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

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

5 files changed, 974 insertions, 0 deletions

diff --git a/include/basegfx/matrix/b2dhommatrix.hxx b/include/basegfx/matrix/b2dhommatrix.hxx
new file mode 100644
index 0000000000..8067b8e1c6
--- /dev/null
+++ b/include/basegfx/matrix/b2dhommatrix.hxx
@@ -0,0 +1,158 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/config.h>
+
+#include <ostream>
+
+#include <sal/types.h>
+#include <basegfx/basegfxdllapi.h>
+#include <array>
+
+namespace basegfx
+{
+    class B2DTuple;
+
+    class SAL_WARN_UNUSED BASEGFX_DLLPUBLIC B2DHomMatrix
+    {
+    private:
+        // Since this is a graphics matrix, the last row is always 0 0 1, so we don't bother to store it.
+        std::array<std::array<double, 3>, 2> mfValues {
+            std::array<double, 3>{ 1.0, 0.0, 0.0 },
+            std::array<double, 3>{ 0.0, 1.0, 0.0 } };
+
+    public:
+        constexpr B2DHomMatrix() = default;
+
+        /** constructor to allow setting all needed values for a 3x2 matrix at once. The
+            parameter f_0x1 e.g. is the same as using set(0, 1, f)
+         */
+        constexpr B2DHomMatrix(double f_0x0, double f_0x1, double f_0x2, double f_1x0, double f_1x1, double f_1x2)
+        {
+            mfValues[0][0] = f_0x0;
+            mfValues[0][1] = f_0x1;
+            mfValues[0][2] = f_0x2;
+            mfValues[1][0] = f_1x0;
+            mfValues[1][1] = f_1x1;
+            mfValues[1][2] = f_1x2;
+        }
+
+        /** Convenience creator for declaration of the matrix that is commonly
+            used by web standards (SVG, CSS, HTML).
+
+           Values a,b,c,d,e,f represent the following values in the matrix:
+              [a,c,e]      [a,c,e]
+              [b,d,f]  or  [b,d,f]
+                           [0,0,1]
+
+        */
+        static B2DHomMatrix abcdef(double da, double db, double dc, double dd, double de, double df)
+        {
+            return B2DHomMatrix(da, dc, de, db, dd, df);
+        }
+
+        // Convenience accessor for value at 0,0 position in the matrix
+        double a() const { return get(0,0); }
+        // Convenience accessor for value at 1,0 position in the matrix
+        double b() const { return get(1,0); }
+        // Convenience accessor for value at 0,1 position in the matrix
+        double c() const { return get(0,1); }
+        // Convenience accessor for value at 1,1 position in the matrix
+        double d() const { return get(1,1); }
+        // Convenience accessor for value at 0,2 position in the matrix
+        double e() const { return get(0,2); }
+        // Convenience accessor for value at 1,2 position in the matrix
+        double f() const { return get(1,2); }
+
+        double get(sal_uInt16 nRow, sal_uInt16 nColumn) const
+        {
+            return mfValues[nRow][nColumn];
+        }
+
+        void set(sal_uInt16 nRow, sal_uInt16 nColumn, double fValue)
+        {
+            mfValues[nRow][nColumn] = fValue;
+        }
+
+        /** allow setting all needed values for a 3x2 matrix in one call. The
+            parameter f_0x1 e.g. is the same as using set(0, 1, f)
+         */
+        void set3x2(double f_0x0, double f_0x1, double f_0x2, double f_1x0, double f_1x1, double f_1x2);
+
+        // reset to a standard matrix
+        bool isIdentity() const;
+        void identity();
+
+        bool isInvertible() const;
+        bool invert();
+
+        void rotate(double fRadiant);
+
+        void translate(double fX, double fY);
+        void translate(const B2DTuple& rTuple);
+
+        void scale(double fX, double fY);
+        void scale(const B2DTuple& rTuple);
+
+        // Shearing-Matrices
+        void shearX(double fSx);
+        void shearY(double fSy);
+
+        bool operator==(const B2DHomMatrix& rMat) const;
+        bool operator!=(const B2DHomMatrix& rMat) const;
+
+        // matrix multiplication from the left to the local
+        B2DHomMatrix& operator*=(const B2DHomMatrix& rMat);
+
+        /**
+         * Help routine to decompose given homogen 3x3 matrix to components. A correction of the
+         * components is done to avoid inaccuracies.
