#i97509# continued matrix tooling and adapting the usages now to all the ooo code

8 files changed, 376 insertions, 221 deletions

diff --git a/basegfx/source/matrix/b2dhommatrix.cxx b/basegfx/source/matrix/b2dhommatrix.cxx
index 352113fa8ed3..a7777352effb 100644
--- a/basegfx/source/matrix/b2dhommatrix.cxx
+++ b/basegfx/source/matrix/b2dhommatrix.cxx
@@ -36,6 +36,9 @@
 #include <hommatrixtemplate.hxx>
 #include <basegfx/tuple/b2dtuple.hxx>
 #include <basegfx/vector/b2dvector.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
+
+///////////////////////////////////////////////////////////////////////////////
 
 namespace basegfx
 {
@@ -60,6 +63,17 @@ namespace basegfx
     {
     }
 
+    B2DHomMatrix::B2DHomMatrix(double f_0x0, double f_0x1, double f_0x2, double f_1x0, double f_1x1, double f_1x2)
+    :   mpImpl( IdentityMatrix::get() ) // use common identity matrix, will be made unique with 1st set-call
+    {
+        mpImpl->set(0, 0, f_0x0);
+        mpImpl->set(0, 1, f_0x1);
+        mpImpl->set(0, 2, f_0x2);
+        mpImpl->set(1, 0, f_1x0);
+        mpImpl->set(1, 1, f_1x1);
+        mpImpl->set(1, 2, f_1x2);
+    }
+
     B2DHomMatrix& B2DHomMatrix::operator=(const B2DHomMatrix& rMat)
     {
         mpImpl = rMat.mpImpl;
@@ -81,6 +95,16 @@ namespace basegfx
         mpImpl->set(nRow, nColumn, fValue);
     }
 
+    void B2DHomMatrix::set3x2(double f_0x0, double f_0x1, double f_0x2, double f_1x0, double f_1x1, double f_1x2)
+    {
+        mpImpl->set(0, 0, f_0x0);
+        mpImpl->set(0, 1, f_0x1);
+        mpImpl->set(0, 2, f_0x2);
+        mpImpl->set(1, 0, f_1x0);
+        mpImpl->set(1, 1, f_1x1);
+        mpImpl->set(1, 2, f_1x2);
+    }
+
     bool B2DHomMatrix::isLastLineDefault() const
     {
         return mpImpl->isLastLineDefault();
@@ -206,56 +230,9 @@ namespace basegfx
         if(!fTools::equalZero(fRadiant))
         {
             double fSin(0.0);
-            double fCos(0.0);
-
-            // is the rotation angle an approximate multiple of pi/2?
-            // If yes, 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).
-            if( fTools::equalZero( fmod( fRadiant, F_PI2 ) ) )
-            {
-                // determine quadrant
-                const sal_Int32 nQuad(
-                    (4 + fround( 4/F_2PI*fmod( fRadiant, F_2PI ) )) % 4 );
-                switch( nQuad )
-                {
-                    case 0: // -2pi,0,2pi
-                        fSin = 0.0;
-                        fCos = 1.0;
-                        break;
-
-                    case 1: // -3/2pi,1/2pi
-                        fSin = 1.0;
-                        fCos = 0.0;
-                        break;
-
-                    case 2: // -pi,pi
-                        fSin = 0.0;
-                        fCos = -1.0;
-                        break;
-
-                    case 3: // -1/2pi,3/2pi
-                        fSin = -1.0;
-                        fCos = 0.0;
-                        break;
-
-                    default:
-                        OSL_ENSURE( false,
-                                    "B2DHomMatrix::rotate(): Impossible case reached" );
-                }
-            }
-            else
-            {
-                // TODO(P1): Maybe use glibc's sincos here (though
-                // that's kinda non-portable...)
-                fSin = sin(fRadiant);
-                fCos = cos(fRadiant);
-            }
+            double fCos(1.0);
 
