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

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

1 files changed, 3702 insertions, 0 deletions

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: */