+         *
+         * See basegfx::utils::createScaleShearXRotateTranslateB2DHomMatrix() for the opposite, to
+         * compose a homogen 3x3 matrix from components.
+         */
+        bool decompose(B2DTuple& rScale, B2DTuple& rTranslate, double& rRotate, double& rShearX) const;
+
+    private:
+        void computeAdjoint(double (&dst)[6]) const;
+        double computeDeterminant(double (&dst)[6]) const;
+        void doMulMatrix(const B2DHomMatrix& rMat);
+    };
+
+    inline B2DHomMatrix operator*(const B2DHomMatrix& rMatA, const B2DHomMatrix& rMatB)
+    {
+        B2DHomMatrix aMul(rMatB);
+        aMul *= rMatA;
+        return aMul;
+    }
+
+    template<typename charT, typename traits>
+    std::basic_ostream<charT, traits> & operator <<(
+        std::basic_ostream<charT, traits> & stream, B2DHomMatrix const & matrix)
+    {
+        return stream
+            << '[' << matrix.get(0, 0) << ' ' << matrix.get(0, 1) << ' '
+            << matrix.get(0, 2) << "; " << matrix.get(1, 0) << ' '
+            << matrix.get(1, 1) << ' ' << matrix.get(1, 2) << ']';
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/include/basegfx/matrix/b2dhommatrixtools.hxx b/include/basegfx/matrix/b2dhommatrixtools.hxx
new file mode 100644
index 0000000000..9b81f33d2a
--- /dev/null
+++ b/include/basegfx/matrix/b2dhommatrixtools.hxx
@@ -0,0 +1,218 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/types.h>
+#include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/point/b2dpoint.hxx>
+#include <basegfx/tuple/b2dtuple.hxx>
+#include <utility>
+#include <basegfx/basegfxdllapi.h>
+
+namespace basegfx { class B2DRange; }
+
+namespace basegfx::utils
+{
+        /** If the rotation angle is an approximate multiple of pi/2,
+            force fSin/fCos to -1/0/1, to maintain orthogonality (which
+            might also be advantageous for the other cases, but: for
+            multiples of pi/2, the exact values _can_ be attained. It
+            would be largely unintuitive, if a 180 degrees rotation
+            would introduce slight roundoff errors, instead of exactly
+            mirroring the coordinate system)
+         */
+        void createSinCosOrthogonal(double& o_rSin, double& rCos, double fRadiant);
+
+        /** Tooling methods for on-the-fly matrix generation e.g. for inline
+            multiplications
+         */
+        BASEGFX_DLLPUBLIC B2DHomMatrix createScaleB2DHomMatrix(double fScaleX, double fScaleY);
+        BASEGFX_DLLPUBLIC B2DHomMatrix createShearXB2DHomMatrix(double fShearX);
+        BASEGFX_DLLPUBLIC B2DHomMatrix createShearYB2DHomMatrix(double fShearY);
+        BASEGFX_DLLPUBLIC B2DHomMatrix createRotateB2DHomMatrix(double fRadiant);
+        BASEGFX_DLLPUBLIC B2DHomMatrix createTranslateB2DHomMatrix(double fTranslateX, double fTranslateY);
+
+        /// inline versions for parameters as tuples
+        inline B2DHomMatrix createScaleB2DHomMatrix(const B2DTuple& rScale)
+        {
+            return createScaleB2DHomMatrix(rScale.getX(), rScale.getY());
+        }
+
+        inline B2DHomMatrix createTranslateB2DHomMatrix(const B2DTuple& rTranslate)
+        {
+            return createTranslateB2DHomMatrix(rTranslate.getX(), rTranslate.getY());
+        }
+
+        /** Tooling methods for faster completely combined matrix creation
+            when scale, shearX, rotation and translation needs to be done in
+            exactly that order. It's faster since it directly calculates
+            each matrix value based on a symbolic calculation of the three
+            matrix multiplications.
