Quelle  b2dpolygontools.cxx   Sprache: C

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

#include <basegfx/numeric/ftools.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <osl/diagnose.h>
#include <rtl/math.hxx>
#include <sal/log.hxx>
#include <basegfx/polygon/b2dpolygon.hxx>
#include <basegfx/polygon/b2dpolypolygon.hxx>
#include <basegfx/range/b2drange.hxx>
#include <basegfx/curve/b2dcubicbezier.hxx>
#include <basegfx/point/b3dpoint.hxx>
#include <basegfx/matrix/b3dhommatrix.hxx>
#include <basegfx/matrix/b2dhommatrix.hxx>
#include <basegfx/curve/b2dbeziertools.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx>

// #i37443#
#define ANGLE_BOUND_START_VALUE     (2.25)
#define ANGLE_BOUND_MINIMUM_VALUE   (0.1)
#define STEPSPERQUARTER     (3)

namespace basegfx::utils
{
        void openWithGeometryChange(B2DPolygon& rCandidate)
        {
            if(!rCandidate.isClosed())
                return;

            if(rCandidate.count())
            {
                rCandidate.append(rCandidate.getB2DPoint(0));

                if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(0))
                {
                    rCandidate.setPrevControlPoint(rCandidate.count() - 1, rCandidate.getPrevControlPoint(0));
                    rCandidate.resetPrevControlPoint(0);
                }
            }

            rCandidate.setClosed(false);
        }

        void closeWithGeometryChange(B2DPolygon& rCandidate)
        {
            if(rCandidate.isClosed())
                return;

            while(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
            {
                if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(rCandidate.count() - 1))
                {
                    rCandidate.setPrevControlPoint(0, rCandidate.getPrevControlPoint(rCandidate.count() - 1));
                }

                rCandidate.remove(rCandidate.count() - 1);
            }

            rCandidate.setClosed(true);
        }

        void checkClosed(B2DPolygon& rCandidate)
        {
            // #i80172# Removed unnecessary assertion
            // OSL_ENSURE(!rCandidate.isClosed(), "checkClosed: already closed (!)");

            if(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
            {
                closeWithGeometryChange(rCandidate);
            }
        }

        // Get successor and predecessor indices. Returning the same index means there
        // is none. Same for successor.
        sal_uInt32 getIndexOfPredecessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
        {
            OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");

            if(nIndex)
            {
                return nIndex - 1;
            }
            else if(rCandidate.count())
            {
                return rCandidate.count() - 1;
            }
            else
            {
                return nIndex;
            }
        }

        sal_uInt32 getIndexOfSuccessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
        {
            OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");

            if(nIndex + 1 < rCandidate.count())
            {
                return nIndex + 1;
            }
            else if(nIndex + 1 == rCandidate.count())
            {
                return 0;
            }
            else
            {
                return nIndex;
            }
        }

        B2VectorOrientation getOrientation(const B2DPolygon& rCandidate)
        {
            B2VectorOrientation eRetval(B2VectorOrientation::Neutral);

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

                if(fTools::equalZero(fSignedArea))
                {
                    // B2VectorOrientation::Neutral, already set
                }
                if(fSignedArea > 0.0)
                {
                    eRetval = B2VectorOrientation::Positive;
                }
                else if(fSignedArea < 0.0)
                {
                    eRetval = B2VectorOrientation::Negative;
                }
            }

            return eRetval;
        }

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

        B2DPolygon adaptiveSubdivideByDistance(const B2DPolygon& rCandidate, double fDistanceBound, int nRecurseLimit)
        {
            if(rCandidate.areControlPointsUsed())
            {
                const sal_uInt32 nPointCount(rCandidate.count());
                B2DPolygon aRetval;

                if(nPointCount)
                {
                    // prepare edge-oriented loop
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                    B2DCubicBezier aBezier;
                    aBezier.setStartPoint(rCandidate.getB2DPoint(0));

                    // perf: try to avoid too many reallocations by guessing the result's pointcount
                    aRetval.reserve(nPointCount*4);

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

                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
                    {
                        // get next and control points
                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                        aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
                        aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
                        aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                        aBezier.testAndSolveTrivialBezier();

                        if(aBezier.isBezier())
                        {
                            // add curved edge and generate DistanceBound
                            double fBound(0.0);

                            if(fDistanceBound == 0.0)
                            {
                                // If not set, use B2DCubicBezier functionality to guess a rough value
                                const double fRoughLength((aBezier.getEdgeLength() + aBezier.getControlPolygonLength()) / 2.0);

                                // take 1/100th of the rough curve length
                                fBound = fRoughLength * 0.01;
                            }
                            else
                            {
                                // use given bound value
                                fBound = fDistanceBound;
                            }

                            // make sure bound value is not too small. The base units are 1/100th mm, thus
                            // just make sure it's not smaller then 1/100th of that
                            if(fBound < 0.01)
                            {
                                fBound = 0.01;
                            }

                            // call adaptive subdivide which adds edges to aRetval accordingly
                            aBezier.adaptiveSubdivideByDistance(aRetval, fBound, nRecurseLimit);
                        }
                        else
                        {
                            // add non-curved edge
                            aRetval.append(aBezier.getEndPoint());
                        }

                        // prepare next step
                        aBezier.setStartPoint(aBezier.getEndPoint());
                    }

                    if(rCandidate.isClosed())
                    {
                        // set closed flag and correct last point (which is added double now).
                        closeWithGeometryChange(aRetval);
                    }
                }

                return aRetval;
            }
            else
            {
                return rCandidate;
            }
        }

        B2DPolygon adaptiveSubdivideByAngle(const B2DPolygon& rCandidate, double fAngleBound)
        {
            if(rCandidate.areControlPointsUsed())
            {
                const sal_uInt32 nPointCount(rCandidate.count());
                B2DPolygon aRetval;

                if(nPointCount)
                {
                    // prepare edge-oriented loop
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                    B2DCubicBezier aBezier;
                    aBezier.setStartPoint(rCandidate.getB2DPoint(0));

                    // perf: try to avoid too many reallocations by guessing the result's pointcount
                    aRetval.reserve(nPointCount*4);

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

                    // #i37443# prepare convenient AngleBound if none was given
                    if(fAngleBound == 0.0)
                    {
                        fAngleBound = ANGLE_BOUND_START_VALUE;
                    }
                    else if(fTools::less(fAngleBound, ANGLE_BOUND_MINIMUM_VALUE))
                    {
                        fAngleBound = 0.1;
                    }

                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
                    {
                        // get next and control points
                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                        aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
                        aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
                        aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                        aBezier.testAndSolveTrivialBezier();

                        if(aBezier.isBezier())
                        {
                            // call adaptive subdivide
                            aBezier.adaptiveSubdivideByAngle(aRetval, fAngleBound);
                        }
                        else
                        {
                            // add non-curved edge
                            aRetval.append(aBezier.getEndPoint());
                        }

                        // prepare next step
                        aBezier.setStartPoint(aBezier.getEndPoint());
                    }

                    if(rCandidate.isClosed())
                    {
                        // set closed flag and correct last point (which is added double now).
                        closeWithGeometryChange(aRetval);
                    }
                }

                return aRetval;
            }
            else
            {
                return rCandidate;
            }
        }

        bool isInside(const B2DPolygon& rCandidate, const B2DPoint& rPoint, bool bWithBorder)
        {
            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);

            if(bWithBorder && isPointOnPolygon(aCandidate, rPoint))
            {
                return true;
            }
            else
            {
                bool bRetval(false);
                const sal_uInt32 nPointCount(aCandidate.count());

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

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

                        // cross-over in Y? tdf#130150 use full precision, no need for epsilon
                        const bool bCompYA(aPreviousPoint.getY() > rPoint.getY());
                        const bool bCompYB(aCurrentPoint.getY() > rPoint.getY());

                        if(bCompYA != bCompYB)
                        {
                            // cross-over in X? tdf#130150 use full precision, no need for epsilon
                            const bool bCompXA(aPreviousPoint.getX() > rPoint.getX());
                            const bool bCompXB(aCurrentPoint.getX() > rPoint.getX());

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

                                // tdf#130150 use full precision, no need for epsilon
                                if(fCompare > rPoint.getX())
                                {
                                    bRetval = !bRetval;
                                }
                            }
                        }
                    }
                }

                return bRetval;
            }
        }

        bool isInside(const B2DPolygon& rCandidate, const B2DPolygon& rPolygon, bool bWithBorder)
        {
            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
            const B2DPolygon aPolygon(rPolygon.areControlPointsUsed() ? rPolygon.getDefaultAdaptiveSubdivision() : rPolygon);
            const sal_uInt32 nPointCount(aPolygon.count());

            for(sal_uInt32 a(0); a < nPointCount; a++)
            {
                const B2DPoint aTestPoint(aPolygon.getB2DPoint(a));

                if(!isInside(aCandidate, aTestPoint, bWithBorder))
                {
                    return false;
                }
            }

            return true;
        }

        B2DRange getRange(const B2DPolygon& rCandidate)
        {
            // changed to use internally buffered version at B2DPolygon
            return rCandidate.getB2DRange();
        }

        double getSignedArea(const B2DPolygon& rCandidate)
        {
            const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
            double fRetval(0.0);
            const sal_uInt32 nPointCount(aCandidate.count());

            if(nPointCount > 2)
            {
                for(sal_uInt32 a(0); a < nPointCount; a++)
                {
                    const B2DPoint aPreviousPoint(aCandidate.getB2DPoint((!a) ? nPointCount - 1 : a - 1));
                    const B2DPoint aCurrentPoint(aCandidate.getB2DPoint(a));

                    fRetval += aPreviousPoint.getX() * aCurrentPoint.getY();
                    fRetval -= aPreviousPoint.getY() * aCurrentPoint.getX();
                }

                // correct to zero if small enough. Also test the quadratic
                // of the result since the precision is near quadratic due to
                // the algorithm
                if(fTools::equalZero(fRetval) || fTools::equalZero(fRetval * fRetval))
                {
                    fRetval = 0.0;
                }
            }

            return fRetval;
        }

        double getArea(const B2DPolygon& rCandidate)
        {
            double fRetval(0.0);

            if(rCandidate.count() > 2 || rCandidate.areControlPointsUsed())
            {
                fRetval = getSignedArea(rCandidate);
                const double fZero(0.0);

                if(fTools::less(fRetval, fZero))
                {
                    fRetval = -fRetval;
                }
            }

            return fRetval;
        }

        double getEdgeLength(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
        {
            const sal_uInt32 nPointCount(rCandidate.count());
            OSL_ENSURE(nIndex < nPointCount, "getEdgeLength: Access to polygon out of range (!)");
            double fRetval(0.0);

            if(nPointCount)
            {
                const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);

                if(rCandidate.areControlPointsUsed())
                {
                    B2DCubicBezier aEdge;

                    aEdge.setStartPoint(rCandidate.getB2DPoint(nIndex));
                    aEdge.setControlPointA(rCandidate.getNextControlPoint(nIndex));
                    aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                    aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

                    fRetval = aEdge.getLength();
                }
                else
                {
                    const B2DPoint aCurrent(rCandidate.getB2DPoint(nIndex));
                    const B2DPoint aNext(rCandidate.getB2DPoint(nNextIndex));

                    fRetval = B2DVector(aNext - aCurrent).getLength();
                }
            }

            return fRetval;
        }

        double getLength(const B2DPolygon& rCandidate)
        {
            double fRetval(0.0);
            const sal_uInt32 nPointCount(rCandidate.count());

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

                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( nPointCount == 1 )
            {
                // only one point (i.e. no edge) - simply take that point
                aRetval = rCandidate.getB2DPoint(0);
            }
            else if(nPointCount > 1)
            {
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                sal_uInt32 nIndex(0);
                bool bIndexDone(false);

                // get length if not given
                if(fTools::equalZero(fLength))
                {
                    fLength = getLength(rCandidate);
                }

                if (fDistance < 0.0)
                {
                    // handle fDistance < 0.0
                    if(rCandidate.isClosed())
                    {
                        // if fDistance < 0.0 increment with multiple of fLength
                        sal_uInt32 nCount(sal_uInt32(-fDistance / fLength));
                        fDistance += double(nCount + 1) * fLength;
                    }
                    else
                    {
                        // crop to polygon start
                        fDistance = 0.0;
                        bIndexDone = true;
                    }
                }
                else if(fTools::moreOrEqual(fDistance, fLength))
                {
                    // handle fDistance >= fLength
                    if(rCandidate.isClosed())
                    {
                        // if fDistance >= fLength decrement with multiple of fLength
                        sal_uInt32 nCount(sal_uInt32(fDistance / fLength));
                        fDistance -= static_cast<double>(nCount) * fLength;
                    }
                    else
                    {
                        // crop to polygon end
                        fDistance = 0.0;
                        nIndex = nEdgeCount;
                        bIndexDone = true;
                    }
                }

                // look for correct index. fDistance is now [0.0 .. fLength[
                double fEdgeLength(getEdgeLength(rCandidate, nIndex));

                while(!bIndexDone)
                {
                    // edge found must be on the half-open range
                    // [0,fEdgeLength).
                    // Note that in theory, we cannot move beyond
                    // the last polygon point, since fDistance>=fLength
                    // is checked above. Unfortunately, with floating-
                    // point calculations, this case might happen.
                    // Handled by nIndex check below
                    if (nIndex+1 < nEdgeCount && fTools::moreOrEqual(fDistance, fEdgeLength))
                    {
                        // go to next edge
                        fDistance -= fEdgeLength;
                        fEdgeLength = getEdgeLength(rCandidate, ++nIndex);
                    }
                    else
                    {
                        // it's on this edge, stop
                        bIndexDone = true;
                    }
                }

                // get the point using nIndex
                aRetval = rCandidate.getB2DPoint(nIndex);

                // if fDistance != 0.0, move that length on the edge. The edge
                // length is in fEdgeLength.
                if(!fTools::equalZero(fDistance))
                {
                    if(fTools::moreOrEqual(fDistance, fEdgeLength))
                    {
                        // end point of chosen edge
                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
                        aRetval = rCandidate.getB2DPoint(nNextIndex);
                    }
                    else if(fTools::equalZero(fDistance))
                    {
                        // start point of chosen edge
                    }
                    else
                    {
                        // inside edge
                        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
                        const B2DPoint aNextPoint(rCandidate.getB2DPoint(nNextIndex));
                        bool bDone(false);

                        // add calculated average value to the return value
                        if(rCandidate.areControlPointsUsed())
                        {
                            // get as bezier segment
                            const B2DCubicBezier aBezierSegment(
                                aRetval, rCandidate.getNextControlPoint(nIndex),
                                rCandidate.getPrevControlPoint(nNextIndex), aNextPoint);

                            if(aBezierSegment.isBezier())
                            {
                                // use B2DCubicBezierHelper to bridge the non-linear gap between
                                // length and bezier distances
                                const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fDistance));

                                aRetval = aBezierSegment.interpolatePoint(fBezierDistance);
                                bDone = true;
                            }
                        }

                        if(!bDone)
                        {
                            const double fRelativeInEdge(fDistance / fEdgeLength);
                            aRetval = interpolate(aRetval, aNextPoint, fRelativeInEdge);
                        }
                    }
                }
            }

            return aRetval;
        }

        B2DPoint getPositionRelative(const B2DPolygon& rCandidate, double fDistance, double fLength)
        {
            // get length if not given
            if(fTools::equalZero(fLength))
            {
                fLength = getLength(rCandidate);
            }

            // multiply fDistance with real length to get absolute position and
            // use getPositionAbsolute
            return getPositionAbsolute(rCandidate, fDistance * fLength, fLength);
        }

        B2DPolygon getSnippetAbsolute(const B2DPolygon& rCandidate, double fFrom, double fTo, double fLength)
        {
            const sal_uInt32 nPointCount(rCandidate.count());

            if(nPointCount)
            {
                // get length if not given
                if(fTools::equalZero(fLength))
                {
                    fLength = getLength(rCandidate);
                }

                // test and correct fFrom
                if (fFrom < 0.0)
                {
                    fFrom = 0.0;
                }

                // test and correct fTo
                if(fTools::more(fTo, fLength))
                {
                    fTo = fLength;
                }

                // test and correct relationship of fFrom, fTo
                if(fTools::more(fFrom, fTo))
                {
                    fFrom = fTo = (fFrom + fTo) / 2.0;
                }

                if(fTools::equalZero(fFrom) && fTools::equal(fTo, fLength))
                {
                    // no change, result is the whole polygon
                    return rCandidate;
                }
                else
                {
                    B2DPolygon aRetval;
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                    double fPositionOfStart(0.0);
                    bool bStartDone(false);
                    bool bEndDone(false);

                    for(sal_uInt32 a(0); !(bStartDone && bEndDone) && a < nEdgeCount; a++)
                    {
                        const double fEdgeLength(getEdgeLength(rCandidate, a));

                        if(!bStartDone)
                        {
                            if(fTools::equalZero(fFrom))
                            {
                                aRetval.append(rCandidate.getB2DPoint(a));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
                                }

                                bStartDone = true;
                            }
                            else if(fTools::moreOrEqual(fFrom, fPositionOfStart) && fTools::less(fFrom, fPositionOfStart + fEdgeLength))
                            {
                                // calculate and add start point
                                if(fTools::equalZero(fEdgeLength))
                                {
                                    aRetval.append(rCandidate.getB2DPoint(a));

                                    if(rCandidate.areControlPointsUsed())
                                    {
                                        aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
                                    }
                                }
                                else
                                {
                                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                                    const B2DPoint aStart(rCandidate.getB2DPoint(a));
                                    const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
                                    bool bDone(false);

                                    if(rCandidate.areControlPointsUsed())
                                    {
                                        const B2DCubicBezier aBezierSegment(
                                            aStart, rCandidate.getNextControlPoint(a),
                                            rCandidate.getPrevControlPoint(nNextIndex), aEnd);

                                        if(aBezierSegment.isBezier())
                                        {
                                            // use B2DCubicBezierHelper to bridge the non-linear gap between
                                            // length and bezier distances
                                            const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                            const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fFrom - fPositionOfStart));
                                            B2DCubicBezier aRight;

                                            aBezierSegment.split(fBezierDistance, nullptr, &aRight);
                                            aRetval.append(aRight.getStartPoint());
                                            aRetval.setNextControlPoint(aRetval.count() - 1, aRight.getControlPointA());
                                            bDone = true;
                                        }
                                    }

                                    if(!bDone)
                                    {
                                        const double fRelValue((fFrom - fPositionOfStart) / fEdgeLength);
                                        aRetval.append(interpolate(aStart, aEnd, fRelValue));
                                    }
                                }

                                bStartDone = true;

                                // if same point, end is done, too.
                                if(rtl::math::approxEqual(fFrom, fTo))
                                {
                                    bEndDone = true;
                                }
                            }
                        }

                        if(!bEndDone && fTools::moreOrEqual(fTo, fPositionOfStart) && fTools::less(fTo, fPositionOfStart + fEdgeLength))
                        {
                            // calculate and add end point
                            if(fTools::equalZero(fEdgeLength))
                            {
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                                aRetval.append(rCandidate.getB2DPoint(nNextIndex));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
                                }
                            }
                            else
                            {
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                                const B2DPoint aStart(rCandidate.getB2DPoint(a));
                                const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
                                bool bDone(false);

                                if(rCandidate.areControlPointsUsed())
                                {
                                    const B2DCubicBezier aBezierSegment(
                                        aStart, rCandidate.getNextControlPoint(a),
                                        rCandidate.getPrevControlPoint(nNextIndex), aEnd);

                                    if(aBezierSegment.isBezier())
                                    {
                                        // use B2DCubicBezierHelper to bridge the non-linear gap between
                                        // length and bezier distances
                                        const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                        const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fTo - fPositionOfStart));
                                        B2DCubicBezier aLeft;

                                        aBezierSegment.split(fBezierDistance, &aLeft, nullptr);
                                        aRetval.append(aLeft.getEndPoint());
                                        aRetval.setPrevControlPoint(aRetval.count() - 1, aLeft.getControlPointB());
                                        bDone = true;
                                    }
                                }

                                if(!bDone)
                                {
                                    const double fRelValue((fTo - fPositionOfStart) / fEdgeLength);
                                    aRetval.append(interpolate(aStart, aEnd, fRelValue));
                                }
                            }

                            bEndDone = true;
                        }

                        if(!bEndDone)
                        {
                            if(bStartDone)
                            {
                                // add segments end point
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                                aRetval.append(rCandidate.getB2DPoint(nNextIndex));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(nNextIndex));
                                }
                            }

                            // increment fPositionOfStart
                            fPositionOfStart += fEdgeLength;
                        }
                    }
                    return aRetval;
                }
            }
            else
            {
                return rCandidate;
            }
        }

        CutFlagValue findCut(
            const B2DPoint& rEdge1Start, const B2DVector& rEdge1Delta,
            const B2DPoint& rEdge2Start, const B2DVector& rEdge2Delta,
            CutFlagValue aCutFlags,
            double* pCut1, double* pCut2)
        {
            CutFlagValue aRetval(CutFlagValue::NONE);
            double fCut1(0.0);
            double fCut2(0.0);
            bool bFinished(!static_cast<bool>(aCutFlags & CutFlagValue::ALL));

            // test for same points?
            if(!bFinished
                && (aCutFlags & (CutFlagValue::START1|CutFlagValue::END1))
                && (aCutFlags & (CutFlagValue::START2|CutFlagValue::END2)))
            {
                // same startpoint?
                if((aCutFlags & (CutFlagValue::START1|CutFlagValue::START2)) == (CutFlagValue::START1|CutFlagValue::START2))
                {
                    if(rEdge1Start.equal(rEdge2Start))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::START1|CutFlagValue::START2);
                    }
                }

                // same endpoint?
                if(!bFinished && (aCutFlags & (CutFlagValue::END1|CutFlagValue::END2)) == (CutFlagValue::END1|CutFlagValue::END2))
                {
                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                    if(aEnd1.equal(aEnd2))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::END1|CutFlagValue::END2);
                        fCut1 = fCut2 = 1.0;
                    }
                }

                // startpoint1 == endpoint2?
                if(!bFinished && (aCutFlags & (CutFlagValue::START1|CutFlagValue::END2)) == (CutFlagValue::START1|CutFlagValue::END2))
                {
                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                    if(rEdge1Start.equal(aEnd2))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::START1|CutFlagValue::END2);
                        fCut1 = 0.0;
                        fCut2 = 1.0;
                    }
                }

                // startpoint2 == endpoint1?
                if(!bFinished&& (aCutFlags & (CutFlagValue::START2|CutFlagValue::END1)) == (CutFlagValue::START2|CutFlagValue::END1))
                {
                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

                    if(rEdge2Start.equal(aEnd1))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::START2|CutFlagValue::END1);
                        fCut1 = 1.0;
                        fCut2 = 0.0;
                    }
                }
            }

            if(!bFinished && (aCutFlags & CutFlagValue::LINE))
            {
                if(aCutFlags & CutFlagValue::START1)
                {
                    // start1 on line 2 ?
                    if(isPointOnEdge(rEdge1Start, rEdge2Start, rEdge2Delta, &fCut2))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::LINE|CutFlagValue::START1);
                    }
                }

                if(!bFinished && (aCutFlags & CutFlagValue::START2))
                {
                    // start2 on line 1 ?
                    if(isPointOnEdge(rEdge2Start, rEdge1Start, rEdge1Delta, &fCut1))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::LINE|CutFlagValue::START2);
                    }
                }

                if(!bFinished && (aCutFlags & CutFlagValue::END1))
                {
                    // end1 on line 2 ?
                    const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

                    if(isPointOnEdge(aEnd1, rEdge2Start, rEdge2Delta, &fCut2))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::LINE|CutFlagValue::END1);
                    }
                }

                if(!bFinished && (aCutFlags & CutFlagValue::END2))
                {
                    // end2 on line 1 ?
                    const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

                    if(isPointOnEdge(aEnd2, rEdge1Start, rEdge1Delta, &fCut1))
                    {
                        bFinished = true;
                        aRetval = (CutFlagValue::LINE|CutFlagValue::END2);
                    }
                }

                if(!bFinished)
                {
                    // cut in line1, line2 ?
                    fCut1 = (rEdge1Delta.getX() * rEdge2Delta.getY()) - (rEdge1Delta.getY() * rEdge2Delta.getX());

                    if(!fTools::equalZero(fCut1))
                    {
                        fCut1 = (rEdge2Delta.getY() * (rEdge2Start.getX() - rEdge1Start.getX())
                            + rEdge2Delta.getX() * (rEdge1Start.getY() - rEdge2Start.getY())) / fCut1;

                        const double fZero(0.0);
                        const double fOne(1.0);

                        // inside parameter range edge1 AND fCut2 is calculable
                        if(fTools::more(fCut1, fZero) && fTools::less(fCut1, fOne)
                            && (!fTools::equalZero(rEdge2Delta.getX()) || !fTools::equalZero(rEdge2Delta.getY())))
                        {
                            // take the more precise calculation of the two possible
                            if(fabs(rEdge2Delta.getX()) > fabs(rEdge2Delta.getY()))
                            {
                                fCut2 = (rEdge1Start.getX() + fCut1
                                    * rEdge1Delta.getX() - rEdge2Start.getX()) / rEdge2Delta.getX();
                            }
                            else
                            {
                                fCut2 = (rEdge1Start.getY() + fCut1
                                    * rEdge1Delta.getY() - rEdge2Start.getY()) / rEdge2Delta.getY();
                            }

                            // inside parameter range edge2, too
                            if(fTools::more(fCut2, fZero) && fTools::less(fCut2, fOne))
                            {
                                aRetval = CutFlagValue::LINE;
                            }
                        }
                    }
                }
            }

            // copy values if wanted
            if(pCut1)
            {
                *pCut1 = fCut1;
            }

            if(pCut2)
            {
                *pCut2 = fCut2;
            }

            return aRetval;
        }

        bool isPointOnEdge(
            const B2DPoint& rPoint,
            const B2DPoint& rEdgeStart,
            const B2DVector& rEdgeDelta,
            double* pCut)
        {
            bool bDeltaXIsZero(fTools::equalZero(rEdgeDelta.getX()));
            bool bDeltaYIsZero(fTools::equalZero(rEdgeDelta.getY()));
            const double fZero(0.0);
            const double fOne(1.0);

            if(bDeltaXIsZero && bDeltaYIsZero)
            {
                // no line, just a point
                return false;
            }
            else if(bDeltaXIsZero)
            {
                // vertical line
                if(fTools::equal(rPoint.getX(), rEdgeStart.getX()))
                {
                    double fValue = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();

                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
                    {
                        if(pCut)
                        {
                            *pCut = fValue;
                        }

                        return true;
                    }
                }
            }
            else if(bDeltaYIsZero)
            {
                // horizontal line
                if(fTools::equal(rPoint.getY(), rEdgeStart.getY()))
                {
                    double fValue = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();

                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
                    {
                        if(pCut)
                        {
                            *pCut = fValue;
                        }

                        return true;
                    }
                }
            }
            else
            {
                // any angle line
                double fTOne = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();
                double fTTwo = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();

                if(fTools::equal(fTOne, fTTwo))
                {
                    // same parameter representation, point is on line. Take
                    // middle value for better results
                    double fValue = (fTOne + fTTwo) / 2.0;

                    if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
                    {
                        // point is inside line bounds, too
                        if(pCut)
                        {
                            *pCut = fValue;
                        }

                        return true;
                    }
                }
            }

            return false;
        }

        void applyLineDashing(
            const B2DPolygon& rCandidate,
            const std::vector<double>& rDotDashArray,
            B2DPolyPolygon* pLineTarget,
            B2DPolyPolygon* pGapTarget,
            double fDotDashLength)
        {
            // clear targets in any case
            if(pLineTarget)
            {
                pLineTarget->clear();
            }

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

            // call version that uses callbacks
            applyLineDashing(
                rCandidate,
                rDotDashArray,
                // provide callbacks as lambdas
                (!pLineTarget
                    ? std::function<void(const basegfx::B2DPolygon&)>()
                    : [&pLineTarget](const basegfx::B2DPolygon& rSnippet){ pLineTarget->append(rSnippet); }),
                (!pGapTarget
                    ? std::function<void(const basegfx::B2DPolygon&)>()
                    : [&pGapTarget](const basegfx::B2DPolygon& rSnippet){ pGapTarget->append(rSnippet); }),
                fDotDashLength);
        }

        static void implHandleSnippet(
            const B2DPolygon& rSnippet,
            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rTargetCallback,
            B2DPolygon& rFirst,
            B2DPolygon& rLast)
        {
            if(rSnippet.isClosed())
            {
                if(!rFirst.count())
                {
                    rFirst = rSnippet;
                }
                else
                {
                    if(rLast.count())
                    {
                        rTargetCallback(rLast);
                    }

                    rLast = rSnippet;
                }
            }
            else
            {
                rTargetCallback(rSnippet);
            }
        }

        static void implHandleFirstLast(
            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rTargetCallback,
            B2DPolygon& rFirst,
            B2DPolygon& rLast)
        {
            if(rFirst.count() && rLast.count()
                && rFirst.getB2DPoint(0).equal(rLast.getB2DPoint(rLast.count() - 1)))
            {
                // start of first and end of last are the same -> merge them
                rLast.append(rFirst);
                rLast.removeDoublePoints();
                rFirst.clear();
            }

            if(rLast.count())
            {
                rTargetCallback(rLast);
            }

            if(rFirst.count())
            {
                rTargetCallback(rFirst);
            }
        }

        void applyLineDashing(
            const B2DPolygon& rCandidate,
            const std::vector<double>& rDotDashArray,
            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rLineTargetCallback,
            const std::function<void(const basegfx::B2DPolygon& rSnippet)>& rGapTargetCallback,
            double fDotDashLength)
        {
            const sal_uInt32 nPointCount(rCandidate.count());
            const sal_uInt32 nDotDashCount(rDotDashArray.size());

            if(fDotDashLength <= 0.0)
            {
                fDotDashLength = std::accumulate(rDotDashArray.begin(), rDotDashArray.end(), 0.0);
            }

            if(fDotDashLength <= 0.0 || (!rLineTargetCallback && !rGapTargetCallback) || !nPointCount)
            {
                // parameters make no sense, just add source to targets
                if (rLineTargetCallback)
                    rLineTargetCallback(rCandidate);

                if (rGapTargetCallback)
                    rGapTargetCallback(rCandidate);

                return;
            }

            // precalculate maximal acceptable length of candidate polygon assuming
            // we want to create a maximum of fNumberOfAllowedSnippets. For
            // fNumberOfAllowedSnippets use ca. 65536, double due to line & gap.
            static const double fNumberOfAllowedSnippets(65535.0 * 2.0);
            const double fAllowedLength((fNumberOfAllowedSnippets * fDotDashLength) / double(rDotDashArray.size()));
            const double fCandidateLength(basegfx::utils::getLength(rCandidate));
            std::vector<double> aDotDashArray(rDotDashArray);

            if(fCandidateLength > fAllowedLength)
            {
                // we would produce more than fNumberOfAllowedSnippets, so
                // adapt aDotDashArray to exactly produce assumed number. Also
                // assert this to let the caller know about it.
                // If this asserts: Please think about checking your DotDashArray
                // before calling this function or evtl. use the callback version
                // to *not* produce that much of data. Even then, you may still
                // think about producing too much runtime (!)
                assert(true && "applyLineDashing: potentially too expensive to do the requested dismantle - please consider stretched LineDash pattern (!)");

                // calculate correcting factor, apply to aDotDashArray and fDotDashLength
                // to enlarge these as needed
                const double fFactor(fCandidateLength / fAllowedLength);
                std::for_each(aDotDashArray.begin(), aDotDashArray.end(), [&fFactor](double &f){ f *= fFactor; });
            }

            // prepare current edge's start
            B2DCubicBezier aCurrentEdge;
            const bool bIsClosed(rCandidate.isClosed());
            const sal_uInt32 nEdgeCount(bIsClosed ? nPointCount : nPointCount - 1);
            aCurrentEdge.setStartPoint(rCandidate.getB2DPoint(0));

            // prepare DotDashArray iteration and the line/gap switching bool
            sal_uInt32 nDotDashIndex(0);
            bool bIsLine(true);
            double fDotDashMovingLength(aDotDashArray[0]);
            B2DPolygon aSnippet;

            // remember 1st and last snippets to try to merge after execution
            // is complete and hand to callback
            B2DPolygon aFirstLine, aLastLine;
            B2DPolygon aFirstGap, aLastGap;

            // iterate over all edges
            for(sal_uInt32 a(0); a < nEdgeCount; a++)
            {
                // update current edge (fill in C1, C2 and end point)
                double fLastDotDashMovingLength(0.0);
                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                aCurrentEdge.setControlPointA(rCandidate.getNextControlPoint(a));
                aCurrentEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                aCurrentEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

                // check if we have a trivial bezier segment -> possible fallback to edge
                aCurrentEdge.testAndSolveTrivialBezier();

                if(aCurrentEdge.isBezier())
                {
                    // bezier segment
                    const B2DCubicBezierHelper aCubicBezierHelper(aCurrentEdge);
                    const double fEdgeLength(aCubicBezierHelper.getLength());

                    if(!fTools::equalZero(fEdgeLength))
                    {
                        while(fTools::less(fDotDashMovingLength, fEdgeLength))
                        {
                            // new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
                            const bool bHandleLine(bIsLine && rLineTargetCallback);
                            const bool bHandleGap(!bIsLine && rGapTargetCallback);

                            if(bHandleLine || bHandleGap)
                            {
                                const double fBezierSplitStart(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));
                                const double fBezierSplitEnd(aCubicBezierHelper.distanceToRelative(fDotDashMovingLength));
                                B2DCubicBezier aBezierSnippet(aCurrentEdge.snippet(fBezierSplitStart, fBezierSplitEnd));

                                if(!aSnippet.count())
                                {
                                    aSnippet.append(aBezierSnippet.getStartPoint());
                                }

                                aSnippet.appendBezierSegment(aBezierSnippet.getControlPointA(), aBezierSnippet.getControlPointB(), aBezierSnippet.getEndPoint());

                                if(bHandleLine)
                                {
                                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
                                }

                                if(bHandleGap)
                                {
                                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
                                }

                                aSnippet.clear();
                            }

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

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

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

                            aCurrentEdge.split(fBezierSplit, nullptr, &aRight);

                            if(!aSnippet.count())
                            {
                                aSnippet.append(aRight.getStartPoint());
                            }

                            aSnippet.appendBezierSegment(aRight.getControlPointA(), aRight.getControlPointB(), aRight.getEndPoint());
                        }

                        // prepare move to next edge
                        fDotDashMovingLength -= fEdgeLength;
                    }
                }
                else
                {
                    // simple edge
                    const double fEdgeLength(aCurrentEdge.getEdgeLength());

                    if(!fTools::equalZero(fEdgeLength))
                    {
                        while(fTools::less(fDotDashMovingLength, fEdgeLength))
                        {
                            // new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
                            const bool bHandleLine(bIsLine && rLineTargetCallback);
                            const bool bHandleGap(!bIsLine && rGapTargetCallback);

                            if(bHandleLine || bHandleGap)
                            {
                                if(!aSnippet.count())
                                {
                                    aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
                                }

                                aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fDotDashMovingLength / fEdgeLength));

                                if(bHandleLine)
                                {
                                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
                                }

                                if(bHandleGap)
                                {
                                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
                                }

                                aSnippet.clear();
                            }

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

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

                        if(bHandleLine || bHandleGap)
                        {
                            if(!aSnippet.count())
                            {
                                aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
                            }

                            aSnippet.append(aCurrentEdge.getEndPoint());
                        }

                        // prepare move to next edge
                        fDotDashMovingLength -= fEdgeLength;
                    }
                }

                // prepare next edge step (end point gets new start point)
                aCurrentEdge.setStartPoint(aCurrentEdge.getEndPoint());
            }

            // append last intermediate results (if exists)
            if(aSnippet.count())
            {
                const bool bHandleLine(bIsLine && rLineTargetCallback);
                const bool bHandleGap(!bIsLine && rGapTargetCallback);

                if(bHandleLine)
                {
                    implHandleSnippet(aSnippet, rLineTargetCallback, aFirstLine, aLastLine);
                }

                if(bHandleGap)
                {
                    implHandleSnippet(aSnippet, rGapTargetCallback, aFirstGap, aLastGap);
                }
            }

            if(bIsClosed && rLineTargetCallback)
            {
                implHandleFirstLast(rLineTargetCallback, aFirstLine, aLastLine);
            }

            if(bIsClosed && rGapTargetCallback)
            {
                implHandleFirstLast(rGapTargetCallback, aFirstGap, aLastGap);
            }
        }

        // test if point is inside epsilon-range around an edge defined
        // by the two given points. Can be used for HitTesting. The epsilon-range
        // is defined to be the rectangle centered to the given edge, using height
        // 2 x fDistance, and the circle around both points with radius fDistance.
        bool isInEpsilonRange(const B2DPoint& rEdgeStart, const B2DPoint& rEdgeEnd, const B2DPoint& rTestPosition, double fDistance)
        {
            // build edge vector
            const B2DVector aEdge(rEdgeEnd - rEdgeStart);
            bool bDoDistanceTestStart(false);
            bool bDoDistanceTestEnd(false);

            if(aEdge.equalZero())
            {
                // no edge, just a point. Do one of the distance tests.
                bDoDistanceTestStart = true;
            }
            else
            {
                // edge has a length. Create perpendicular vector.
                const B2DVector aPerpend(getPerpendicular(aEdge));
                double fCut(
                    (aPerpend.getY() * (rTestPosition.getX() - rEdgeStart.getX())
                    + aPerpend.getX() * (rEdgeStart.getY() - rTestPosition.getY())) /
                    (aEdge.getX() * aEdge.getX() + aEdge.getY() * aEdge.getY()));
                const double fZero(0.0);
                const double fOne(1.0);

                if(fTools::less(fCut, fZero))
                {
                    // left of rEdgeStart
                    bDoDistanceTestStart = true;
                }
                else if(fTools::more(fCut, fOne))
                {
                    // right of rEdgeEnd
                    bDoDistanceTestEnd = true;
                }
                else
                {
                    // inside line [0.0 .. 1.0]
                    const B2DPoint aCutPoint(interpolate(rEdgeStart, rEdgeEnd, fCut));
                    const B2DVector aDelta(rTestPosition - aCutPoint);
                    const double fDistanceSquare(aDelta.scalar(aDelta));

                    return fDistanceSquare <= fDistance * fDistance;
                }
            }

            if(bDoDistanceTestStart)
            {
                const B2DVector aDelta(rTestPosition - rEdgeStart);
                const double fDistanceSquare(aDelta.scalar(aDelta));

                if(fDistanceSquare <= fDistance * fDistance)
                {
                    return true;
                }
            }
            else if(bDoDistanceTestEnd)
            {
                const B2DVector aDelta(rTestPosition - rEdgeEnd);
                const double fDistanceSquare(aDelta.scalar(aDelta));

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

            return false;
        }

        // test if point is inside epsilon-range around the given Polygon. Can be used
        // for HitTesting. The epsilon-range is defined to be the tube around the polygon
        // with distance fDistance and rounded edges (start and end point).
        bool isInEpsilonRange(const B2DPolygon& rCandidate, const B2DPoint& rTestPosition, double fDistance)
        {
            // force to non-bezier polygon
            const B2DPolygon& aCandidate(rCandidate.getDefaultAdaptiveSubdivision());
            const sal_uInt32 nPointCount(aCandidate.count());

            if(!nPointCount)
                return false;

            const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
            B2DPoint aCurrent(aCandidate.getB2DPoint(0));

            if(nEdgeCount)
            {
                // edges
                for(sal_uInt32 a(0); a < nEdgeCount; a++)
                {
                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                    const B2DPoint aNext(aCandidate.getB2DPoint(nNextIndex));

                    if(isInEpsilonRange(aCurrent, aNext, rTestPosition, fDistance))
                    {
                        return true;
                    }

                    // prepare next step
                    aCurrent = aNext;
                }
            }
            else
            {
                // no edges, but points -> not closed. Check single point. Just
                // use isInEpsilonRange with twice the same point, it handles those well
                if(isInEpsilonRange(aCurrent, aCurrent, rTestPosition, fDistance))
                {
                    return true;
                }
            }

            return false;
        }

        // Calculates distance of curve point to its control point for a Bézier curve, that
        // approximates a unit circle arc. fAngle is the center angle of the circle arc. The
        // constrain 0<=fAngle<=pi/2 must not be violated to give a useful accuracy. For details
        // and alternatives read document "ApproxCircleInfo.odt", attachment of bug tdf#121425.
        static double impDistanceBezierPointToControl(double fAngle)
        {
            SAL_WARN_IF(fAngle < 0 || fAngle > M_PI_2,"basegfx","angle not suitable for approximate circle");
            if (0 <= fAngle && fAngle <= M_PI_2)
            {
                return 4.0/3.0 * ( tan(fAngle/4.0));
            }
            else
                return 0;
        }

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

            fRadiusX = std::clamp(fRadiusX, 0.0, 1.0);
            fRadiusY = std::clamp(fRadiusY, 0.0, 1.0);

            if(rtl::math::approxEqual(fZero, fRadiusX) || rtl::math::approxEqual(fZero, fRadiusY))
            {
                // at least in one direction no radius, use rectangle.
                // Do not use createPolygonFromRect() here since original
                // creator (historical reasons) still creates a start point at the
                // bottom center, so do the same here to get the same line patterns.
                // Due to this the order of points is different, too.
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