+            tools::createSinCosOrthogonal(fSin, fCos, fRadiant);
             Impl2DHomMatrix aRotMat;
 
             aRotMat.set(0, 0, fCos);
@@ -474,104 +451,7 @@ namespace basegfx
 
         return true;
     }
-
-/* Old version: Used 3D decompose when shaer was involved and also a determinant test
-   (but only in that case). Keeping as comment since it also worked and to allow a
-   fallback in case the new version makes trouble somehow. Definitely missing in the 2nd
-   case is the sign correction for Y-Scale, this would need to be added following the above
-   pattern
-
-    bool B2DHomMatrix::decompose(B2DTuple& rScale, B2DTuple& rTranslate, double& rRotate, double& rShearX) const
-    {
-        // when perspective is used, decompose is not made here
-        if(!mpImpl->isLastLineDefault())
-            return false;
-
-        // test for rotation and shear
-        if(fTools::equalZero(get(0, 1))
-           && fTools::equalZero(get(1, 0)))
-        {
-            // no rotation and shear, direct value extraction
-            rRotate = rShearX = 0.0;
-
-            // copy scale values
-            rScale.setX(get(0, 0));
-            rScale.setY(get(1, 1));
-
-            // copy translation values
-            rTranslate.setX(get(0, 2));
-            rTranslate.setY(get(1, 2));
-
-            return true;
-        }
-        else
-        {
-            // test if shear is zero. That's the case, if the unit vectors in the matrix
-            // are perpendicular -> scalar is zero
-            const ::basegfx::B2DVector aUnitVecX(get(0, 0), get(1, 0));
-            const ::basegfx::B2DVector aUnitVecY(get(0, 1), get(1, 1));
-
-            if(fTools::equalZero(aUnitVecX.scalar(aUnitVecY)))
-            {
-                // no shear, direct value extraction
-                rShearX = 0.0;
-
-                // calculate rotation
-                rShearX = 0.0;
-                rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
-
-                // calculate scale values
-                rScale.setX(aUnitVecX.getLength());
-                rScale.setY(aUnitVecY.getLength());
-
-                // copy translation values
-                rTranslate.setX(get(0, 2));
-                rTranslate.setY(get(1, 2));
-
-                return true;
-            }
-            else
-            {
-                // If determinant is zero, decomposition is not possible
-                if(0.0 == determinant())
-                    return false;
-
-                // copy 2x2 matrix and translate vector to 3x3 matrix
-                ::basegfx::B3DHomMatrix a3DHomMat;
-
-                a3DHomMat.set(0, 0, get(0, 0));
-                a3DHomMat.set(0, 1, get(0, 1));
-                a3DHomMat.set(1, 0, get(1, 0));
-                a3DHomMat.set(1, 1, get(1, 1));
-                a3DHomMat.set(0, 3, get(0, 2));
-                a3DHomMat.set(1, 3, get(1, 2));
-
-                ::basegfx::B3DTuple r3DScale, r3DTranslate, r3DRotate, r3DShear;
-
-                if(a3DHomMat.decompose(r3DScale, r3DTranslate, r3DRotate, r3DShear))
-                {
-                    // copy scale values
-                    rScale.setX(r3DScale.getX());
-                    rScale.setY(r3DScale.getY());
-
-                    // copy shear
-                    rShearX = r3DShear.getX();
-
-                    // copy rotate
-                    rRotate = r3DRotate.getZ();
-
-                    // copy translate
-                    rTranslate.setX(r3DTranslate.getX());
-                    rTranslate.setY(r3DTranslate.getY());
-
-                    return true;
-                }
-            }
-        }
-
-        return false;
-    } */
-
 } // end of namespace basegfx
 
+///////////////////////////////////////////////////////////////////////////////
 // eof
diff --git a/basegfx/source/matrix/b2dhommatrixtools.cxx b/basegfx/source/matrix/b2dhommatrixtools.cxx
index 59a1ff432fc7..c9c3180d3e4a 100644
--- a/basegfx/source/matrix/b2dhommatrixtools.cxx
+++ b/basegfx/source/matrix/b2dhommatrixtools.cxx
@@ -38,6 +38,330 @@
 