+            Inline versions for parameters as tuples added, too.
+         */
+        BASEGFX_DLLPUBLIC B2DHomMatrix createScaleShearXRotateTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY);
+        inline B2DHomMatrix createScaleShearXRotateTranslateB2DHomMatrix(
+            const B2DTuple& rScale,
+            double fShearX,
+            double fRadiant,
+            const B2DTuple& rTranslate)
+        {
+            return createScaleShearXRotateTranslateB2DHomMatrix(
+                rScale.getX(), rScale.getY(),
+                fShearX,
+                fRadiant,
+                rTranslate.getX(), rTranslate.getY());
+        }
+
+        BASEGFX_DLLPUBLIC B2DHomMatrix createShearXRotateTranslateB2DHomMatrix(
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY);
+        inline B2DHomMatrix createShearXRotateTranslateB2DHomMatrix(
+            double fShearX,
+            double fRadiant,
+            const B2DTuple& rTranslate)
+        {
+            return createShearXRotateTranslateB2DHomMatrix(
+                fShearX,
+                fRadiant,
+                rTranslate.getX(), rTranslate.getY());
+        }
+
+        BASEGFX_DLLPUBLIC B2DHomMatrix createScaleTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fTranslateX, double fTranslateY);
+        inline B2DHomMatrix createScaleTranslateB2DHomMatrix(
+            const B2DTuple& rScale,
+            const B2DTuple& rTranslate)
+        {
+            return createScaleTranslateB2DHomMatrix(
+                rScale.getX(), rScale.getY(),
+                rTranslate.getX(), rTranslate.getY());
+        }
+
+        /// special for the often used case of rotation around a point
+        BASEGFX_DLLPUBLIC B2DHomMatrix createRotateAroundPoint(
+            double fPointX, double fPointY,
+            double fRadiant);
+        inline B2DHomMatrix createRotateAroundPoint(
+            const B2DTuple& rPoint,
+            double fRadiant)
+        {
+            return createRotateAroundPoint(
+                rPoint.getX(), rPoint.getY(),
+                fRadiant);
+        }
+
+        /// special for creating a mapping for a Range rotated around it's center
+        /// while keeping AspectRatio unchanged and staying inside the given Range
+        /// by optimally using the available space (no overlap or outside allowed)
+        B2DHomMatrix createRotateAroundCenterKeepAspectRatioStayInsideRange(
+            const basegfx::B2DRange& rTargetRange,
+            double fRotate);
+
+        /// special for the case to map from source range to target range
+        BASEGFX_DLLPUBLIC B2DHomMatrix createSourceRangeTargetRangeTransform(
+            const B2DRange& rSourceRange,
+            const B2DRange& rTargetRange);
+
+        /// create based on given CoordinateSystem which is defined by origin and x/yaxis
+        BASEGFX_DLLPUBLIC B2DHomMatrix createCoordinateSystemTransform(
+            const B2DPoint& rOrigin,
+            const B2DVector& rX,
+            const B2DVector& rY);
+
+        /// get column vector from B2dHomMatrix, e.g. to extract coordinate system origin and x/yaxis
+        BASEGFX_DLLPUBLIC B2DTuple getColumn(const B2DHomMatrix& rMatrix, sal_uInt16 nCol);
+
+
+        class BASEGFX_DLLPUBLIC B2DHomMatrixBufferedDecompose
+        {
+        private:
+            B2DVector              maScale;
+            B2DVector              maTranslate;
+            double                 mfRotate;
+            double                 mfShearX;
+
+        public:
+            B2DHomMatrixBufferedDecompose(const B2DHomMatrix& rB2DHomMatrix = B2DHomMatrix())
+            :   mfRotate(0.0),
+                mfShearX(0.0)
+            {
+                rB2DHomMatrix.decompose(maScale, maTranslate, mfRotate, mfShearX);
