AOO410/main/basegfx/source/matrix/b2dhommatrix.cxx - openoffice - Git at Google

 /**************************************************************
  *
  * 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
  *
  * Unless required by applicable law or agreed to in writing,
  * software distributed under the License is distributed on an
  * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
  * KIND, either express or implied.  See the License for the
  * specific language governing permissions and limitations
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 // MARKER(update_precomp.py): autogen include statement, do not remove
 #include "precompiled_basegfx.hxx"
 #include <osl/diagnose.h>
 #include <rtl/instance.hxx>
 #include <basegfx/matrix/b2dhommatrix.hxx>
 #include <hommatrixtemplate.hxx>
 #include <basegfx/tuple/b2dtuple.hxx>
 #include <basegfx/vector/b2dvector.hxx>
 #include <basegfx/matrix/b2dhommatrixtools.hxx>

 ///////////////////////////////////////////////////////////////////////////////

 namespace basegfx
 {
     class Impl2DHomMatrix : public ::basegfx::internal::ImplHomMatrixTemplate< 3 >
     {
     };

     namespace { struct IdentityMatrix : public rtl::Static< B2DHomMatrix::ImplType,
                                                             IdentityMatrix > {}; }

 	B2DHomMatrix::B2DHomMatrix() :
         mpImpl( IdentityMatrix::get() ) // use common identity matrix
 	{
 	}

 	B2DHomMatrix::B2DHomMatrix(const B2DHomMatrix& rMat) :
         mpImpl(rMat.mpImpl)
 	{
 	}

 	B2DHomMatrix::~B2DHomMatrix()
 	{
 	}

 	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;
 		return *this;
 	}

     void B2DHomMatrix::makeUnique()
     {
         mpImpl.make_unique();
     }

 	double B2DHomMatrix::get(sal_uInt16 nRow, sal_uInt16 nColumn) const
 	{
 		return mpImpl->get(nRow, nColumn);
 	}

 	void B2DHomMatrix::set(sal_uInt16 nRow, sal_uInt16 nColumn, double fValue)
 	{
 		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();
 	}

 	bool B2DHomMatrix::isIdentity() const
 	{
 		if(mpImpl.same_object(IdentityMatrix::get()))
 			return true;

 		return mpImpl->isIdentity();
 	}

 	void B2DHomMatrix::identity()
 	{
         mpImpl = IdentityMatrix::get();
 	}

 	bool B2DHomMatrix::isInvertible() const
 	{
 		return mpImpl->isInvertible();
 	}

 	bool B2DHomMatrix::invert()
 	{
 		Impl2DHomMatrix aWork(*mpImpl);
 		sal_uInt16* pIndex = new sal_uInt16[mpImpl->getEdgeLength()];
 		sal_Int16 nParity;

 		if(aWork.ludcmp(pIndex, nParity))
 		{
 			mpImpl->doInvert(aWork, pIndex);
 			delete[] pIndex;

 			return true;
 		}

 		delete[] pIndex;
 		return false;
 	}

 	bool B2DHomMatrix::isNormalized() const
 	{
 		return mpImpl->isNormalized();
 	}

 	void B2DHomMatrix::normalize()
 	{
 		if(!const_cast<const B2DHomMatrix*>(this)->mpImpl->isNormalized())
 			mpImpl->doNormalize();
 	}

 	double B2DHomMatrix::determinant() const
 	{
 		return mpImpl->doDeterminant();
 	}

 	double B2DHomMatrix::trace() const
 	{
 		return mpImpl->doTrace();
 	}

 	void B2DHomMatrix::transpose()
 	{
 		mpImpl->doTranspose();
 	}

 	B2DHomMatrix& B2DHomMatrix::operator+=(const B2DHomMatrix& rMat)
 	{
 		mpImpl->doAddMatrix(*rMat.mpImpl);
 		return *this;
 	}

 	B2DHomMatrix& B2DHomMatrix::operator-=(const B2DHomMatrix& rMat)
 	{
 		mpImpl->doSubMatrix(*rMat.mpImpl);
 		return *this;
 	}

 	B2DHomMatrix& B2DHomMatrix::operator*=(double fValue)
 	{
 		const double fOne(1.0);

 		if(!fTools::equal(fOne, fValue))
 			mpImpl->doMulMatrix(fValue);

 		return *this;
 	}

 	B2DHomMatrix& B2DHomMatrix::operator/=(double fValue)
 	{
 		const double fOne(1.0);

 		if(!fTools::equal(fOne, fValue))
 			mpImpl->doMulMatrix(1.0 / fValue);

 		return *this;
 	}

 	B2DHomMatrix& B2DHomMatrix::operator*=(const B2DHomMatrix& rMat)
 	{
 		if(!rMat.isIdentity())
 			mpImpl->doMulMatrix(*rMat.mpImpl);

 		return *this;
 	}

 	bool B2DHomMatrix::operator==(const B2DHomMatrix& rMat) const
 	{
 		if(mpImpl.same_object(rMat.mpImpl))
 			return true;

 		return mpImpl->isEqual(*rMat.mpImpl);
 	}

 	bool B2DHomMatrix::operator!=(const B2DHomMatrix& rMat) const
 	{
         return !(*this == rMat);
 	}

 	void B2DHomMatrix::rotate(double fRadiant)
 	{
 		if(!fTools::equalZero(fRadiant))
 		{
 			double fSin(0.0);
 			double fCos(1.0);

 			tools::createSinCosOrthogonal(fSin, fCos, fRadiant);
 			Impl2DHomMatrix aRotMat;

 			aRotMat.set(0, 0, fCos);
 			aRotMat.set(1, 1, fCos);
 			aRotMat.set(1, 0, fSin);
 			aRotMat.set(0, 1, -fSin);

 			mpImpl->doMulMatrix(aRotMat);
 		}
 	}

 	void B2DHomMatrix::translate(double fX, double fY)
 	{
 		if(!fTools::equalZero(fX) || !fTools::equalZero(fY))
 		{
 			Impl2DHomMatrix aTransMat;

 			aTransMat.set(0, 2, fX);
 			aTransMat.set(1, 2, fY);

 			mpImpl->doMulMatrix(aTransMat);
 		}
 	}

 	void B2DHomMatrix::scale(double fX, double fY)
 	{
 		const double fOne(1.0);

 		if(!fTools::equal(fOne, fX) || !fTools::equal(fOne, fY))
 		{
 			Impl2DHomMatrix aScaleMat;

 			aScaleMat.set(0, 0, fX);
 			aScaleMat.set(1, 1, fY);

 			mpImpl->doMulMatrix(aScaleMat);
 		}
 	}

 	void B2DHomMatrix::shearX(double fSx)
 	{
 		// #i76239# do not test againt 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
 		if(!fTools::equalZero(fSx))
 		{
 			Impl2DHomMatrix aShearXMat;

 			aShearXMat.set(0, 1, fSx);

 			mpImpl->doMulMatrix(aShearXMat);
 		}
 	}

 	void B2DHomMatrix::shearY(double fSy)
 	{
 		// #i76239# do not test againt 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
 		if(!fTools::equalZero(fSy))
 		{
 			Impl2DHomMatrix aShearYMat;

 			aShearYMat.set(1, 0, fSy);

 			mpImpl->doMulMatrix(aShearYMat);
 		}
 	}

 	/** Decomposition

 	   New, optimized version with local shearX detection. Old version (keeping
 	   below, is working well, too) used the 3D matrix decomposition when
 	   shear was used. Keeping old version as comment below since it may get
 	   necessary to add the determinant() test from there here, too.
 	*/
 	bool B2DHomMatrix::decompose(B2DTuple& rScale, B2DTuple& rTranslate, double& rRotate, double& rShearX) const
 	{
 		// when perspective is used, decompose is not made here
 		if(!mpImpl->isLastLineDefault())
 		{
 			return false;
 		}

 		// reset rotate and shear and copy translation values in every case
 		rRotate = rShearX = 0.0;
 		rTranslate.setX(get(0, 2));
 		rTranslate.setY(get(1, 2));

 		// test for rotation and shear
 		if(fTools::equalZero(get(0, 1)) && fTools::equalZero(get(1, 0)))
 		{
 			// no rotation and shear, copy scale values
 			rScale.setX(get(0, 0));
 			rScale.setY(get(1, 1));
 		}
 		else
 		{
 			// get the unit vectors of the transformation -> the perpendicular vectors
 			B2DVector aUnitVecX(get(0, 0), get(1, 0));
 			B2DVector aUnitVecY(get(0, 1), get(1, 1));
 			const double fScalarXY(aUnitVecX.scalar(aUnitVecY));

 			// Test if shear is zero. That's the case if the unit vectors in the matrix
 			// are perpendicular -> scalar is zero. This is also the case when one of
 			// the unit vectors is zero.
 			if(fTools::equalZero(fScalarXY))
 			{
 				// calculate unsigned scale values
 				rScale.setX(aUnitVecX.getLength());
 				rScale.setY(aUnitVecY.getLength());

 				// check unit vectors for zero lengths
 				const bool bXIsZero(fTools::equalZero(rScale.getX()));
 				const bool bYIsZero(fTools::equalZero(rScale.getY()));

 				if(bXIsZero || bYIsZero)
 				{
 					// still extract as much as possible. Scalings are already set
 					if(!bXIsZero)
 					{
 						// get rotation of X-Axis
 						rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
 					}
 					else if(!bYIsZero)
 					{
 						// get rotation of X-Axis. When assuming X and Y perpendicular
 						// and correct rotation, it's the Y-Axis rotation minus 90 degrees
 						rRotate = atan2(aUnitVecY.getY(), aUnitVecY.getX()) - M_PI_2;
 					}

 					// one or both unit vectors do not extist, determinant is zero, no decomposition possible.
 					// Eventually used rotations or shears are lost
 					return false;
 				}
 				else
 				{
 					// no shear
 					// calculate rotation of X unit vector relative to (1, 0)
 					rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());

 					// use orientation to evtl. correct sign of Y-Scale
 					const double fCrossXY(aUnitVecX.cross(aUnitVecY));

 					if(fCrossXY < 0.0)
 					{
 						rScale.setY(-rScale.getY());
 					}
 				}
 			}
 			else
 			{
 				// fScalarXY is not zero, thus both unit vectors exist. No need to handle that here
 				// shear, extract it
 				double fCrossXY(aUnitVecX.cross(aUnitVecY));

 				// get rotation by calculating angle of X unit vector relative to (1, 0).
 				// This is before the parallell test following the motto to extract
 				// as much as possible
 				rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());

 				// get unsigned scale value for X. It will not change and is useful
 				// for further corrections
 				rScale.setX(aUnitVecX.getLength());

 				if(fTools::equalZero(fCrossXY))
 				{
 					// extract as much as possible
 					rScale.setY(aUnitVecY.getLength());

 					// unit vectors are parallel, thus not linear independent. No
 					// useful decomposition possible. This should not happen since
 					// the only way to get the unit vectors nearly parallell is
 					// a very big shearing. Anyways, be prepared for hand-filled
 					// matrices
 					// Eventually used rotations or shears are lost
 					return false;
 				}
 				else
 				{
 					// calculate the contained shear
 					rShearX = fScalarXY / fCrossXY;

 					if(!fTools::equalZero(rRotate))
 					{
 						// To be able to correct the shear for aUnitVecY, rotation needs to be
 						// removed first. Correction of aUnitVecX is easy, it will be rotated back to (1, 0).
 						aUnitVecX.setX(rScale.getX());
 						aUnitVecX.setY(0.0);

 						// for Y correction we rotate the UnitVecY back about -rRotate
 						const double fNegRotate(-rRotate);
 						const double fSin(sin(fNegRotate));
 						const double fCos(cos(fNegRotate));

 						const double fNewX(aUnitVecY.getX() * fCos - aUnitVecY.getY() * fSin);
 						const double fNewY(aUnitVecY.getX() * fSin + aUnitVecY.getY() * fCos);

 						aUnitVecY.setX(fNewX);
 						aUnitVecY.setY(fNewY);
 					}

 					// Correct aUnitVecY and fCrossXY to fShear=0. Rotation is already removed.
 					// Shear correction can only work with removed rotation
 					aUnitVecY.setX(aUnitVecY.getX() - (aUnitVecY.getY() * rShearX));
 					fCrossXY = aUnitVecX.cross(aUnitVecY);

 					// calculate unsigned scale value for Y, after the corrections since
 					// the shear correction WILL change the length of aUnitVecY
 					rScale.setY(aUnitVecY.getLength());

 					// use orientation to set sign of Y-Scale
 					if(fCrossXY < 0.0)
 					{
 						rScale.setY(-rScale.getY());
 					}
 				}
 			}
 		}

 		return true;
 	}
 } // end of namespace basegfx

 ///////////////////////////////////////////////////////////////////////////////
 // eof
	/**************************************************************
	*
	* 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
	*
	* Unless required by applicable law or agreed to in writing,
	* software distributed under the License is distributed on an
	* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
	* KIND, either express or implied. See the License for the
	* specific language governing permissions and limitations
	* under the License.
	*
	*************************************************************/



	// MARKER(update_precomp.py): autogen include statement, do not remove
	#include "precompiled_basegfx.hxx"
	#include <osl/diagnose.h>
	#include <rtl/instance.hxx>
	#include <basegfx/matrix/b2dhommatrix.hxx>
	#include <hommatrixtemplate.hxx>
	#include <basegfx/tuple/b2dtuple.hxx>
	#include <basegfx/vector/b2dvector.hxx>
	#include <basegfx/matrix/b2dhommatrixtools.hxx>

	///////////////////////////////////////////////////////////////////////////////

	namespace basegfx
	{
	class Impl2DHomMatrix : public ::basegfx::internal::ImplHomMatrixTemplate< 3 >
	{
	};

	namespace { struct IdentityMatrix : public rtl::Static< B2DHomMatrix::ImplType,
	IdentityMatrix > {}; }

	B2DHomMatrix::B2DHomMatrix() :
	mpImpl( IdentityMatrix::get() ) // use common identity matrix
	{
	}

	B2DHomMatrix::B2DHomMatrix(const B2DHomMatrix& rMat) :
	mpImpl(rMat.mpImpl)
	{
	}

	B2DHomMatrix::~B2DHomMatrix()
	{
	}

	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;
	return *this;
	}

	void B2DHomMatrix::makeUnique()
	{
	mpImpl.make_unique();
	}

	double B2DHomMatrix::get(sal_uInt16 nRow, sal_uInt16 nColumn) const
	{
	return mpImpl->get(nRow, nColumn);
	}

	void B2DHomMatrix::set(sal_uInt16 nRow, sal_uInt16 nColumn, double fValue)
	{
	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();
	}

	bool B2DHomMatrix::isIdentity() const
	{
	if(mpImpl.same_object(IdentityMatrix::get()))
	return true;

	return mpImpl->isIdentity();
	}

	void B2DHomMatrix::identity()
	{
	mpImpl = IdentityMatrix::get();
	}

	bool B2DHomMatrix::isInvertible() const
	{
	return mpImpl->isInvertible();
	}

	bool B2DHomMatrix::invert()
	{
	Impl2DHomMatrix aWork(*mpImpl);
	sal_uInt16* pIndex = new sal_uInt16[mpImpl->getEdgeLength()];
	sal_Int16 nParity;

	if(aWork.ludcmp(pIndex, nParity))
	{
	mpImpl->doInvert(aWork, pIndex);
	delete[] pIndex;

	return true;
	}

	delete[] pIndex;
	return false;
	}

	bool B2DHomMatrix::isNormalized() const
	{
	return mpImpl->isNormalized();
	}

	void B2DHomMatrix::normalize()
	{
	if(!const_cast<const B2DHomMatrix*>(this)->mpImpl->isNormalized())
	mpImpl->doNormalize();
	}

	double B2DHomMatrix::determinant() const
	{
	return mpImpl->doDeterminant();
	}

	double B2DHomMatrix::trace() const
	{
	return mpImpl->doTrace();
	}

	void B2DHomMatrix::transpose()
	{
	mpImpl->doTranspose();
	}

	B2DHomMatrix& B2DHomMatrix::operator+=(const B2DHomMatrix& rMat)
	{
	mpImpl->doAddMatrix(*rMat.mpImpl);
	return *this;
	}

	B2DHomMatrix& B2DHomMatrix::operator-=(const B2DHomMatrix& rMat)
	{
	mpImpl->doSubMatrix(*rMat.mpImpl);
	return *this;
	}

	B2DHomMatrix& B2DHomMatrix::operator*=(double fValue)
	{
	const double fOne(1.0);

	if(!fTools::equal(fOne, fValue))
	mpImpl->doMulMatrix(fValue);

	return *this;
	}

	B2DHomMatrix& B2DHomMatrix::operator/=(double fValue)
	{
	const double fOne(1.0);

	if(!fTools::equal(fOne, fValue))
	mpImpl->doMulMatrix(1.0 / fValue);

	return *this;
	}

	B2DHomMatrix& B2DHomMatrix::operator*=(const B2DHomMatrix& rMat)
	{
	if(!rMat.isIdentity())
	mpImpl->doMulMatrix(*rMat.mpImpl);

	return *this;
	}

	bool B2DHomMatrix::operator==(const B2DHomMatrix& rMat) const
	{
	if(mpImpl.same_object(rMat.mpImpl))
	return true;

	return mpImpl->isEqual(*rMat.mpImpl);
	}

	bool B2DHomMatrix::operator!=(const B2DHomMatrix& rMat) const
	{
	return !(*this == rMat);
	}

	void B2DHomMatrix::rotate(double fRadiant)
	{
	if(!fTools::equalZero(fRadiant))
	{
	double fSin(0.0);
	double fCos(1.0);

	tools::createSinCosOrthogonal(fSin, fCos, fRadiant);
	Impl2DHomMatrix aRotMat;

	aRotMat.set(0, 0, fCos);
	aRotMat.set(1, 1, fCos);
	aRotMat.set(1, 0, fSin);
	aRotMat.set(0, 1, -fSin);

	mpImpl->doMulMatrix(aRotMat);
	}
	}

	void B2DHomMatrix::translate(double fX, double fY)
	{
	if(!fTools::equalZero(fX) \|\| !fTools::equalZero(fY))
	{
	Impl2DHomMatrix aTransMat;

	aTransMat.set(0, 2, fX);
	aTransMat.set(1, 2, fY);

	mpImpl->doMulMatrix(aTransMat);
	}
	}

	void B2DHomMatrix::scale(double fX, double fY)
	{
	const double fOne(1.0);

	if(!fTools::equal(fOne, fX) \|\| !fTools::equal(fOne, fY))
	{
	Impl2DHomMatrix aScaleMat;

	aScaleMat.set(0, 0, fX);
	aScaleMat.set(1, 1, fY);

	mpImpl->doMulMatrix(aScaleMat);
	}
	}

	void B2DHomMatrix::shearX(double fSx)
	{
	// #i76239# do not test againt 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
	if(!fTools::equalZero(fSx))
	{
	Impl2DHomMatrix aShearXMat;

	aShearXMat.set(0, 1, fSx);

	mpImpl->doMulMatrix(aShearXMat);
	}
	}

	void B2DHomMatrix::shearY(double fSy)
	{
	// #i76239# do not test againt 1.0, but against 0.0. We are talking about a value not on the diagonal (!)
	if(!fTools::equalZero(fSy))
	{
	Impl2DHomMatrix aShearYMat;

	aShearYMat.set(1, 0, fSy);

	mpImpl->doMulMatrix(aShearYMat);
	}
	}

	/** Decomposition

	New, optimized version with local shearX detection. Old version (keeping
	below, is working well, too) used the 3D matrix decomposition when
	shear was used. Keeping old version as comment below since it may get
	necessary to add the determinant() test from there here, too.
	*/
	bool B2DHomMatrix::decompose(B2DTuple& rScale, B2DTuple& rTranslate, double& rRotate, double& rShearX) const
	{
	// when perspective is used, decompose is not made here
	if(!mpImpl->isLastLineDefault())
	{
	return false;
	}

	// reset rotate and shear and copy translation values in every case
	rRotate = rShearX = 0.0;
	rTranslate.setX(get(0, 2));
	rTranslate.setY(get(1, 2));

	// test for rotation and shear
	if(fTools::equalZero(get(0, 1)) && fTools::equalZero(get(1, 0)))
	{
	// no rotation and shear, copy scale values
	rScale.setX(get(0, 0));
	rScale.setY(get(1, 1));
	}
	else
	{
	// get the unit vectors of the transformation -> the perpendicular vectors
	B2DVector aUnitVecX(get(0, 0), get(1, 0));
	B2DVector aUnitVecY(get(0, 1), get(1, 1));
	const double fScalarXY(aUnitVecX.scalar(aUnitVecY));

	// Test if shear is zero. That's the case if the unit vectors in the matrix
	// are perpendicular -> scalar is zero. This is also the case when one of
	// the unit vectors is zero.
	if(fTools::equalZero(fScalarXY))
	{
	// calculate unsigned scale values
	rScale.setX(aUnitVecX.getLength());
	rScale.setY(aUnitVecY.getLength());

	// check unit vectors for zero lengths
	const bool bXIsZero(fTools::equalZero(rScale.getX()));
	const bool bYIsZero(fTools::equalZero(rScale.getY()));

	if(bXIsZero \|\| bYIsZero)
	{
	// still extract as much as possible. Scalings are already set
	if(!bXIsZero)
	{
	// get rotation of X-Axis
	rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());
	}
	else if(!bYIsZero)
	{
	// get rotation of X-Axis. When assuming X and Y perpendicular
	// and correct rotation, it's the Y-Axis rotation minus 90 degrees
	rRotate = atan2(aUnitVecY.getY(), aUnitVecY.getX()) - M_PI_2;
	}

	// one or both unit vectors do not extist, determinant is zero, no decomposition possible.
	// Eventually used rotations or shears are lost
	return false;
	}
	else
	{
	// no shear
	// calculate rotation of X unit vector relative to (1, 0)
	rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());

	// use orientation to evtl. correct sign of Y-Scale
	const double fCrossXY(aUnitVecX.cross(aUnitVecY));

	if(fCrossXY < 0.0)
	{
	rScale.setY(-rScale.getY());
	}
	}
	}
	else
	{
	// fScalarXY is not zero, thus both unit vectors exist. No need to handle that here
	// shear, extract it
	double fCrossXY(aUnitVecX.cross(aUnitVecY));

	// get rotation by calculating angle of X unit vector relative to (1, 0).
	// This is before the parallell test following the motto to extract
	// as much as possible
	rRotate = atan2(aUnitVecX.getY(), aUnitVecX.getX());

	// get unsigned scale value for X. It will not change and is useful
	// for further corrections
	rScale.setX(aUnitVecX.getLength());

	if(fTools::equalZero(fCrossXY))
	{
	// extract as much as possible
	rScale.setY(aUnitVecY.getLength());

	// unit vectors are parallel, thus not linear independent. No
	// useful decomposition possible. This should not happen since
	// the only way to get the unit vectors nearly parallell is
	// a very big shearing. Anyways, be prepared for hand-filled
	// matrices
	// Eventually used rotations or shears are lost
	return false;
	}
	else
	{
	// calculate the contained shear
	rShearX = fScalarXY / fCrossXY;

	if(!fTools::equalZero(rRotate))
	{
	// To be able to correct the shear for aUnitVecY, rotation needs to be
	// removed first. Correction of aUnitVecX is easy, it will be rotated back to (1, 0).
	aUnitVecX.setX(rScale.getX());
	aUnitVecX.setY(0.0);

	// for Y correction we rotate the UnitVecY back about -rRotate
	const double fNegRotate(-rRotate);
	const double fSin(sin(fNegRotate));
	const double fCos(cos(fNegRotate));

	const double fNewX(aUnitVecY.getX() * fCos - aUnitVecY.getY() * fSin);
	const double fNewY(aUnitVecY.getX() * fSin + aUnitVecY.getY() * fCos);

	aUnitVecY.setX(fNewX);
	aUnitVecY.setY(fNewY);
	}

	// Correct aUnitVecY and fCrossXY to fShear=0. Rotation is already removed.
	// Shear correction can only work with removed rotation
	aUnitVecY.setX(aUnitVecY.getX() - (aUnitVecY.getY() * rShearX));
	fCrossXY = aUnitVecX.cross(aUnitVecY);

	// calculate unsigned scale value for Y, after the corrections since
	// the shear correction WILL change the length of aUnitVecY
	rScale.setY(aUnitVecY.getLength());

	// use orientation to set sign of Y-Scale
	if(fCrossXY < 0.0)
	{
	rScale.setY(-rScale.getY());
	}
	}
	}
	}

	return true;
	}
	} // end of namespace basegfx

	///////////////////////////////////////////////////////////////////////////////
	// eof