 namespace basegfx
 {
+    namespace tools
+    {
+        void createSinCosOrthogonal(double& o_rSin, double& o_rCos, double fRadiant)
+        {
+            if( fTools::equalZero( fmod( fRadiant, F_PI2 ) ) )
+            {
+                // determine quadrant
+                const sal_Int32 nQuad(
+                    (4 + fround( 4/F_2PI*fmod( fRadiant, F_2PI ) )) % 4 );
+                switch( nQuad )
+                {
+                    case 0: // -2pi,0,2pi
+                        o_rSin = 0.0;
+                        o_rCos = 1.0;
+                        break;
+
+                    case 1: // -3/2pi,1/2pi
+                        o_rSin = 1.0;
+                        o_rCos = 0.0;
+                        break;
+
+                    case 2: // -pi,pi
+                        o_rSin = 0.0;
+                        o_rCos = -1.0;
+                        break;
+
+                    case 3: // -1/2pi,3/2pi
+                        o_rSin = -1.0;
+                        o_rCos = 0.0;
+                        break;
+
+                    default:
+                        OSL_ENSURE( false, "createSinCos: Impossible case reached" );
+                }
+            }
+            else
+            {
+                // TODO(P1): Maybe use glibc's sincos here (though
+                // that's kinda non-portable...)
+                o_rSin = sin(fRadiant);
+                o_rCos = cos(fRadiant);
+            }
+        }
+
+        B2DHomMatrix createScaleB2DHomMatrix(double fScaleX, double fScaleY)
+        {
+            B2DHomMatrix aRetval;
+            const double fOne(1.0);
+
+            if(!fTools::equal(fScaleX, fOne))
+            {
+                aRetval.set(0, 0, fScaleX);
+            }
+
+            if(!fTools::equal(fScaleY, fOne))
+            {
+                aRetval.set(1, 1, fScaleY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createShearXB2DHomMatrix(double fShearX)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fShearX))
+            {
+                aRetval.set(0, 1, fShearX);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createShearYB2DHomMatrix(double fShearY)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fShearY))
+            {
+                aRetval.set(1, 0, fShearY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createRotateB2DHomMatrix(double fRadiant)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fRadiant))
+            {
+                double fSin(0.0);
+                double fCos(1.0);
+
+                createSinCosOrthogonal(fSin, fCos, fRadiant);
+                aRetval.set(0, 0, fCos);
+                aRetval.set(1, 1, fCos);
+                aRetval.set(1, 0, fSin);
+                aRetval.set(0, 1, -fSin);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createTranslateB2DHomMatrix(double fTranslateX, double fTranslateY)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!(fTools::equalZero(fTranslateX) && fTools::equalZero(fTranslateY)))
+            {
+                aRetval.set(0, 2, fTranslateX);
+                aRetval.set(1, 2, fTranslateY);
+            }
+
+            return aRetval;
+        }
+
+        B2DHomMatrix createScaleShearXRotateTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY)
+        {
+            const double fOne(1.0);
+
+            if(fTools::equal(fScaleX, fOne) && fTools::equal(fScaleY, fOne))
+            {
+                /// no scale, take shortcut
+                return createShearXRotateTranslateB2DHomMatrix(fShearX, fRadiant, fTranslateX, fTranslateY);
+            }
+            else
+            {
+                /// scale used
+                if(fTools::equalZero(fShearX))
+                {
+                    /// no shear
+                    if(fTools::equalZero(fRadiant))
+                    {
+                        /// no rotate, take shortcut
+                        return createScaleTranslateB2DHomMatrix(fScaleX, fScaleY, fTranslateX, fTranslateY);
+                    }
+                    else
+                    {
+                        /// rotate and scale used, no shear
+                        double fSin(0.0);
+                        double fCos(1.0);
+
+                        createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fCos * fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * -fSin,
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ fSin * fScaleX,
+                            /* Row 1, Column 1 */ fScaleY * fCos,
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                }
+                else
+                {
+                    /// scale and shear used
+                    if(fTools::equalZero(fRadiant))
+                    {
+                        /// scale and shear, but no rotate
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * fShearX,
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ 0.0,
+                            /* Row 1, Column 1 */ fScaleY,
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                    else
+                    {
+                        /// scale, shear and rotate used
+                        double fSin(0.0);
+                        double fCos(1.0);
+
+                        createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                        B2DHomMatrix aRetval(
+                            /* Row 0, Column 0 */ fCos * fScaleX,
+                            /* Row 0, Column 1 */ fScaleY * ((fCos * fShearX) - fSin),
+                            /* Row 0, Column 2 */ fTranslateX,
+                            /* Row 1, Column 0 */ fSin * fScaleX,
+                            /* Row 1, Column 1 */ fScaleY * ((fSin * fShearX) + fCos),
+                            /* Row 1, Column 2 */ fTranslateY);
+
+                        return aRetval;
+                    }
+                }
+            }
+        }
+
+        B2DHomMatrix createShearXRotateTranslateB2DHomMatrix(
+            double fShearX,
+            double fRadiant,
+            double fTranslateX, double fTranslateY)
+        {
+            if(fTools::equalZero(fShearX))
+            {
+                /// no shear
+                if(fTools::equalZero(fRadiant))
+                {
+                    /// no shear, no rotate, take shortcut
+                    return createTranslateB2DHomMatrix(fTranslateX, fTranslateY);
+                }
+                else
+                {
+                    /// no shear, but rotate used
+                    double fSin(0.0);
+                    double fCos(1.0);
+
+                    createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fCos,
+                        /* Row 0, Column 1 */ -fSin,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ fSin,
+                        /* Row 1, Column 1 */ fCos,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+            else
+            {
+                /// shear used
+                if(fTools::equalZero(fRadiant))
+                {
+                    /// no rotate, but shear used
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ 1.0,
+                        /* Row 0, Column 1 */ fShearX,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ 0.0,
+                        /* Row 1, Column 1 */ 1.0,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+                else
+                {
+                    /// shear and rotate used
+                    double fSin(0.0);
+                    double fCos(1.0);
+
+                    createSinCosOrthogonal(fSin, fCos, fRadiant);
+
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fCos,
+                        /* Row 0, Column 1 */ (fCos * fShearX) - fSin,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ fSin,
+                        /* Row 1, Column 1 */ (fSin * fShearX) + fCos,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+        }
+
+        B2DHomMatrix createScaleTranslateB2DHomMatrix(
+            double fScaleX, double fScaleY,
+            double fTranslateX, double fTranslateY)
+        {
+            const double fOne(1.0);
+
+            if(fTools::equal(fScaleX, fOne) && fTools::equal(fScaleY, fOne))
+            {
+                /// no scale, take shortcut
+                return createTranslateB2DHomMatrix(fTranslateX, fTranslateY);
+            }
+            else
+            {
+                /// scale used
+                if(fTools::equalZero(fTranslateX) && fTools::equalZero(fTranslateY))
+                {
+                    /// no translate, but scale.
+                    B2DHomMatrix aRetval;
+
+                    aRetval.set(0, 0, fScaleX);
+                    aRetval.set(1, 1, fScaleY);
+
+                    return aRetval;
+                }
+                else
+                {
+                    /// translate and scale
+                    B2DHomMatrix aRetval(
+                        /* Row 0, Column 0 */ fScaleX,
+                        /* Row 0, Column 1 */ 0.0,
+                        /* Row 0, Column 2 */ fTranslateX,
+                        /* Row 1, Column 0 */ 0.0,
+                        /* Row 1, Column 1 */ fScaleY,
+                        /* Row 1, Column 2 */ fTranslateY);
+
+                    return aRetval;
+                }
+            }
+        }
+
+        B2DHomMatrix createRotateAroundPoint(
+            double fPointX, double fPointY,
+            double fRadiant)
+        {
+            B2DHomMatrix aRetval;
+
+            if(!fTools::equalZero(fRadiant))
+            {
+                aRetval = createTranslateB2DHomMatrix(-fPointX, -fPointY);
+                aRetval.rotate(fRadiant);
+                aRetval.translate(fPointX, fPointY);
+            }
+
+            return aRetval;
+        }
+    } // end of namespace tools
 } // end of namespace basegfx
 
 ///////////////////////////////////////////////////////////////////////////////
diff --git a/basegfx/source/polygon/b2dlinegeometry.cxx b/basegfx/source/polygon/b2dlinegeometry.cxx
index 1a9264ab769e..c22b5ea94011 100644
--- a/basegfx/source/polygon/b2dlinegeometry.cxx
+++ b/basegfx/source/polygon/b2dlinegeometry.cxx
@@ -40,6 +40,7 @@
 #include <basegfx/range/b2drange.hxx>
 #include <basegfx/matrix/b2dhommatrix.hxx>
 #include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 
 //////////////////////////////////////////////////////////////////////////////
 
@@ -85,11 +86,9 @@ namespace basegfx
                 // get size of the arrow
                 const B2DRange aArrowSize(getRange(rArrow));
 
-                // build ArrowTransform
-                B2DHomMatrix aArrowTransform;
-
-                // center in X, align with axis in Y
-                aArrowTransform.translate(-aArrowSize.getCenter().getX(), -aArrowSize.getMinimum().getY());
+                // build ArrowTransform; center in X, align with axis in Y
+                B2DHomMatrix aArrowTransform(basegfx::tools::createTranslateB2DHomMatrix(
+                    -aArrowSize.getCenter().getX(), -aArrowSize.getMinimum().getY()));
 
                 // scale to target size
                 const double fArrowScale(fWidth / (aArrowSize.getRange().getX()));
diff --git a/basegfx/source/polygon/b2dpolygonclipper.cxx b/basegfx/source/polygon/b2dpolygonclipper.cxx
index f0d325942c07..87e44ed3d063 100644
--- a/basegfx/source/polygon/b2dpolygonclipper.cxx
+++ b/basegfx/source/polygon/b2dpolygonclipper.cxx
@@ -40,6 +40,7 @@
 #include <basegfx/polygon/b2dpolypolygontools.hxx>
 #include <basegfx/curve/b2dcubicbezier.hxx>
 #include <basegfx/tools/rectcliptools.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 
 //////////////////////////////////////////////////////////////////////////////
 
@@ -361,11 +362,10 @@ namespace basegfx
             else if(rCandidate.count())
             {
                 const B2DVector aEdge(rPointB - rPointA);
-                B2DHomMatrix aMatrixTransform;
                 B2DPolygon aCandidate(rCandidate);
 
                 // translate and rotate polygon so that given edge is on x axis
-                aMatrixTransform.translate(-rPointA.getX(), -rPointA.getY());
+                B2DHomMatrix aMatrixTransform(basegfx::tools::createTranslateB2DHomMatrix(-rPointA.getX(), -rPointA.getY()));
                 aMatrixTransform.rotate(-atan2(aEdge.getY(), aEdge.getX()));
                 aCandidate.transform(aMatrixTransform);
 
@@ -395,11 +395,10 @@ namespace basegfx
             else if(rCandidate.count())
             {
                 const B2DVector aEdge(rPointB - rPointA);
-                B2DHomMatrix aMatrixTransform;
                 B2DPolyPolygon aCandidate(rCandidate);
 
                 // translate and rotate polygon so that given edge is on x axis
-                aMatrixTransform.translate(-rPointA.getX(), -rPointA.getY());
+                B2DHomMatrix aMatrixTransform(basegfx::tools::createTranslateB2DHomMatrix(-rPointA.getX(), -rPointA.getY()));
                 aMatrixTransform.rotate(-atan2(aEdge.getY(), aEdge.getX()));
                 aCandidate.transform(aMatrixTransform);
 
diff --git a/basegfx/source/polygon/b2dpolygontools.cxx b/basegfx/source/polygon/b2dpolygontools.cxx
index c1e5dc80d8c4..6e288786df6d 100644
--- a/basegfx/source/polygon/b2dpolygontools.cxx
+++ b/basegfx/source/polygon/b2dpolygontools.cxx
@@ -34,7 +34,6 @@
 #include <basegfx/polygon/b2dpolygontools.hxx>
 #include <osl/diagnose.h>
 #include <rtl/math.hxx>
-
 #include <basegfx/polygon/b2dpolygon.hxx>
 #include <basegfx/polygon/b2dpolypolygon.hxx>
 #include <basegfx/range/b2drange.hxx>
@@ -44,6 +43,7 @@
 #include <basegfx/matrix/b3dhommatrix.hxx>
 #include <basegfx/matrix/b2dhommatrix.hxx>
 #include <basegfx/curve/b2dbeziertools.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 
 #include <numeric>
 #include <limits>
@@ -1887,29 +1887,10 @@ namespace basegfx
 
         B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY )
         {
-            const double fOne(1.0);
             B2DPolygon aRetval(createPolygonFromUnitCircle());
+            const B2DHomMatrix aMatrix(createScaleTranslateB2DHomMatrix(fRadiusX, fRadiusY, rCenter.getX(), rCenter.getY()));
 
-            // transformation necessary?
-            const sal_Bool bScale(!fTools::equal(fRadiusX, fOne) || !fTools::equal(fRadiusY, fOne));
-            const sal_Bool bTranslate(!rCenter.equalZero());
-
-            if(bScale || bTranslate)
-            {
-                B2DHomMatrix aMatrix;
-
-                if(bScale)
-                {
-                    aMatrix.scale(fRadiusX, fRadiusY);
-                }
-
-                if(bTranslate)
-                {
-                    aMatrix.translate(rCenter.getX(), rCenter.getY());
-                }
-
-                aRetval.transform(aMatrix);
-            }
+            aRetval.transform(aMatrix);
 
             return aRetval;
         }
@@ -2050,28 +2031,9 @@ namespace basegfx
         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()));
 
-            // transformation necessary?
-            const double fOne(1.0);
-            const sal_Bool bScale(!fTools::equal(fRadiusX, fOne) || !fTools::equal(fRadiusY, fOne));
-            const sal_Bool bTranslate(!rCenter.equalZero());
-
-            if(bScale || bTranslate)
-            {
-                B2DHomMatrix aMatrix;
-
-                if(bScale)
-                {
-                    aMatrix.scale(fRadiusX, fRadiusY);
-                }
-
-                if(bTranslate)
-                {
-                    aMatrix.translate(rCenter.getX(), rCenter.getY());
-                }
-
-                aRetval.transform(aMatrix);
-            }
+            aRetval.transform(aMatrix);
 
             return aRetval;
         }
@@ -2701,11 +2663,7 @@ namespace basegfx
 
             if(nPointCount)
             {
-                B2DHomMatrix aMatrix;
-
-                aMatrix.translate(-rCenter.getX(), -rCenter.getY());
-                aMatrix.rotate(fAngle);
-                aMatrix.translate(rCenter.getX(), rCenter.getY());
+                const B2DHomMatrix aMatrix(basegfx::tools::createRotateAroundPoint(rCenter, fAngle));
 
                 aRetval.transform(aMatrix);
             }
diff --git a/basegfx/source/polygon/b2dsvgpolypolygon.cxx b/basegfx/source/polygon/b2dsvgpolypolygon.cxx
index 2247c237d90f..e38ec3809fb1 100644
--- a/basegfx/source/polygon/b2dsvgpolypolygon.cxx
+++ b/basegfx/source/polygon/b2dsvgpolypolygon.cxx
@@ -36,6 +36,7 @@
 #include <basegfx/polygon/b2dpolygontools.hxx>
 #include <basegfx/polygon/b2dpolypolygon.hxx>
 #include <basegfx/matrix/b2dhommatrix.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 #include <rtl/ustring.hxx>
 #include <rtl/math.hxx>
 
@@ -705,7 +706,7 @@ namespace basegfx
                                 // |y1'| = |-sin phi  cos phi|  |(y1 - y2)/2|
                                 const B2DPoint p1(nLastX, nLastY);
                                 const B2DPoint p2(nX, nY);
-                                B2DHomMatrix aTransform; aTransform.rotate(-fPhi*M_PI/180);
+                                B2DHomMatrix aTransform(basegfx::tools::createRotateB2DHomMatrix(-fPhi*M_PI/180));
 
                                 const B2DPoint p1_prime( aTransform * B2DPoint(((p1-p2)/2.0)) );
 
@@ -797,8 +798,7 @@ namespace basegfx
                                         fTheta1, fTheta2 ));
 
                                 // transform ellipse by rotation & move to final center
-                                aTransform.identity();
-                                aTransform.scale(fRX,fRY);
+                                aTransform = basegfx::tools::createScaleB2DHomMatrix(fRX, fRY);
                                 aTransform.translate(aCenter_prime.getX(),
                                                      aCenter_prime.getY());
                                 aTransform.rotate(fPhi*M_PI/180);
diff --git a/basegfx/source/tools/gradienttools.cxx b/basegfx/source/tools/gradienttools.cxx
index 9e78039cd590..51989899ebf4 100644
--- a/basegfx/source/tools/gradienttools.cxx
+++ b/basegfx/source/tools/gradienttools.cxx
@@ -32,9 +32,9 @@
 #include "precompiled_basegfx.hxx"
 
 #include <basegfx/tools/gradienttools.hxx>
-
 #include <basegfx/point/b2dpoint.hxx>
 #include <basegfx/range/b2drange.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 
 namespace basegfx
 {
@@ -79,9 +79,8 @@ namespace basegfx
             B2DPoint aCenter(0.5, 0.5);
             aCenter *= o_rGradientInfo.maTextureTransform;
 
-            o_rGradientInfo.maTextureTransform.translate(-aCenter.getX(), -aCenter.getY());
-            o_rGradientInfo.maTextureTransform.rotate(fAngle);
-            o_rGradientInfo.maTextureTransform.translate(aCenter.getX(), aCenter.getY());
+            o_rGradientInfo.maTextureTransform = basegfx::tools::createRotateAroundPoint(aCenter, fAngle)
+                * o_rGradientInfo.maTextureTransform;
         }
 
         // add object translate
@@ -158,9 +157,8 @@ namespace basegfx
                 B2DPoint aCenter(0.5, 0.5);
                 aCenter *= o_rGradientInfo.maTextureTransform;
 
-                o_rGradientInfo.maTextureTransform.translate(-aCenter.getX(), -aCenter.getY());
-                o_rGradientInfo.maTextureTransform.rotate(fAngle);
-                o_rGradientInfo.maTextureTransform.translate(aCenter.getX(), aCenter.getY());
+                o_rGradientInfo.maTextureTransform = basegfx::tools::createRotateAroundPoint(aCenter, fAngle)
+                    * o_rGradientInfo.maTextureTransform;
             }
         }
 
@@ -232,9 +230,8 @@ namespace basegfx
             B2DPoint aCenter(0.5, 0.5);
             aCenter *= o_rGradientInfo.maTextureTransform;
 
-            o_rGradientInfo.maTextureTransform.translate(-aCenter.getX(), -aCenter.getY());
-            o_rGradientInfo.maTextureTransform.rotate(fAngle);
-            o_rGradientInfo.maTextureTransform.translate(aCenter.getX(), aCenter.getY());
+            o_rGradientInfo.maTextureTransform = basegfx::tools::createRotateAroundPoint(aCenter, fAngle)
+                * o_rGradientInfo.maTextureTransform;
         }
 
         // add defined offsets after rotation
diff --git a/basegfx/source/tools/unopolypolygon.cxx b/basegfx/source/tools/unopolypolygon.cxx
index 6d8fcd83edb0..05dbe5b1c823 100755
--- a/basegfx/source/tools/unopolypolygon.cxx
+++ b/basegfx/source/tools/unopolypolygon.cxx
@@ -44,8 +44,8 @@
 #include <basegfx/tools/canvastools.hxx>
 #include <basegfx/polygon/b2dpolygon.hxx>
 #include <basegfx/polygon/b2dpolypolygontools.hxx>
-
 #include <basegfx/tools/unopolypolygon.hxx>
+#include <basegfx/matrix/b2dhommatrixtools.hxx>
 
 
 using namespace ::com::sun::star;
@@ -138,9 +138,7 @@ namespace unotools
 
         if( !aOffset.equalZero() )
         {
-            B2DHomMatrix aTranslate;
-            aTranslate.translate( aOffset.getX(), aOffset.getY() );
-
+            const B2DHomMatrix aTranslate(tools::createTranslateB2DHomMatrix(aOffset));
             aSrcPoly.transform( aTranslate );
         }