("
+                     << c1_part1.p0.x << ","
+                     << c1_part1.p1.x << ","
+                     << c1_part1.p2.x << ","
+                     << c1_part1.p3.x << ",t),bez("
+                     << c1_part1.p0.y+0.01 << ","
+                     << c1_part1.p1.y+0.01 << ","
+                     << c1_part1.p2.y+0.01 << ","
+                     << c1_part1.p3.y+0.01 << ",t) title \"part\"";
+            }
+
+            if( i+2<sizeof(someCurves)/sizeof(Bezier) )
+                std::cout << ",\\" << std::endl;
+            else
+                std::cout << std::endl;
+        }
+    }
+#endif
+
+#ifdef WITH_SAFEFOCUSPARAM_DETAILED_TEST
+    // test safe parameter range algorithm
+    const double safeParams3_xOffset( curr_Offset );
+    curr_Offset += 20;
+    if( sizeof(someCurves)/sizeof(Bezier) > 1 )
+    {
+        Bezier c1( someCurves[0] );
+        Bezier c2( someCurves[1] );
+
+        c1.p0.x += safeParams3_xOffset;
+        c1.p1.x += safeParams3_xOffset;
+        c1.p2.x += safeParams3_xOffset;
+        c1.p3.x += safeParams3_xOffset;
+        c2.p0.x += safeParams3_xOffset;
+        c2.p1.x += safeParams3_xOffset;
+        c2.p2.x += safeParams3_xOffset;
+        c2.p3.x += safeParams3_xOffset;
+
+        double t1, t2;
+
+        Bezier focus;
+#ifdef WITH_SAFEFOCUSPARAM_CALCFOCUS
+        Impl_calcFocus( focus, c2 );
+#else
+        focus = c2;
+#endif
+
+        // determine safe range on c1, output happens here
+        Impl_calcSafeParams_focus( t1, t2,
+                                   c1, focus );
+    }
+#endif
+
+#ifdef WITH_BEZIERCLIP_TEST
+    std::vector< std::pair<double, double> >                                result;
+    std::back_insert_iterator< std::vector< std::pair<double, double> > > ii(result);
+
+    // test full bezier clipping
+    const double bezierClip_xOffset( curr_Offset );
+    std::cout << std::endl << std::endl << "# bezier clip testing" << std::endl
+         << "plot [t=0:1] ";
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        for( j=i+1; j<sizeof(someCurves)/sizeof(Bezier); ++j )
+        {
+            Bezier c1( someCurves[i] );
+            Bezier c2( someCurves[j] );
+
+            c1.p0.x += bezierClip_xOffset;
+            c1.p1.x += bezierClip_xOffset;
+            c1.p2.x += bezierClip_xOffset;
+            c1.p3.x += bezierClip_xOffset;
+            c2.p0.x += bezierClip_xOffset;
+            c2.p1.x += bezierClip_xOffset;
+            c2.p2.x += bezierClip_xOffset;
+            c2.p3.x += bezierClip_xOffset;
+
+            std::cout << " bez("
+                 << c1.p0.x << ","
+                 << c1.p1.x << ","
+                 << c1.p2.x << ","
+                 << c1.p3.x << ",t),bez("
+                 << c1.p0.y << ","
+                 << c1.p1.y << ","
+                 << c1.p2.y << ","
+                 << c1.p3.y << ",t), bez("
+                 << c2.p0.x << ","
+                 << c2.p1.x << ","
+                 << c2.p2.x << ","
+                 << c2.p3.x << ",t),bez("
+                 << c2.p0.y << ","
+                 << c2.p1.y << ","
+                 << c2.p2.y << ","
+                 << c2.p3.y << ",t), '-' using (bez("
+                 << c1.p0.x << ","
+                 << c1.p1.x << ","
+                 << c1.p2.x << ","
+                 << c1.p3.x
+                 << ",$1)):(bez("
+                 << c1.p0.y << ","
+                 << c1.p1.y << ","
+                 << c1.p2.y << ","
+                 << c1.p3.y << ",$1)) title \"bezier " << i << " clipped against " << j << " (t on " << i << ")\", "
+                 << " '-' using (bez("
+                 << c2.p0.x << ","
+                 << c2.p1.x << ","
+                 << c2.p2.x << ","
+                 << c2.p3.x
+                 << ",$1)):(bez("
+                 << c2.p0.y << ","
+                 << c2.p1.y << ","
+                 << c2.p2.y << ","
+                 << c2.p3.y << ",$1)) title \"bezier " << i << " clipped against " << j << " (t on " << j << ")\"";
+
+            if( i+2<sizeof(someCurves)/sizeof(Bezier) )
+                std::cout << ",\\" << std::endl;
+            else
+                std::cout << std::endl;
+        }
+    }
+    for( i=0; i<sizeof(someCurves)/sizeof(Bezier); ++i )
+    {
+        for( j=i+1; j<sizeof(someCurves)/sizeof(Bezier); ++j )
+        {
+            result.clear();
+            Bezier c1( someCurves[i] );
+            Bezier c2( someCurves[j] );
+
+            c1.p0.x += bezierClip_xOffset;
+            c1.p1.x += bezierClip_xOffset;
+            c1.p2.x += bezierClip_xOffset;
+            c1.p3.x += bezierClip_xOffset;
+            c2.p0.x += bezierClip_xOffset;
+            c2.p1.x += bezierClip_xOffset;
+            c2.p2.x += bezierClip_xOffset;
+            c2.p3.x += bezierClip_xOffset;
+
+            clipBezier( ii, 0.00001, c1, c2 );
+
+            for( k=0; k<result.size(); ++k )
+            {
+                std::cout << result[k].first << std::endl;
+            }
+            std::cout << "e" << std::endl;
+
+            for( k=0; k<result.size(); ++k )
+            {
+                std::cout << result[k].second << std::endl;
+            }
+            std::cout << "e" << std::endl;
+        }
+    }
+#endif
+
+    return 0;
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/workbench/bezierclip.hxx b/basegfx/source/workbench/bezierclip.hxx
new file mode 100644
index 0000000000..54cceb414f
--- /dev/null
+++ b/basegfx/source/workbench/bezierclip.hxx
@@ -0,0 +1,84 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <vector>
+
+struct Point2D
+{
+    typedef double value_type;
+    Point2D( double _x, double _y ) : x(_x), y(_y) {}
+    Point2D() : x(), y() {}
+    double x;
+    double y;
+};
+
+struct Bezier
+{
+    Point2D p0;
+    Point2D p1;
+    Point2D p2;
+    Point2D p3;
+
+    Point2D&        operator[]( int i ) { return reinterpret_cast<Point2D*>(this)[i]; }
+    const Point2D&  operator[]( int i ) const { return reinterpret_cast<const Point2D*>(this)[i]; }
+};
+
+struct FatLine
+{
+    // line L through p1 and p4 in normalized implicit form
+    double a;
+    double b;
+    double c;
+
+    // the upper and lower distance from this line
+    double dMin;
+    double dMax;
+};
+
+template <typename DataType> DataType calcLineDistance( const DataType& a,
+                                                        const DataType& b,
+                                                        const DataType& c,
+                                                        const DataType& x,
+                                                        const DataType& y )
+{
+    return a*x + b*y + c;
+}
+
+typedef std::vector< Point2D > Polygon2D;
+
+/* little abs template */
+template <typename NumType> NumType absval( NumType x )
+{
+    return x<0 ? -x : x;
+}
+
+Polygon2D convexHull( const Polygon2D& rPoly );
+
+// TODO: find proper epsilon here (try std::numeric_limits<NumType>::epsilon()?)!
+constexpr auto DBL_EPSILON = 1.0e-100;
+
+/* little approximate comparisons */
+template <typename NumType> bool tolZero( NumType n ) { return fabs(n) < DBL_EPSILON; }
+template <typename NumType> bool tolEqual( NumType n1, NumType n2 ) { return tolZero(n1-n2); }
+template <typename NumType> bool tolLessEqual( NumType n1, NumType n2 ) { return tolEqual(n1,n2) || n1<n2; }
+template <typename NumType> bool tolGreaterEqual( NumType n1, NumType n2 ) { return tolEqual(n1,n2) || n1>n2; }
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/workbench/convexhull.cxx b/basegfx/source/workbench/convexhull.cxx
new file mode 100644
index 0000000000..ddcb040465
--- /dev/null
+++ b/basegfx/source/workbench/convexhull.cxx
@@ -0,0 +1,200 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#include <algorithm>
+#include <vector>
+
+#include <bezierclip.hxx>
+
+/* Implements the theta function from Sedgewick: Algorithms in XXX, chapter 24 */
+template <class PointType> double theta( const PointType& p1, const PointType& p2 )
+{
+    typename PointType::value_type dx, dy, ax, ay;
+    double t;
+
+    dx = p2.x - p1.x; ax = absval( dx );
+    dy = p2.y - p1.y; ay = absval( dy );
+    t = (ax+ay == 0) ? 0 : (double) dy/(ax+ay);
+    if( dx < 0 )
+        t = 2-t;
+    else if( dy < 0 )
+        t = 4+t;
+
+    return t*90.0;
+}
+
+/* Model of LessThanComparable for theta sort.
+ * Uses the theta function from Sedgewick: Algorithms in XXX, chapter 24
+ */
+template <class PointType> class ThetaCompare
+{
+public:
+    explicit ThetaCompare( const PointType& rRefPoint ) : maRefPoint( rRefPoint ) {}
+
+    bool operator() ( const PointType& p1, const PointType& p2 )
+    {
+        // return true, if p1 precedes p2 in the angle relative to maRefPoint
+        return theta(maRefPoint, p1) < theta(maRefPoint, p2);
+    }
+
+    double operator() ( const PointType& p ) const
+    {
+        return theta(maRefPoint, p);
+    }
+
+private:
+    PointType maRefPoint;
+};
+
+/* Implementation of the predicate 'counter-clockwise' for three points, from Sedgewick: Algorithms in XXX, chapter 24 */
+template <class PointType, class CmpFunctor> typename PointType::value_type ccw( const PointType& p0, const PointType& p1, const PointType& p2, CmpFunctor& thetaCmp )
+{
+    typename PointType::value_type dx1, dx2, dy1, dy2;
+    typename PointType::value_type theta0( thetaCmp(p0) );
+    typename PointType::value_type theta1( thetaCmp(p1) );
+    typename PointType::value_type theta2( thetaCmp(p2) );
+
+#if 0
+    if( theta0 == theta1 ||
+        theta0 == theta2 ||
+        theta1 == theta2 )
+    {
+        // cannot reliably compare, as at least two points are
+        // theta-equal. See bug description below
+        return 0;
+    }
+#endif
+
+    dx1 = p1.x - p0.x; dy1 = p1.y - p0.y;
+    dx2 = p2.x - p0.x; dy2 = p2.y - p0.y;
+
+    if( dx1*dy2 > dy1*dx2 )
+        return +1;
+
+    if( dx1*dy2 < dy1*dx2 )
+        return -1;
+
+    if( (dx1*dx2 < 0) || (dy1*dy2 < 0) )
+        return -1;
+
+    if( (dx1*dx1 + dy1*dy1) < (dx2*dx2 + dy2*dy2) )
+        return +1;
+
+    return 0;
+}
+
+/*
+ Bug
+ ===
+
+ Sometimes, the resulting polygon is not the convex hull (see below
+ for an edge configuration to reproduce that problem)
+
+ Problem analysis:
+ =================
+
+ The root cause of this bug is the fact that the second part of
+ the algorithm (the 'wrapping' of the point set) relies on the
+ previous theta sorting. Namely, it is required that the
+ generated point ordering, when interpreted as a polygon, is not
+ self-intersecting. This property, although, cannot be
+ guaranteed due to limited floating point accuracy. For example,
+ for two points very close together, and at the same time very
+ far away from the theta reference point p1, can appear on the
+ same theta value (because floating point accuracy is limited),
+ although on different rays to p1 when inspected locally.
+
+ Example:
+
+                    /
+             P3    /
+               |\ /
+               | /
+               |/ \
+             P2    \
+                    \
+      ...____________\
+     P1
+
+ Here, P2 and P3 are theta-equal relative to P1, but the local
+ ccw measure always says 'left turn'. Thus, the convex hull is
+ wrong at this place.
+
+ Solution:
+ =========
+
+ If two points are theta-equal and checked via ccw, ccw must
+ also classify them as 'equal'. Thus, the second stage of the
+ convex hull algorithm sorts the first one out, effectively
+ reducing a cluster of theta-equal points to only one. This
+ single point can then be treated correctly.
+*/
+
+/* Implementation of Graham's convex hull algorithm, see Sedgewick: Algorithms in XXX, chapter 25 */
+Polygon2D convexHull( const Polygon2D& rPoly )
+{
+    const Polygon2D::size_type N( rPoly.size() );
+    Polygon2D result( N + 1 );
+    std::copy(rPoly.begin(), rPoly.end(), result.begin()+1 );
+    Polygon2D::size_type min, i;
+
+    // determine safe point on hull (smallest y value)
+    for( min=1, i=2; i<=N; ++i )
+    {
+        if( result[i].y < result[min].y )
+            min = i;
+    }
+
+    // determine safe point on hull (largest x value)
+    for( i=1; i<=N; ++i )
+    {
+        if( result[i].y == result[min].y &&
+            result[i].x > result[min].x )
+        {
+            min = i;
+        }
+    }
+
+    // TODO: add inner elimination optimization from Sedgewick: Algorithms in XXX, chapter 25
+    // TODO: use radix sort instead of std::sort(), calc theta only once and store
+
+    // setup first point and sort
+    std::swap( result[1], result[min] );
+    ThetaCompare<Point2D> cmpFunc(result[1]);
+    std::sort( result.begin()+1, result.end(), cmpFunc );
+
+    // setup sentinel
+    result[0] = result[N];
+
+    // generate convex hull
+    Polygon2D::size_type M;
+    for( M=3, i=4; i<=N; ++i )
+    {
+        while( ccw(result[M], result[M-1], result[i], cmpFunc) >= 0 )
+            --M;
+
+        ++M;
+        std::swap( result[M], result[i] );
+    }
+
+    // copy range [1,M] to output
+    return Polygon2D( result.begin()+1, result.begin()+M+1 );
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/basegfx/source/workbench/gauss.hxx b/basegfx/source/workbench/gauss.hxx
new file mode 100644
index 0000000000..4ef050ccbc
--- /dev/null
+++ b/basegfx/source/workbench/gauss.hxx
@@ -0,0 +1,163 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+/** This method eliminates elements below main diagonal in the given
+    matrix by gaussian elimination.
+
+    @param matrix
+    The matrix to operate on. Last column is the result vector (right
+    hand side of the linear equation). After successful termination,
+    the matrix is upper triangular. The matrix is expected to be in
+    row major order.
+
+    @param rows
+    Number of rows in matrix
+
+    @param cols
+    Number of columns in matrix
+
+    @param minPivot
+    If the pivot element gets lesser than minPivot, this method fails,
+    otherwise, elimination succeeds and true is returned.
+
+    @return true, if elimination succeeded.
+ */
+
+#pragma once
+
+template <class Matrix, typename BaseType>
+bool eliminate(     Matrix&         matrix,
+                    int             rows,
+                    int             cols,
+                    const BaseType& minPivot    )
+{
+    /* i, j, k *must* be signed, when looping like: j>=0 ! */
+    /* eliminate below main diagonal */
+    for(int i=0; i<cols-1; ++i)
+    {
+        /* find best pivot */
+        int max = i;
+        for(int j=i+1; j<rows; ++j)
+            if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) )
+                max = j;
+
+        /* check pivot value */
+        if( fabs(matrix[ max*cols + i ]) < minPivot )
+            return false;   /* pivot too small! */
+
+        /* interchange rows 'max' and 'i' */
+        for(int k=0; k<cols; ++k)
+        {
+            std::swap(matrix[ i*cols + k ], matrix[ max*cols + k ]);
+        }
+
+        /* eliminate column */
+        for(int j=i+1; j<rows; ++j)
+            for(int k=cols-1; k>=i; --k)
+                matrix[ j*cols + k ] -= matrix[ i*cols + k ] *
+                    matrix[ j*cols + i ] / matrix[ i*cols + i ];
+    }
+
+    /* everything went well */
+    return true;
+}
+
+/** Retrieve solution vector of linear system by substituting backwards.
+
+    This operation _relies_ on the previous successful
+    application of eliminate()!
+
+    @param matrix
+    Matrix in upper diagonal form, as e.g. generated by eliminate()
+
+    @param rows
+    Number of rows in matrix
+
+    @param cols
+    Number of columns in matrix
+
+    @param result
+    Result vector. Given matrix must have space for one column (rows entries).
+
+    @return true, if back substitution was possible (i.e. no division
+    by zero occurred).
+ */
+template <class Matrix, class Vector, typename BaseType>
+bool substitute(    const Matrix&   matrix,
+                    int             rows,
+                    int             cols,
+                    Vector&         result  )
+{
+    BaseType    temp;
+
+    /* j, k *must* be signed, when looping like: j>=0 ! */
+    /* substitute backwards */
+    for(int j=rows-1; j>=0; --j)
+    {
+        temp = 0.0;
+        for(int k=j+1; k<cols-1; ++k)
+            temp += matrix[ j*cols + k ] * result[k];
+
+        if( matrix[ j*cols + j ] == 0.0 )
+            return false;   /* imminent division by zero! */
+
+        result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
+    }
+
+    /* everything went well */
+    return true;
+}
+
+/** This method determines solution of given linear system, if any
+
+    This is a wrapper for eliminate and substitute, given matrix must
+    contain right side of equation as the last column.
+
+    @param matrix
+    The matrix to operate on. Last column is the result vector (right
+    hand side of the linear equation). After successful termination,
+    the matrix is upper triangular. The matrix is expected to be in
+    row major order.
+
+    @param rows
+    Number of rows in matrix
+
+    @param cols
+    Number of columns in matrix
+
+    @param minPivot
+    If the pivot element gets lesser than minPivot, this method fails,
+    otherwise, elimination succeeds and true is returned.
+
+    @return true, if elimination succeeded.
+ */
+template <class Matrix, class Vector, typename BaseType>
+bool solve( Matrix&     matrix,
+            int         rows,
+            int         cols,
+            Vector&     result,
+            BaseType    minPivot    )
+{
+    if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) )
+        return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result);
+
+    return false;
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */