# Cppcheck report - LibreOffice: basegfx/source/polygon/b2dpolygontools.cxx

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    /* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
    /*
     * This file is part of the LibreOffice project.
     *
     * This Source Code Form is subject to the terms of the Mozilla Public
     * License, v. 2.0. If a copy of the MPL was not distributed with this
     * file, You can obtain one at http://mozilla.org/MPL/2.0/.
     *
     * This file incorporates work covered by the following license notice:
     *
     *   Licensed to the Apache Software Foundation (ASF) under one or more
     *   contributor license agreements. See the NOTICE file distributed
     *   with this work for additional information regarding copyright
     *   ownership. The ASF licenses this file to you under the Apache
     *   License, Version 2.0 (the "License"); you may not use this file
     *   except in compliance with the License. You may obtain a copy of
     *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
     */

    #include <basegfx/numeric/ftools.hxx>
    #include <basegfx/polygon/b2dpolygontools.hxx>
    #include <osl/diagnose.h>
    #include <rtl/math.hxx>
    #include <rtl/instance.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/polygon/b2dpolypolygoncutter.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>

    #include <numeric>
    #include <limits>

    // #i37443#
    #define ANGLE_BOUND_START_VALUE     (2.25)
    #define ANGLE_BOUND_MINIMUM_VALUE   (0.1)
    #define COUNT_SUBDIVIDE_DEFAULT     (4L)
    #ifdef DBG_UTIL
    static double fAngleBoundStartValue = ANGLE_BOUND_START_VALUE;
    #endif
    #define STEPSPERQUARTER     (3)

    namespace basegfx
    {
        namespace tools
        {
            void openWithGeometryChange(B2DPolygon& rCandidate)
            {
                if(rCandidate.isClosed())
                {
                    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())
                {
                    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 - 1L;
                }
                else if(rCandidate.count())
                {
                    return rCandidate.count() - 1L;
                }
                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 + 1L < rCandidate.count())
                {
                    return nIndex + 1L;
                }
                else if(nIndex + 1L == rCandidate.count())
                {
                    return 0L;
                }
                else
                {
                    return nIndex;
                }
            }

            B2VectorOrientation getOrientation(const B2DPolygon& rCandidate)
            {
                B2VectorOrientation eRetval(ORIENTATION_NEUTRAL);

                if(rCandidate.count() > 2L || rCandidate.areControlPointsUsed())
                {
                    const double fSignedArea(getSignedArea(rCandidate));

                    if(fTools::equalZero(fSignedArea))
                    {
                        // ORIENTATION_NEUTRAL, already set
                    }
                    if(fSignedArea > 0.0)
                    {
                        eRetval = ORIENTATION_POSITIVE;
                    }
                    else if(fSignedArea < 0.0)
                    {
                        eRetval = ORIENTATION_NEGATIVE;
                    }
                }

                return eRetval;
            }

            B2VectorContinuity getContinuityInPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
            {
                return rCandidate.getContinuityInPoint(nIndex);
            }

            B2DPolygon adaptiveSubdivideByDistance(const B2DPolygon& rCandidate, double fDistanceBound)
            {
                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 realloctions by guessing the result's pointcount
                        aRetval.reserve(nPointCount*4);

                        // add start point (always)
                        aRetval.append(aBezier.getStartPoint());

                        for(sal_uInt32 a(0L); 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(0.0 == fDistanceBound)
                                {
                                    // 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);
                            }
                            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 realloctions 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(0.0 == fAngleBound)
                        {
    #ifdef DBG_UTIL
                            fAngleBound = fAngleBoundStartValue;
    #else
                            fAngleBound = ANGLE_BOUND_START_VALUE;
    #endif
                        }
                        else if(fTools::less(fAngleBound, ANGLE_BOUND_MINIMUM_VALUE))
                        {
                            fAngleBound = 0.1;
                        }

                        for(sal_uInt32 a(0L); 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, true);
                            }
                            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 adaptiveSubdivideByCount(const B2DPolygon& rCandidate, sal_uInt32 nCount)
            {
                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 realloctions by guessing the result's pointcount
                        aRetval.reserve(nPointCount*4);

                        // add start point (always)
                        aRetval.append(aBezier.getStartPoint());

                        // #i37443# prepare convenient count if none was given
                        if(0L == nCount)
                        {
                            nCount = COUNT_SUBDIVIDE_DEFAULT;
                        }

                        for(sal_uInt32 a(0L); 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.adaptiveSubdivideByCount(aRetval, nCount);
                            }
                            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, true))
                {
                    return true;
                }
                else
                {
                    bool bRetval(false);
                    const sal_uInt32 nPointCount(aCandidate.count());

                    if(nPointCount)
                    {
                        B2DPoint aCurrentPoint(aCandidate.getB2DPoint(nPointCount - 1L));

                        for(sal_uInt32 a(0L); a < nPointCount; a++)
                        {
                            const B2DPoint aPreviousPoint(aCurrentPoint);
                            aCurrentPoint = aCandidate.getB2DPoint(a);

                            // cross-over in Y?
                            const bool bCompYA(fTools::more(aPreviousPoint.getY(), rPoint.getY()));
                            const bool bCompYB(fTools::more(aCurrentPoint.getY(), rPoint.getY()));

                            if(bCompYA != bCompYB)
                            {
                                // cross-over in X?
                                const bool bCompXA(fTools::more(aPreviousPoint.getX(), rPoint.getX()));
                                const bool bCompXB(fTools::more(aCurrentPoint.getX(), rPoint.getX()));

                                if(bCompXA == bCompXB)
                                {
                                    if(bCompXA)
                                    {
                                        bRetval = !bRetval;
                                    }
                                }
                                else
                                {
                                    const double fCompare(
                                        aCurrentPoint.getX() - (aCurrentPoint.getY() - rPoint.getY()) *
                                        (aPreviousPoint.getX() - aCurrentPoint.getX()) /
                                        (aPreviousPoint.getY() - aCurrentPoint.getY()));

                                    if(fTools::more(fCompare, rPoint.getX()))
                                    {
                                        bRetval = !bRetval;
                                    }
                                }
                            }
                        }
                    }

                    return bRetval;
                }
            }

            bool 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(0L); 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(0L); a < nPointCount; a++)
                    {
                        const B2DPoint aPreviousPoint(aCandidate.getB2DPoint((!a) ? nPointCount - 1L : a - 1L));
                        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)
            {
                double fRetval(0.0);
                const sal_uInt32 nPointCount(rCandidate.count());

                if(nPointCount)
                {
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);

                    if(rCandidate.areControlPointsUsed())
                    {
                        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( 1L == nPointCount )
                {
                    // only one point (i.e. no edge) - simply take that point
                    aRetval = rCandidate.getB2DPoint(0);
                }
                else if(nPointCount > 1L)
                {
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                    sal_uInt32 nIndex(0L);
                    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 + 1L) * 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 -= (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 < 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
                            aRetval = aRetval;
                        }
                        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(0L); !(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, 0, &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(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, 0);
                                            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(CUTFLAG_NONE);
                double fCut1(0.0);
                double fCut2(0.0);
                bool bFinished(!((bool)(aCutFlags & CUTFLAG_ALL)));

                // test for same points?
                if(!bFinished
                    && (aCutFlags & (CUTFLAG_START1|CUTFLAG_END1))
                    && (aCutFlags & (CUTFLAG_START2|CUTFLAG_END2)))
                {
                    // same startpoint?
                    if(!bFinished && (aCutFlags & (CUTFLAG_START1|CUTFLAG_START2)) == (CUTFLAG_START1|CUTFLAG_START2))
                    {
                        if(rEdge1Start.equal(rEdge2Start))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_START1|CUTFLAG_START2);
                        }
                    }

                    // same endpoint?
                    if(!bFinished && (aCutFlags & (CUTFLAG_END1|CUTFLAG_END2)) == (CUTFLAG_END1|CUTFLAG_END2))
                    {
                        const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
                        const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                        if(aEnd1.equal(aEnd2))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_END1|CUTFLAG_END2);
                            fCut1 = fCut2 = 1.0;
                        }
                    }

                    // startpoint1 == endpoint2?
                    if(!bFinished && (aCutFlags & (CUTFLAG_START1|CUTFLAG_END2)) == (CUTFLAG_START1|CUTFLAG_END2))
                    {
                        const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                        if(rEdge1Start.equal(aEnd2))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_START1|CUTFLAG_END2);
                            fCut1 = 0.0;
                            fCut2 = 1.0;
                        }
                    }

                    // startpoint2 == endpoint1?
                    if(!bFinished&& (aCutFlags & (CUTFLAG_START2|CUTFLAG_END1)) == (CUTFLAG_START2|CUTFLAG_END1))
                    {
                        const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

                        if(rEdge2Start.equal(aEnd1))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_START2|CUTFLAG_END1);
                            fCut1 = 1.0;
                            fCut2 = 0.0;
                        }
                    }
                }

                if(!bFinished && (aCutFlags & CUTFLAG_LINE))
                {
                    if(!bFinished && (aCutFlags & CUTFLAG_START1))
                    {
                        // start1 on line 2 ?
                        if(isPointOnEdge(rEdge1Start, rEdge2Start, rEdge2Delta, &fCut2))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_LINE|CUTFLAG_START1);
                        }
                    }

                    if(!bFinished && (aCutFlags & CUTFLAG_START2))
                    {
                        // start2 on line 1 ?
                        if(isPointOnEdge(rEdge2Start, rEdge1Start, rEdge1Delta, &fCut1))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_LINE|CUTFLAG_START2);
                        }
                    }

                    if(!bFinished && (aCutFlags & CUTFLAG_END1))
                    {
                        // end1 on line 2 ?
                        const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

                        if(isPointOnEdge(aEnd1, rEdge2Start, rEdge2Delta, &fCut2))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_LINE|CUTFLAG_END1);
                        }
                    }

                    if(!bFinished && (aCutFlags & CUTFLAG_END2))
                    {
                        // end2 on line 1 ?
                        const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                        if(isPointOnEdge(aEnd2, rEdge1Start, rEdge1Delta, &fCut1))
                        {
                            bFinished = true;
                            aRetval = (CUTFLAG_LINE|CUTFLAG_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 calcable
                            if(fTools::more(fCut1, fZero) && fTools::less(fCut1, fOne)
                                && (!fTools::equalZero(rEdge2Delta.getX()) || !fTools::equalZero(rEdge2Delta.getY())))
                            {
                                // take the mopre 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))
                                {
                                    bFinished = true;<--- Variable 'bFinished' is assigned a value that is never used.
                                    aRetval = CUTFLAG_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)
            {
                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::more(fDotDashLength, 0.0) && (pLineTarget || pGapTarget) && nPointCount)
                {
                    // clear targets
                    if(pLineTarget)
                    {
                        pLineTarget->clear();
                    }

                    if(pGapTarget)
                    {
                        pGapTarget->clear();
                    }

                    // prepare current edge's start
                    B2DCubicBezier aCurrentEdge;
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? 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(rDotDashArray[0]);
                    B2DPolygon aSnippet;

                    // 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 && pLineTarget);
                                    const bool bHandleGap(!bIsLine && pGapTarget);

                                    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)
                                        {
                                            pLineTarget->append(aSnippet);
                                        }
                                        else
                                        {
                                            pGapTarget->append(aSnippet);
                                        }

                                        aSnippet.clear();
                                    }

                                    // prepare next DotDashArray step and flip line/gap flag
                                    fLastDotDashMovingLength = fDotDashMovingLength;
                                    fDotDashMovingLength += rDotDashArray[(++nDotDashIndex) % nDotDashCount];
                                    bIsLine = !bIsLine;
                                }

                                // append closing snippet [fLastDotDashMovingLength, fEdgeLength]
                                const bool bHandleLine(bIsLine && pLineTarget);
                                const bool bHandleGap(!bIsLine && pGapTarget);

                                if(bHandleLine || bHandleGap)
                                {
                                    B2DCubicBezier aRight;
                                    const double fBezierSplit(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));

                                    aCurrentEdge.split(fBezierSplit, 0, &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 && pLineTarget);
                                    const bool bHandleGap(!bIsLine && pGapTarget);

                                    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)
                                        {
                                            pLineTarget->append(aSnippet);
                                        }
                                        else
                                        {
                                            pGapTarget->append(aSnippet);
                                        }

                                        aSnippet.clear();
                                    }

                                    // prepare next DotDashArray step and flip line/gap flag
                                    fLastDotDashMovingLength = fDotDashMovingLength;
                                    fDotDashMovingLength += rDotDashArray[(++nDotDashIndex) % nDotDashCount];
                                    bIsLine = !bIsLine;
                                }

                                // append snippet [fLastDotDashMovingLength, fEdgeLength]
                                const bool bHandleLine(bIsLine && pLineTarget);
                                const bool bHandleGap(!bIsLine && pGapTarget);

                                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())
                    {
                        if(bIsLine && pLineTarget)
                        {
                            pLineTarget->append(aSnippet);
                        }
                        else if(!bIsLine && pGapTarget)
                        {
                            pGapTarget->append(aSnippet);
                        }
                    }

                    // check if start and end polygon may be merged
                    if(pLineTarget)
                    {
                        const sal_uInt32 nCount(pLineTarget->count());

                        if(nCount > 1)
                        {
                            // these polygons were created above, there exists none with less than two points,
                            // thus dircet point access below is allowed
                            const B2DPolygon aFirst(pLineTarget->getB2DPolygon(0));
                            B2DPolygon aLast(pLineTarget->getB2DPolygon(nCount - 1));

                            if(aFirst.getB2DPoint(0).equal(aLast.getB2DPoint(aLast.count() - 1)))
                            {
                                // start of first and end of last are the same -> merge them
                                aLast.append(aFirst);
                                aLast.removeDoublePoints();
                                pLineTarget->setB2DPolygon(0, aLast);
                                pLineTarget->remove(nCount - 1);
                            }
                        }
                    }

                    if(pGapTarget)
                    {
                        const sal_uInt32 nCount(pGapTarget->count());

                        if(nCount > 1)
                        {
                            // these polygons were created above, there exists none with less than two points,
                            // thus dircet point access below is allowed
                            const B2DPolygon aFirst(pGapTarget->getB2DPolygon(0));
                            B2DPolygon aLast(pGapTarget->getB2DPolygon(nCount - 1));

                            if(aFirst.getB2DPoint(0).equal(aLast.getB2DPoint(aLast.count() - 1)))
                            {
                                // start of first and end of last are the same -> merge them
                                aLast.append(aFirst);
                                aLast.removeDoublePoints();
                                pGapTarget->setB2DPolygon(0, aLast);
                                pGapTarget->remove(nCount - 1);
                            }
                        }
                    }
                }
                else
                {
                    // parameters make no sense, just add source to targets
                    if(pLineTarget)
                    {
                        pLineTarget->append(rCandidate);
                    }

                    if(pGapTarget)
                    {
                        pGapTarget->append(rCandidate);
                    }
                }
            }

            // 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));

                        if(fDistanceSquare <= fDistance * fDistance)
                        {
                            return true;
                        }
                        else
                        {
                            return false;
                        }
                    }
                }

                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)
                {
                    const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
                    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;
            }

            B2DPolygon createPolygonFromRect( const B2DRectangle& rRect, double fRadiusX, double fRadiusY )
            {
                const double fZero(0.0);
                const double fOne(1.0);

                // crop to useful values
                if(fTools::less(fRadiusX, fZero))
                {
                    fRadiusX = fZero;
                }
                else if(fTools::more(fRadiusX, fOne))
                {
                    fRadiusX = fOne;
                }

                if(fTools::less(fRadiusY, fZero))
                {
                    fRadiusY = fZero;
                }
                else if(fTools::more(fRadiusY, fOne))
                {
                    fRadiusY = fOne;
                }

                if(fZero == fRadiusX || fZero == fRadiusY)
                {
                    B2DPolygon aRetval;

                    // 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());
                    aRetval.append(aBottomCenter);

                    aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMaxY() ) );
                    aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMinY() ) );
                    aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMinY() ) );
                    aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMaxY() ) );

                    // close
                    aRetval.setClosed( true );

                    return aRetval;
                }
                else if(fOne == fRadiusX && 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((M_SQRT2 - 1.0) * 4.0 / 3.0);

                    // create start point at bottom center
                    if(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 envolved
                    if(fOne == fRadiusX || fOne == fRadiusY)
                    {
                        aRetval.removeDoublePoints();
                    }

                    return aRetval;
                }
            }

            B2DPolygon createPolygonFromRect( const B2DRectangle& rRect )
            {
                B2DPolygon aRetval;

                aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMinY() ) );
                aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMinY() ) );
                aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMaxY() ) );
                aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMaxY() ) );

                // close
                aRetval.setClosed( true );

                return aRetval;
            }

            namespace
            {
                struct theUnitPolygon :
                    public rtl::StaticWithInit<B2DPolygon, theUnitPolygon>
                {
                    B2DPolygon operator () ()
                    {
                        B2DPolygon aRetval;

                        aRetval.append( B2DPoint( 0.0, 0.0 ) );
                        aRetval.append( B2DPoint( 1.0, 0.0 ) );
                        aRetval.append( B2DPoint( 1.0, 1.0 ) );
                        aRetval.append( B2DPoint( 0.0, 1.0 ) );

                        // close
                        aRetval.setClosed( true );

                        return aRetval;
                    }
                };
            }

            B2DPolygon createUnitPolygon()
            {
                return theUnitPolygon::get();
            }

            B2DPolygon createPolygonFromCircle( const B2DPoint& rCenter, double fRadius )
            {
                return createPolygonFromEllipse( rCenter, fRadius, fRadius );
            }

            B2DPolygon impCreateUnitCircle(sal_uInt32 nStartQuadrant)
            {
                B2DPolygon aUnitCircle;
                const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
                const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));
                const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER));

                B2DPoint aPoint(1.0, 0.0);
                B2DPoint aForward(1.0, fScaledKappa);
                B2DPoint aBackward(1.0, -fScaledKappa);

                if(0 != nStartQuadrant)
                {
                    const B2DHomMatrix aQuadrantMatrix(createRotateB2DHomMatrix(F_PI2 * (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;
            }

            namespace
            {
                struct theUnitHalfCircle :
                    public rtl::StaticWithInit<B2DPolygon, theUnitHalfCircle>
                {
                    B2DPolygon operator()()
                    {
                        B2DPolygon aUnitHalfCircle;
                        const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
                        const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));
                        const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER));
                        B2DPoint aPoint(1.0, 0.0);
                        B2DPoint aForward(1.0, fScaledKappa);
                        B2DPoint aBackward(1.0, -fScaledKappa);

                        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;
                    }
                };
            }

            B2DPolygon createHalfUnitCircle()
            {
                return theUnitHalfCircle::get();
            }

            namespace
            {
                struct theUnitCircleStartQuadrantOne :
                    public rtl::StaticWithInit<B2DPolygon, theUnitCircleStartQuadrantOne>
                {
                    B2DPolygon operator()() { return impCreateUnitCircle(1); }
                };

                struct theUnitCircleStartQuadrantTwo :
                    public rtl::StaticWithInit<B2DPolygon, theUnitCircleStartQuadrantTwo>
                {
                    B2DPolygon operator()() { return impCreateUnitCircle(2); }
                };

                struct theUnitCircleStartQuadrantThree :
                    public rtl::StaticWithInit<B2DPolygon, theUnitCircleStartQuadrantThree>
                {
                    B2DPolygon operator()() { return impCreateUnitCircle(3); }
                };

                struct theUnitCircleStartQuadrantZero :
                    public rtl::StaticWithInit<B2DPolygon, theUnitCircleStartQuadrantZero>
                {
                    B2DPolygon operator()() { return impCreateUnitCircle(0); }
                };
            }

            B2DPolygon createPolygonFromUnitCircle(sal_uInt32 nStartQuadrant)
            {
                switch(nStartQuadrant % 4)
                {
                    case 1 :
                        return theUnitCircleStartQuadrantOne::get();

                    case 2 :
                        return theUnitCircleStartQuadrantTwo::get();

                    case 3 :
                        return theUnitCircleStartQuadrantThree::get();

                    default : // case 0 :
                        return theUnitCircleStartQuadrantZero::get();
                }
            }

            B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY )
            {
                B2DPolygon aRetval(createPolygonFromUnitCircle());
                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 .. F_2PI[ where F_2PI
                // falls back to 0.0 to ensure a unique definition
                if(fTools::less(fStart, 0.0))
                {
                    fStart = 0.0;
                }

                if(fTools::moreOrEqual(fStart, F_2PI))
                {
                    fStart = 0.0;
                }

                if(fTools::less(fEnd, 0.0))
                {
                    fEnd = 0.0;
                }

                if(fTools::moreOrEqual(fEnd, F_2PI))
                {
                    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(F_PI2 / STEPSPERQUARTER);
                    const sal_uInt32 nStartSegment(sal_uInt32(fStart / fAnglePerSegment) % nSegments);
                    const sal_uInt32 nEndSegment(sal_uInt32(fEnd / fAnglePerSegment) % nSegments);
                    const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
                    const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));

                    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(fScaledKappa * ((fEnd - fStart) / fAnglePerSegment));

                        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(fScaledKappa * ((fSegEndRad - fStart) / fAnglePerSegment));
                        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()) * fScaledKappa),
                                aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fScaledKappa),
                                aSegEnd);

                            nSegment = (nSegment + 1) % nSegments;
                            aSegStart = aSegEnd;
                        }

                        // End in this sector
                        const double fSegStartRad(nSegment * fAnglePerSegment);
                        fFactor = fScaledKappa * ((fEnd - fSegStartRad) / fAnglePerSegment);
                        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 > 2L)
                {
                    B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1L));
                    B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));

                    for(sal_uInt32 a(0L); 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(ORIENTATION_NEUTRAL == aOrientation)
                        {
                            // 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 - 1L));
                    B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));

                    for(sal_uInt32 a(0L); 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(ORIENTATION_NEUTRAL == aOrientation)
                        {
                            // 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() && ORIENTATION_NEUTRAL == getOrientationForIndex(aRetval, 0L))
                    {
                        aRetval.remove(0L);
                    }

                    // 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 > 2L)
                {
                    const B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1L));
                    B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));
                    B2DVector aCurrVec(aPrevPoint - aCurrPoint);
                    B2VectorOrientation aOrientation(ORIENTATION_NEUTRAL);

                    for(sal_uInt32 a(0L); a < nPointCount; a++)
                    {
                        const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
                        const B2DVector aNextVec(aNextPoint - aCurrPoint);
                        const B2VectorOrientation aCurrentOrientation(getOrientation(aNextVec, aCurrVec));

                        if(ORIENTATION_NEUTRAL == aOrientation)
                        {
                            // set start value, maybe neutral again
                            aOrientation = aCurrentOrientation;
                        }
                        else
                        {
                            if(ORIENTATION_NEUTRAL != aCurrentOrientation && 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 > 1L)
                {
                    const sal_uInt32 nLoopCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
                    B2DPoint aCurrentPoint(aCandidate.getB2DPoint(0L));

                    for(sal_uInt32 a(0L); a < nLoopCount; a++)
                    {
                        const B2DPoint aNextPoint(aCandidate.getB2DPoint((a + 1L) % nPointCount));

                        if(isPointOnLine(aCurrentPoint, aNextPoint, rPoint, bWithPoints))
                        {
                            return true;
                        }

                        aCurrentPoint = aNextPoint;
                    }
                }
                else if(nPointCount && bWithPoints)
                {
                    return rPoint.equal(aCandidate.getB2DPoint(0L));
                }

                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));

                if(fTools::equalZero(fCrossA))
                {
                    // one point on the line
                    return bWithLine;
                }

                const B2DVector aVectorToB(rEnd - rCandidateB);
                const double fCrossB(aLineVector.cross(aVectorToB));

                if(fTools::equalZero(fCrossB))
                {
                    // 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, B2DPolygon& rTarget)
            {
                const sal_uInt32 nCount(rCandidate.count());

                if(nCount > 2L)
                {
                    const B2DPoint aStart(rCandidate.getB2DPoint(0L));
                    B2DPoint aLast(rCandidate.getB2DPoint(1L));

                    for(sal_uInt32 a(2L); a < nCount; a++)
                    {
                        const B2DPoint aCurrent(rCandidate.getB2DPoint(a));
                        rTarget.append(aStart);
                        rTarget.append(aLast);
                        rTarget.append(aCurrent);

                        // prepare next
                        aLast = aCurrent;
                    }
                }
            }

            namespace
            {
                /// return 0 for input of 0, -1 for negative and 1 for positive input
                inline int lcl_sgn( const double n )
                {
                    return n == 0.0 ? 0 : 1 - 2*int(rtl::math::isSignBitSet(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(0L); 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(0L); 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 > 1L)
                {
                    const double fZero(0.0);
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);
                    B2DCubicBezier aBezier;
                    aBezier.setStartPoint(rCandidate.getB2DPoint(0));

                    for(sal_uInt32 a(0L); 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(DBL_MAX == fRetval || 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(1.0 == rCut)
                    {
                        // correct rEdgeIndex when not last point
                        if(rCandidate.isClosed())
                        {
                            rEdgeIndex = getIndexOfSuccessor(rEdgeIndex, rCandidate);
                            rCut = 0.0;
                        }
                        else
                        {
                            if(rEdgeIndex != nEdgeCount - 1L)
                            {
                                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 && 0.0 != rOriginal.getWidth() && 0.0 != rOriginal.getHeight())
                {
                    B2DPolygon aRetval;

                    for(sal_uInt32 a(0L); 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(0L); 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() && 0 == nIndex)
                        {
                            // 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 CONTINUITY_NONE :
                        {
                            if(rCandidate.isPrevControlPointUsed(nIndex))
                            {
                                if(!rCandidate.isClosed() && 0 == nIndex)
                                {
                                    // 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 CONTINUITY_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(ORIENTATION_NEUTRAL == aOrientation && 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(ORIENTATION_POSITIVE == aOrientation)
                                    {
                                        rCandidate.setControlPoints(nIndex,
                                            aCurrentPoint - (aNormalizedPerpendicular * fLenPrev),
                                            aCurrentPoint + (aNormalizedPerpendicular * fLenNext));
                                    }
                                    else
                                    {
                                        rCandidate.setControlPoints(nIndex,
                                            aCurrentPoint + (aNormalizedPerpendicular * fLenPrev),
                                            aCurrentPoint - (aNormalizedPerpendicular * fLenNext));
                                    }

                                    bRetval = true;
                                }
                            }
                            break;
                        }
                        case CONTINUITY_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(ORIENTATION_NEUTRAL == aOrientation && 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(ORIENTATION_POSITIVE == aOrientation)
                                    {
                                        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(0.0 != fValue)
                {
                    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 - 1L));
                            B2DPoint aCurrent(rCandidate.getB2DPoint(0L));

                            for(sal_uInt32 a(0L); a < nPointCount; a++)
                            {
                                const B2DPoint aNext(rCandidate.getB2DPoint(a + 1L == nPointCount ? 0L : a + 1L));
                                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 - 1L);

                    if(nSegmentCount == nSegments)
                    {
                        aRetval = rCandidate;
                    }
                    else
                    {
                        const double fLength(getLength(rCandidate));
                        const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nSegments : nSegments + 1L);

                        for(sal_uInt32 a(0L); a < nLoopCount; a++)
                        {
                            const double fRelativePos((double)a / (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(0L); 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(0L); 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;
                }
            }

            bool containsOnlyHorizontalAndVerticalEdges(const B2DPolygon& rCandidate)
            {
                if(rCandidate.areControlPointsUsed())
                {
                    return false;
                }

                const sal_uInt32 nPointCount(rCandidate.count());

                if(nPointCount < 2)
                {
                    return true;
                }

                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount + 1 : nPointCount);
                basegfx::B2DPoint aLast(rCandidate.getB2DPoint(0));

                for(sal_uInt32 a(1); a < nEdgeCount; a++)
                {
                    const sal_uInt32 nNextIndex(a % nPointCount);
                    const basegfx::B2DPoint aCurrent(rCandidate.getB2DPoint(nNextIndex));

                    if(!basegfx::fTools::equal(aLast.getX(), aCurrent.getX()) && !basegfx::fTools::equal(aLast.getY(), aCurrent.getY()))
                    {
                        return false;
                    }

                    aLast = aCurrent;
                }

                return true;
            }

            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 com::sun::star::drawing::PointSequence

            B2DPolygon UnoPointSequenceToB2DPolygon(
                const com::sun::star::drawing::PointSequence& rPointSequenceSource,
                bool bCheckClosed)
            {
                B2DPolygon aRetval;
                const sal_uInt32 nLength(rPointSequenceSource.getLength());

                if(nLength)
                {
                    aRetval.reserve(nLength);
                    const com::sun::star::awt::Point* pArray = rPointSequenceSource.getConstArray();
                    const com::sun::star::awt::Point* pArrayEnd = pArray + rPointSequenceSource.getLength();

                    for(;pArray != pArrayEnd; pArray++)
                    {
                        aRetval.append(B2DPoint(pArray->X, pArray->Y));
                    }

                    if(bCheckClosed)
                    {
                        // check for closed state flag
                        tools::checkClosed(aRetval);
                    }
                }

                return aRetval;
            }

            void B2DPolygonToUnoPointSequence(
                const B2DPolygon& rPolygon,
                com::sun::star::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);
                    com::sun::star::awt::Point* pSequence = rPointSequenceRetval.getArray();

                    for(sal_uInt32 b(0); b < nPointCount; b++)
                    {
                        const B2DPoint aPoint(aPolygon.getB2DPoint(b));
                        const com::sun::star::awt::Point aAPIPoint(fround(aPoint.getX()), fround(aPoint.getY()));

                        *pSequence = aAPIPoint;
                        pSequence++;
                    }

                    // copy first point if closed
                    if(bIsClosed)
                    {
                        *pSequence = *rPointSequenceRetval.getArray();
                    }
                }
                else
                {
                    rPointSequenceRetval.realloc(0);
                }
            }

            // converters for com::sun::star::drawing::PointSequence and
            // com::sun::star::drawing::FlagSequence to B2DPolygon (curved polygons)

            B2DPolygon UnoPolygonBezierCoordsToB2DPolygon(
                const com::sun::star::drawing::PointSequence& rPointSequenceSource,
                const com::sun::star::drawing::FlagSequence& rFlagSequenceSource,
                bool bCheckClosed)
            {
                const sal_uInt32 nCount((sal_uInt32)rPointSequenceSource.getLength());
                OSL_ENSURE(nCount == (sal_uInt32)rFlagSequenceSource.getLength(),
                    "UnoPolygonBezierCoordsToB2DPolygon: Unequal count of Points and Flags (!)");

                // prepare new polygon
                B2DPolygon aRetval;
                const com::sun::star::awt::Point* pPointSequence = rPointSequenceSource.getConstArray();
                const com::sun::star::drawing::PolygonFlags* pFlagSequence = rFlagSequenceSource.getConstArray();

                // get first point and flag
                B2DPoint aNewCoordinatePair(pPointSequence->X, pPointSequence->Y); pPointSequence++;
                com::sun::star::drawing::PolygonFlags ePolygonFlag(*pFlagSequence); pFlagSequence++;
                B2DPoint aControlA;
                B2DPoint aControlB;

                // first point is not allowed to be a control point
                OSL_ENSURE(com::sun::star::drawing::PolygonFlags_CONTROL != ePolygonFlag,
                    "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 && com::sun::star::drawing::PolygonFlags_CONTROL == ePolygonFlag)
                    {
                        aControlA = aNewCoordinatePair;
                        bControlA = true;

                        // get next point and flag
                        aNewCoordinatePair = B2DPoint(pPointSequence->X, pPointSequence->Y);
                        ePolygonFlag = *pFlagSequence;
                        pPointSequence++; pFlagSequence++; b++;
                    }

                    if(b < nCount && com::sun::star::drawing::PolygonFlags_CONTROL == ePolygonFlag)
                    {
                        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(com::sun::star::drawing::PolygonFlags_CONTROL == ePolygonFlag || bControlA != bControlB,
                        "basegfx", "UnoPolygonBezierCoordsToB2DPolygon: Illegal source polygon (!)");

                    // the previous writes used the B2DPolyPoygon -> tools::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;
                        bControlB = 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
                if(bCheckClosed)
                {
                    checkClosed(aRetval);
                }

                return aRetval;
            }

            void B2DPolygonToUnoPolygonBezierCoords(
                const B2DPolygon& rPolygon,
                com::sun::star::drawing::PointSequence& rPointSequenceRetval,
                com::sun::star::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< com::sun::star::awt::Point > aCollectPoints;
                            std::vector< com::sun::star::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.push_back(
                                    com::sun::star::awt::Point(
                                        fround(aBezierSegment.getStartPoint().getX()),
                                        fround(aBezierSegment.getStartPoint().getY())));
                                aCollectFlags.push_back(com::sun::star::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.push_back(
                                        com::sun::star::awt::Point(
                                            fround(aBezierSegment.getControlPointA().getX()),
                                            fround(aBezierSegment.getControlPointA().getY())));
                                    aCollectFlags.push_back(com::sun::star::drawing::PolygonFlags_CONTROL);

                                    aCollectPoints.push_back(
                                        com::sun::star::awt::Point(
                                            fround(aBezierSegment.getControlPointB().getX()),
                                            fround(aBezierSegment.getControlPointB().getY())));
                                    aCollectFlags.push_back(com::sun::star::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(CONTINUITY_C1 == eCont)
                                    {
                                        aCollectFlags[nStartPointIndex] = com::sun::star::drawing::PolygonFlags_SMOOTH;
                                    }
                                    else if(CONTINUITY_C2 == eCont)
                                    {
                                        aCollectFlags[nStartPointIndex] = com::sun::star::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(com::sun::star::drawing::PolygonFlags_NORMAL);
                            }
                            else
                            {
                                // add last point as closing point
                                const B2DPoint aClosingPoint(rPolygon.getB2DPoint(nPointCount - 1L));
                                aCollectPoints.push_back(
                                    com::sun::star::awt::Point(
                                        fround(aClosingPoint.getX()),
                                        fround(aClosingPoint.getY())));
                                aCollectFlags.push_back(com::sun::star::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((sal_Int32)nTargetCount);
                            rFlagSequenceRetval.realloc((sal_Int32)nTargetCount);
                            com::sun::star::awt::Point* pPointSequence = rPointSequenceRetval.getArray();
                            com::sun::star::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((sal_Int32)nTargetCount);
                        rFlagSequenceRetval.realloc((sal_Int32)nTargetCount);

                        com::sun::star::awt::Point* pPointSequence = rPointSequenceRetval.getArray();
                        com::sun::star::drawing::PolygonFlags* pFlagSequence = rFlagSequenceRetval.getArray();

                        for(sal_uInt32 a(0); a < nPointCount; a++)
                        {
                            const B2DPoint aB2DPoint(rPolygon.getB2DPoint(a));
                            const com::sun::star::awt::Point aAPIPoint(
                                fround(aB2DPoint.getX()),
                                fround(aB2DPoint.getY()));

                            *pPointSequence = aAPIPoint;
                            *pFlagSequence = com::sun::star::drawing::PolygonFlags_NORMAL;
                            pPointSequence++;
                            pFlagSequence++;
                        }

                        if(bClosed)
                        {
                            // add first point as closing point
                            *pPointSequence = *rPointSequenceRetval.getConstArray();
                            *pFlagSequence = com::sun::star::drawing::PolygonFlags_NORMAL;
                        }
                    }
                }
                else
                {
                    rPointSequenceRetval.realloc(0);
                    rFlagSequenceRetval.realloc(0);
                }
            }

        } // end of namespace tools
    } // end of namespace basegfx

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