+            }
+
+            // data access
+            B2DHomMatrix getB2DHomMatrix() const
+            {
+                return createScaleShearXRotateTranslateB2DHomMatrix(
+                    maScale, mfShearX, mfRotate, maTranslate);
+            }
+
+            const B2DVector& getScale() const { return maScale; }
+            const B2DVector& getTranslate() const { return maTranslate; }
+            double getRotate() const { return mfRotate; }
+            double getShearX() const { return mfShearX; }
+        };
+
+        class BASEGFX_DLLPUBLIC B2DHomMatrixBufferedOnDemandDecompose
+        {
+        private:
+            B2DHomMatrix           maB2DHomMatrix;
+            B2DVector              maScale;
+            B2DVector              maTranslate;
+            double                 mfRotate;
+            double                 mfShearX;
+
+            bool                   mbDecomposed : 1;
+
+            void impCheckDecompose()
+            {
+                if(!mbDecomposed)
+                {
+                    maB2DHomMatrix.decompose(maScale, maTranslate, mfRotate, mfShearX);
+                    mbDecomposed = true;
+                }
+            }
+
+        public:
+            B2DHomMatrixBufferedOnDemandDecompose(B2DHomMatrix aB2DHomMatrix = B2DHomMatrix())
+            :   maB2DHomMatrix(std::move(aB2DHomMatrix)),
+                mfRotate(0.0),
+                mfShearX(0.0),
+                mbDecomposed(false)
+            {
+            }
+
+            // data access
+            const B2DHomMatrix& getB2DHomMatrix() const { return maB2DHomMatrix; }
+            const B2DVector& getScale() const { const_cast< B2DHomMatrixBufferedOnDemandDecompose* >(this)->impCheckDecompose(); return maScale; }
+            const B2DVector& getTranslate() const { const_cast< B2DHomMatrixBufferedOnDemandDecompose* >(this)->impCheckDecompose(); return maTranslate; }
+            double getRotate() const { const_cast< B2DHomMatrixBufferedOnDemandDecompose* >(this)->impCheckDecompose(); return mfRotate; }
+            double getShearX() const { const_cast< B2DHomMatrixBufferedOnDemandDecompose* >(this)->impCheckDecompose(); return mfShearX; }
+        };
+} // end of namespace basegfx::utils
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/include/basegfx/matrix/b3dhommatrix.hxx b/include/basegfx/matrix/b3dhommatrix.hxx
new file mode 100644
index 0000000000..29603f88eb
--- /dev/null
+++ b/include/basegfx/matrix/b3dhommatrix.hxx
@@ -0,0 +1,127 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/types.h>
+#include <basegfx/point/b3dpoint.hxx>
+#include <basegfx/vector/b3dvector.hxx>
+#include <o3tl/cow_wrapper.hxx>
+#include <basegfx/basegfxdllapi.h>
+
+namespace basegfx
+{
+    class B3DTuple;
+    class Impl3DHomMatrix;
+
+    class BASEGFX_DLLPUBLIC B3DHomMatrix
+    {
+    public:
+        typedef o3tl::cow_wrapper< Impl3DHomMatrix, o3tl::ThreadSafeRefCountingPolicy > ImplType;
+
+    private:
+        ImplType                                     mpImpl;
+
+    public:
+        B3DHomMatrix();
+        B3DHomMatrix(const B3DHomMatrix& rMat);
+        B3DHomMatrix(B3DHomMatrix&& rMat);
+        ~B3DHomMatrix();
+
+        double get(sal_uInt16 nRow, sal_uInt16 nColumn) const;
+        void set(sal_uInt16 nRow, sal_uInt16 nColumn, double fValue);
+
+        // test if last line is default to see if last line needs to be
+        // involved in calculations
+        bool isLastLineDefault() const;
+
+        bool isIdentity() const;
+        /// Reset to the identity matrix
+        void identity();
+
+        /// Invert the matrix (if possible)
+        void invert();
+
+        /// Calc the matrix determinant
+        double determinant() const;
+
+        /// Rotation
+        void rotate(double fAngleX,double fAngleY,double fAngleZ);
+        void rotate(const B3DTuple& rRotation);
+
+        /// Translation
+        void translate(double fX, double fY, double fZ);
+        void translate(const B3DTuple& rTranslation);
+
+        /// Scaling
+        void scale(double fX, double fY, double fZ);
+        void scale(const B3DTuple& rScale);
+
+        // Shearing-Matrices
+        void shearXY(double fSx, double fSy);
+        void shearXZ(double fSx, double fSz);
+
+        // Projection matrices, used for converting between eye and
+        // clip coordinates
+        void frustum(double fLeft = -1.0, double fRight = 1.0,
+            double fBottom = -1.0, double fTop = 1.0,
+            double fNear = 0.001, double fFar = 1.0);
+
+        void ortho(double fLeft = -1.0, double fRight = 1.0,
+            double fBottom = -1.0, double fTop = 1.0,
+            double fNear = 0.0, double fFar = 1.0);
+
+        // build orientation matrix
+        void orientation(
+            const B3DPoint& rVRP = B3DPoint(0.0,0.0,1.0),
+            B3DVector aVPN = B3DVector(0.0,0.0,1.0),
+            B3DVector aVUV = B3DVector(0.0,1.0,0.0));
+
+        // addition, subtraction
+        B3DHomMatrix& operator+=(const B3DHomMatrix& rMat);
+        B3DHomMatrix& operator-=(const B3DHomMatrix& rMat);
+
+        // comparison
+        bool operator==(const B3DHomMatrix& rMat) const;
+        bool operator!=(const B3DHomMatrix& rMat) const;
+
+        // multiplication, division by constant value
+        B3DHomMatrix& operator*=(double fValue);
+        B3DHomMatrix& operator/=(double fValue);
+
+        // matrix multiplication (from the left)
+        B3DHomMatrix& operator*=(const B3DHomMatrix& rMat);
+
+        // assignment operator
+        B3DHomMatrix& operator=(const B3DHomMatrix& rMat);
+        B3DHomMatrix& operator=(B3DHomMatrix&& rMat);
+
+        // decomposition
+        void decompose(B3DTuple& rScale, B3DTuple& rTranslate, B3DTuple& rRotate, B3DTuple& rShear) const;
+    };
+
+    inline B3DHomMatrix operator*(const B3DHomMatrix& rMatA, const B3DHomMatrix& rMatB)
+    {
+        B3DHomMatrix aMul(rMatB);
+        aMul *= rMatA;
+        return aMul;
+    }
+} // end of namespace basegfx
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/include/basegfx/matrix/b3dhommatrixtools.hxx b/include/basegfx/matrix/b3dhommatrixtools.hxx
new file mode 100644
index 0000000000..6b65d24603
--- /dev/null
+++ b/include/basegfx/matrix/b3dhommatrixtools.hxx
@@ -0,0 +1,44 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <basegfx/basegfxdllapi.h>
+#include <basegfx/matrix/b3dhommatrix.hxx>
+
+namespace com::sun::star::drawing
+{
+struct HomogenMatrix;
+}
+
+namespace basegfx::utils
+{
+/* tooling methods for converting API matrices (drawing::HomogenMatrix) to
+    B3DHomMatrix. drawing::HomogenMatrix4 is not used by OOo
+ */
+BASEGFX_DLLPUBLIC B3DHomMatrix
+UnoHomogenMatrixToB3DHomMatrix(const com::sun::star::drawing::HomogenMatrix& rMatrixIn);
+
+BASEGFX_DLLPUBLIC void
+B3DHomMatrixToUnoHomogenMatrix(const B3DHomMatrix& rMatrixIn,
+                               com::sun::star::drawing::HomogenMatrix& rMatrixOut);
+
+} // end of namespace basegfx::tools
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
diff --git a/include/basegfx/matrix/hommatrixtemplate.hxx b/include/basegfx/matrix/hommatrixtemplate.hxx
new file mode 100644
index 0000000000..4f1300f533
--- /dev/null
+++ b/include/basegfx/matrix/hommatrixtemplate.hxx
@@ -0,0 +1,427 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   Licensed to the Apache Software Foundation (ASF) under one or more
+ *   contributor license agreements. See the NOTICE file distributed
+ *   with this work for additional information regarding copyright
+ *   ownership. The ASF licenses this file to you under the Apache
+ *   License, Version 2.0 (the "License"); you may not use this file
+ *   except in compliance with the License. You may obtain a copy of
+ *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
+ */
+
+#pragma once
+
+#include <sal/types.h>
+#include <basegfx/numeric/ftools.hxx>
+#include <cmath>
+
+namespace basegfx::internal
+    {
+
+        inline constexpr double implGetDefaultValue(sal_uInt16 nRow, sal_uInt16 nColumn)
+        {
+            if(nRow == nColumn)
+                return 1.0;
+            return 0.0;
+        }
+
+        template < sal_uInt16 RowSize > class ImplMatLine
+        {
+            double                                          mfValue[RowSize];
+
+        public:
+            ImplMatLine() = default;
+
+            explicit ImplMatLine(sal_uInt16 nRow)
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    mfValue[a] = implGetDefaultValue(nRow, a);
+                }
+            }
+
+            double get(sal_uInt16 nColumn) const
+            {
+                return mfValue[nColumn];
+            }
+
+            void set(sal_uInt16 nColumn, const double& rValue)
+            {
+                mfValue[nColumn] = rValue;
+            }
+        };
+
+        template < sal_uInt16 RowSize > class ImplHomMatrixTemplate
+        {
+            ImplMatLine< RowSize >                          maLine[RowSize];
+
+        public:
+            // Is last line used?
+            bool isLastLineDefault() const
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    const double fDefault(implGetDefaultValue((RowSize - 1), a));
+                    const double fLineValue(maLine[RowSize-1].get(a));
+
+                    if(fDefault != fLineValue)
+                    {
+                        return false;
+                    }
+                }
+                return true;
+            }
+
+            ImplHomMatrixTemplate()
+            {
+                // complete initialization with identity matrix, all lines
+                // were initialized with a trailing 1 followed by 0's.
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                        maLine[a].set(b, implGetDefaultValue(a, b) );
+                }
+            }
+
+            ImplHomMatrixTemplate(const ImplHomMatrixTemplate& rToBeCopied)
+            {
+                operator=(rToBeCopied);
+            }
+
+            ImplHomMatrixTemplate& operator=(const ImplHomMatrixTemplate& rToBeCopied)
+            {
+                if (this != &rToBeCopied)
+                {
+                    // complete initialization using copy
+                    for(sal_uInt16 a(0); a < RowSize; a++)
+                    {
+                        maLine[a] = rToBeCopied.maLine[a];
+                    }
+                }
+                return *this;
+            }
+
+            static sal_uInt16 getEdgeLength() { return RowSize; }
+
+            double get(sal_uInt16 nRow, sal_uInt16 nColumn) const
+            {
+                return maLine[nRow].get(nColumn);
+            }
+
+            void set(sal_uInt16 nRow, sal_uInt16 nColumn, const double& rValue)
+            {
+                maLine[nRow].set(nColumn, rValue);
+            }
+
+            // Left-upper decomposition
+            bool ludcmp(sal_uInt16 nIndex[], sal_Int16& nParity)
+            {
+                double fBig, fSum, fDum;
+                double fStorage[RowSize];
+                sal_uInt16 a, b, c;
+
+                // #i30874# Initialize nAMax (compiler warns)
+                sal_uInt16 nAMax = 0;
+
+                nParity = 1;
+
+                // Calc the max of each line. If a line is empty,
+                // stop immediately since matrix is not invertible then.
+                for(a = 0; a < RowSize; a++)
+                {
+                    fBig = 0.0;
+
+                    for(b = 0; b < RowSize; b++)
+                    {
+                        double fTemp(fabs(get(a, b)));
+
+                        if(::basegfx::fTools::more(fTemp, fBig))
+                        {
+                            fBig = fTemp;
+                        }
+                    }
+
+                    if(::basegfx::fTools::equalZero(fBig))
+                    {
+                        return false;
+                    }
+
+                    fStorage[a] = 1.0 / fBig;
+                }
+
+                // start normalizing
+                for(b = 0; b < RowSize; b++)
+                {
+                    for(a = 0; a < b; a++)
+                    {
+                        fSum = get(a, b);
+
+                        for(c = 0; c < a; c++)
+                        {
+                            fSum -= get(a, c) * get(c, b);
+                        }
+
+                        set(a, b, fSum);
+                    }
+
+                    fBig = 0.0;
+
+                    for(a = b; a < RowSize; a++)
+                    {
+                        fSum = get(a, b);
+
+                        for(c = 0; c < b; c++)
+                        {
+                            fSum -= get(a, c) * get(c, b);
+                        }
+
+                        set(a, b, fSum);
+                        fDum = fStorage[a] * fabs(fSum);
+
+                        if(::basegfx::fTools::moreOrEqual(fDum, fBig))
+                        {
+                            fBig = fDum;
+                            nAMax = a;
+                        }
+                    }
+
+                    if(b != nAMax)
+                    {
+                        for(c = 0; c < RowSize; c++)
+                        {
+                            fDum = get(nAMax, c);
+                            set(nAMax, c, get(b, c));
+                            set(b, c, fDum);
+                        }
+
+                        nParity = -nParity;
+                        fStorage[nAMax] = fStorage[b];
+                    }
+
+                    nIndex[b] = nAMax;
+
+                    // here the failure of precision occurs
+                    const double fValBB(fabs(get(b, b)));
+
+                    if(::basegfx::fTools::equalZero(fValBB))
+                    {
+                        return false;
+                    }
+
+                    if(b != (RowSize - 1))
+                    {
+                        fDum = 1.0 / get(b, b);
+
+                        for(a = b + 1; a < RowSize; a++)
+                        {
+                            set(a, b, get(a, b) * fDum);
+                        }
+                    }
+                }
+
+                return true;
+            }
+
+            void lubksb(const sal_uInt16 nIndex[], double fRow[]) const
+            {
+                sal_uInt16 b, ip;
+                sal_Int16 a, a2 = -1;
+                double fSum;
+
+                for(a = 0; a < RowSize; a++)
+                {
+                    ip = nIndex[a];
+                    fSum = fRow[ip];
+                    fRow[ip] = fRow[a];
+
+                    if(a2 >= 0)
+                    {
+                        for(b = a2; b < a; b++)
+                        {
+                            fSum -= get(a, b) * fRow[b];
+                        }
+                    }
+                    else if(!::basegfx::fTools::equalZero(fSum))
+                    {
+                        a2 = a;
+                    }
+
+                    fRow[a] = fSum;
+                }
+
+                for(a = (RowSize - 1); a >= 0; a--)
+                {
+                    fSum = fRow[a];
+
+                    for(b = a + 1; b < RowSize; b++)
+                    {
+                        fSum -= get(a, b) * fRow[b];
+                    }
+
+                    const double fValueAA(get(a, a));
+
+                    if(!::basegfx::fTools::equalZero(fValueAA))
+                    {
+                        fRow[a] = fSum / get(a, a);
+                    }
+                }
+            }
+
+            bool isIdentity() const
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                    {
+                        const double fDefault(implGetDefaultValue(a, b));
+                        const double fValueAB(get(a, b));
+
+                        if(!::basegfx::fTools::equal(fDefault, fValueAB))
+                        {
+                            return false;
+                        }
+                    }
+                }
+
+                return true;
+            }
+
+            bool isInvertible() const
+            {
+                ImplHomMatrixTemplate aWork(*this);
+                sal_uInt16 nIndex[RowSize];
+                sal_Int16 nParity;
+
+                return aWork.ludcmp(nIndex, nParity);
+            }
+
+            void doInvert(const ImplHomMatrixTemplate& rWork, const sal_uInt16 nIndex[])
+            {
+                double fArray[RowSize];
+
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    // prepare line
+                    sal_uInt16 b;
+                    for( b = 0; b < RowSize; b++)
+                    {
+                        fArray[b] = implGetDefaultValue(a, b);
+                    }
+
+                    // expand line
+                    rWork.lubksb(nIndex, fArray);
+
+                    // copy line transposed to this matrix
+                    for( b = 0; b < RowSize; b++)
+                    {
+                        set(b, a, fArray[b]);
+                    }
+                }
+            }
+
+            double doDeterminant() const
+            {
+                ImplHomMatrixTemplate aWork(*this);
+                sal_uInt16 nIndex[RowSize];
+                sal_Int16 nParity;
+                double fRetval(0.0);
+
+                if(aWork.ludcmp(nIndex, nParity))
+                {
+                    fRetval = static_cast<double>(nParity);
+                    for(sal_uInt16 a(0); a < RowSize; a++)
+                    {
+                        fRetval *= aWork.get(a, a);
+                    }
+                }
+
+                return fRetval;
+            }
+
+            void doAddMatrix(const ImplHomMatrixTemplate& rMat)
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                    {
+                        set(a, b, get(a, b) + rMat.get(a, b));
+                    }
+                }
+            }
+
+            void doSubMatrix(const ImplHomMatrixTemplate& rMat)
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                    {
+                        set(a, b, get(a, b) - rMat.get(a, b));
+                    }
+                }
+            }
+
+            void doMulMatrix(const double& rfValue)
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                    {
+                        set(a, b, get(a, b) * rfValue);
+                    }
+                }
+            }
+
+            void doMulMatrix(const ImplHomMatrixTemplate& rMat)
+            {
+                // create a copy as source for the original values
+                const ImplHomMatrixTemplate aCopy(*this);
+
+                // TODO: maybe optimize cases where last line is [0 0 1].
+
+                double fValue(0.0);
+
+                for(sal_uInt16 a(0); a < RowSize; ++a)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; ++b)
+                    {
+                        fValue = 0.0;
+
+                        for(sal_uInt16 c(0); c < RowSize; ++c)
+                            fValue += aCopy.get(c, b) * rMat.get(a, c);
+
+                        set(a, b, fValue);
+                    }
+                }
+            }
+
+            bool isEqual(const ImplHomMatrixTemplate& rMat) const
+            {
+                for(sal_uInt16 a(0); a < RowSize; a++)
+                {
+                    for(sal_uInt16 b(0); b < RowSize; b++)
+                    {
+                        const double fValueA(get(a, b));
+                        const double fValueB(rMat.get(a, b));
+
+                        if(!::basegfx::fTools::equal(fValueA, fValueB))
+                        {
+                            return false;
+                        }
+                    }
+                }
+
+                return true;
+            }
+        };
+
+} // namespace basegfx::internal
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */