b2dlinegeometry.cxx

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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
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 *
 * 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
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 *   License, Version 2.0 (the "License"); you may not use this file
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#include <osl/diagnose.h>
#include <sal/log.hxx>
#include <basegfx/polygon/b2dlinegeometry.hxx>
#include <basegfx/point/b2dpoint.hxx>
#include <basegfx/vector/b2dvector.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <basegfx/polygon/b2dpolypolygontools.hxx>
#include <basegfx/range/b2drange.hxx>
#include <basegfx/matrix/b2dhommatrix.hxx>
#include <basegfx/curve/b2dcubicbezier.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx>
#include <com/sun/star/drawing/LineCap.hpp>
#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
#include <basegfx/polygon/b2dpolygontriangulator.hxx>
 
namespace basegfx::utils
{
        B2DPolyPolygon createAreaGeometryForLineStartEnd(
            const B2DPolygon& rCandidate,
            const B2DPolyPolygon& rArrow,
            bool bStart,
            double fWidth,
            double fCandidateLength,
            double fDockingPosition, // 0->top, 1->bottom
            double* pConsumedLength,
            double fShift)
        {
            B2DPolyPolygon aRetval;
            assert((rCandidate.count() > 1) && "createAreaGeometryForLineStartEnd: Line polygon has too few points");
            assert((rArrow.count() > 0) && "createAreaGeometryForLineStartEnd: Empty arrow utils::PolyPolygon");
            assert((fWidth > 0.0) && "createAreaGeometryForLineStartEnd: Width too small");
            assert((fDockingPosition >= 0.0 && fDockingPosition <= 1.0) &&
                "createAreaGeometryForLineStartEnd: fDockingPosition out of range [0.0 .. 1.0]");
 
            if(fWidth < 0.0)
            {
                fWidth = -fWidth;
            }
 
            if(rCandidate.count() > 1 && rArrow.count() && !fTools::equalZero(fWidth))
            {
                if(fDockingPosition < 0.0)
                {
                    fDockingPosition = 0.0;
                }
                else if(fDockingPosition > 1.0)
                {
                    fDockingPosition = 1.0;
                }
 
                // init return value from arrow
                aRetval.append(rArrow);
 
                // get size of the arrow
                const B2DRange aArrowSize(getRange(rArrow));
 
                // build ArrowTransform; center in X, align with axis in Y
                B2DHomMatrix aArrowTransform(basegfx::utils::createTranslateB2DHomMatrix(
                    -aArrowSize.getCenter().getX(), -aArrowSize.getMinimum().getY()));
 
                // scale to target size
                const double fArrowScale(fWidth / (aArrowSize.getWidth()));
                aArrowTransform.scale(fArrowScale, fArrowScale);
 
                // get arrow size in Y
                B2DPoint aUpperCenter(aArrowSize.getCenter().getX(), aArrowSize.getMaximum().getY());
                aUpperCenter *= aArrowTransform;
                const double fArrowYLength(B2DVector(aUpperCenter).getLength());
 
                // move arrow to have docking position centered
                aArrowTransform.translate(0.0, -fArrowYLength * fDockingPosition + fShift);
 
                // prepare polygon length
                if(fTools::equalZero(fCandidateLength))
                {
                    fCandidateLength = getLength(rCandidate);
                }
 
                // get the polygon vector we want to plant this arrow on
                const double fConsumedLength(fArrowYLength * (1.0 - fDockingPosition) - fShift);
                const B2DVector aHead(rCandidate.getB2DPoint(bStart ? 0 : rCandidate.count() - 1));
                const B2DVector aTail(getPositionAbsolute(rCandidate,
                    bStart ? fConsumedLength : fCandidateLength - fConsumedLength, fCandidateLength));
 
                // from that vector, take the needed rotation and add rotate for arrow to transformation
                const B2DVector aTargetDirection(aHead - aTail);
                const double fRotation(atan2(aTargetDirection.getY(), aTargetDirection.getX()) + M_PI_2);
 
                // rotate around docking position
                aArrowTransform.rotate(fRotation);
 
                // move arrow docking position to polygon head
                aArrowTransform.translate(aHead.getX(), aHead.getY());
 
                // transform retval and close
                aRetval.transform(aArrowTransform);
                aRetval.setClosed(true);
 
                // if pConsumedLength is asked for, fill it
                if(pConsumedLength)
                {
                    *pConsumedLength = fConsumedLength;
                }
            }
 
            return aRetval;
        }
} // end of namespace
 
namespace basegfx
{
    // anonymous namespace for local helpers
    namespace
    {
        bool impIsSimpleEdge(const B2DCubicBezier& rCandidate, double fMaxCosQuad, double fMaxPartOfEdgeQuad)
        {
            // isBezier() is true, already tested by caller
            const B2DVector aEdge(rCandidate.getEndPoint() - rCandidate.getStartPoint());
 
            if(aEdge.equalZero())
            {
                // start and end point the same, but control vectors used -> balloon curve loop
                // is not a simple edge
                return false;
            }
 
            // get tangentA and scalar with edge
            const B2DVector aTangentA(rCandidate.getTangent(0.0));
            const double fScalarAE(aEdge.scalar(aTangentA));
 
            if(fTools::lessOrEqual(fScalarAE, 0.0))
            {
                // angle between TangentA and Edge is bigger or equal 90 degrees
                return false;
            }
 
            // get self-scalars for E and A
            const double fScalarE(aEdge.scalar(aEdge));
            const double fScalarA(aTangentA.scalar(aTangentA));
            const double fLengthCompareE(fScalarE * fMaxPartOfEdgeQuad);
 
            if(fTools::moreOrEqual(fScalarA, fLengthCompareE))
            {
                // length of TangentA is more than fMaxPartOfEdge of length of edge
                return false;
            }
 
            if(fTools::lessOrEqual(fScalarAE * fScalarAE, fScalarA * fScalarE * fMaxCosQuad))
            {
                // angle between TangentA and Edge is bigger or equal angle defined by fMaxCos
                return false;
            }
 
            // get tangentB and scalar with edge
            const B2DVector aTangentB(rCandidate.getTangent(1.0));
            const double fScalarBE(aEdge.scalar(aTangentB));
 
            if(fTools::lessOrEqual(fScalarBE, 0.0))
            {
                // angle between TangentB and Edge is bigger or equal 90 degrees
                return false;
            }
 
            // get self-scalar for B
            const double fScalarB(aTangentB.scalar(aTangentB));
 
            if(fTools::moreOrEqual(fScalarB, fLengthCompareE))
            {
                // length of TangentB is more than fMaxPartOfEdge of length of edge
                return false;
            }
 
            if(fTools::lessOrEqual(fScalarBE * fScalarBE, fScalarB * fScalarE * fMaxCosQuad))
            {
                // angle between TangentB and Edge is bigger or equal defined by fMaxCos
                return false;
            }
 
            return true;
        }
 
        void impSubdivideToSimple(const B2DCubicBezier& rCandidate, B2DPolygon& rTarget, double fMaxCosQuad, double fMaxPartOfEdgeQuad, sal_uInt32 nMaxRecursionDepth)
        {
            if(!nMaxRecursionDepth || impIsSimpleEdge(rCandidate, fMaxCosQuad, fMaxPartOfEdgeQuad))
            {
                rTarget.appendBezierSegment(rCandidate.getControlPointA(), rCandidate.getControlPointB(), rCandidate.getEndPoint());
            }
            else
            {
                B2DCubicBezier aLeft, aRight;
                rCandidate.split(0.5, &aLeft, &aRight);
 
                impSubdivideToSimple(aLeft, rTarget, fMaxCosQuad, fMaxPartOfEdgeQuad, nMaxRecursionDepth - 1);
                impSubdivideToSimple(aRight, rTarget, fMaxCosQuad, fMaxPartOfEdgeQuad, nMaxRecursionDepth - 1);
            }
        }
 
        B2DPolygon subdivideToSimple(const B2DPolygon& rCandidate, double fMaxCosQuad, double fMaxPartOfEdgeQuad)
        {
            const sal_uInt32 nPointCount(rCandidate.count());
 
            if(rCandidate.areControlPointsUsed() && nPointCount)
            {
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                B2DPolygon aRetval;
                B2DCubicBezier aEdge;
 
                // prepare edge for loop
                aEdge.setStartPoint(rCandidate.getB2DPoint(0));
                aRetval.append(aEdge.getStartPoint());
 
                for(sal_uInt32 a(0); a < nEdgeCount; a++)
                {
                    // fill B2DCubicBezier
                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                    aEdge.setControlPointA(rCandidate.getNextControlPoint(a));
                    aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                    aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
 
                    // get rid of unnecessary bezier segments
                    aEdge.testAndSolveTrivialBezier();
 
                    if(aEdge.isBezier())
                    {
                        // before splitting recursively with internal simple criteria, use
                        // ExtremumPosFinder to remove those
                        std::vector< double > aExtremumPositions;
 
                        aExtremumPositions.reserve(4);
                        aEdge.getAllExtremumPositions(aExtremumPositions);
 
                        const sal_uInt32 nCount(aExtremumPositions.size());
 
                        if(nCount)
                        {
                            if(nCount > 1)
                            {
                                // create order from left to right
                                std::sort(aExtremumPositions.begin(), aExtremumPositions.end());
                            }
 
                            for(sal_uInt32 b(0); b < nCount;)
                            {
                                // split aEdge at next split pos
                                B2DCubicBezier aLeft;
                                const double fSplitPos(aExtremumPositions[b++]);
 
                                aEdge.split(fSplitPos, &aLeft, &aEdge);
                                aLeft.testAndSolveTrivialBezier();
 
                                // consume left part
                                if(aLeft.isBezier())
                                {
                                    impSubdivideToSimple(aLeft, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
                                }
                                else
                                {
                                    aRetval.append(aLeft.getEndPoint());
                                }
 
                                if(b < nCount)
                                {
                                    // correct the remaining split positions to fit to shortened aEdge
                                    const double fScaleFactor(1.0 / (1.0 - fSplitPos));
 
                                    for(sal_uInt32 c(b); c < nCount; c++)
                                    {
                                        aExtremumPositions[c] = (aExtremumPositions[c] - fSplitPos) * fScaleFactor;
                                    }
                                }
                            }
 
                            // test the shortened rest of aEdge
                            aEdge.testAndSolveTrivialBezier();
 
                            // consume right part
                            if(aEdge.isBezier())
                            {
                                impSubdivideToSimple(aEdge, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
                            }
                            else
                            {
                                aRetval.append(aEdge.getEndPoint());
                            }
                        }
                        else
                        {
                            impSubdivideToSimple(aEdge, aRetval, fMaxCosQuad, fMaxPartOfEdgeQuad, 6);
                        }
                    }
                    else
                    {
                        // straight edge, add point
                        aRetval.append(aEdge.getEndPoint());
                    }
 
                    // prepare edge for next step
                    aEdge.setStartPoint(aEdge.getEndPoint());
                }
 
                // copy closed flag and check for double points
                aRetval.setClosed(rCandidate.isClosed());
                aRetval.removeDoublePoints();
 
                return aRetval;
            }
            else
            {
                return rCandidate;
            }
        }
 
        B2DPolygon createAreaGeometryForEdge(
            const B2DCubicBezier& rEdge,
            double fHalfLineWidth,
            bool bStartRound,
            bool bEndRound,
            bool bStartSquare,
            bool bEndSquare,
            basegfx::triangulator::B2DTriangleVector* pTriangles)
        {
            // create polygon for edge
            // Unfortunately, while it would be geometrically correct to not add
            // the in-between points EdgeEnd and EdgeStart, it leads to rounding
            // errors when converting to integer polygon coordinates for painting
            if(rEdge.isBezier())
            {
                // prepare target and data common for upper and lower
                B2DPolygon aBezierPolygon;
                const B2DVector aPureEdgeVector(rEdge.getEndPoint() - rEdge.getStartPoint());
                const double fEdgeLength(aPureEdgeVector.getLength());
                const bool bIsEdgeLengthZero(fTools::equalZero(fEdgeLength));
                B2DVector aTangentA(rEdge.getTangent(0.0)); aTangentA.normalize();
                B2DVector aTangentB(rEdge.getTangent(1.0)); aTangentB.normalize();
                const B2DVector aNormalizedPerpendicularA(getPerpendicular(aTangentA));
                const B2DVector aNormalizedPerpendicularB(getPerpendicular(aTangentB));
 
                // create upper displacement vectors and check if they cut
                const B2DVector aPerpendStartA(aNormalizedPerpendicularA * -fHalfLineWidth);
                const B2DVector aPerpendEndA(aNormalizedPerpendicularB * -fHalfLineWidth);
                double fCutA(0.0);
                const CutFlagValue aCutA(utils::findCut(
                    rEdge.getStartPoint(), aPerpendStartA,
                    rEdge.getEndPoint(), aPerpendEndA,
                    CutFlagValue::ALL, &fCutA));
                const bool bCutA(aCutA != CutFlagValue::NONE);
 
                // create lower displacement vectors and check if they cut
                const B2DVector aPerpendStartB(aNormalizedPerpendicularA * fHalfLineWidth);
                const B2DVector aPerpendEndB(aNormalizedPerpendicularB * fHalfLineWidth);
                double fCutB(0.0);
                const CutFlagValue aCutB(utils::findCut(
                    rEdge.getEndPoint(), aPerpendEndB,
                    rEdge.getStartPoint(), aPerpendStartB,
                    CutFlagValue::ALL, &fCutB));
                const bool bCutB(aCutB != CutFlagValue::NONE);
 
                // check if cut happens
                const bool bCut(bCutA || bCutB);
                B2DPoint aCutPoint;
 
                // create left edge
                if(bStartRound || bStartSquare)
                {
                    if(bStartRound)
                    {
                        basegfx::B2DPolygon aStartPolygon(utils::createHalfUnitCircle());
 
                        aStartPolygon.transform(
                            utils::createScaleShearXRotateTranslateB2DHomMatrix(
                                fHalfLineWidth, fHalfLineWidth,
                                0.0,
                                atan2(aTangentA.getY(), aTangentA.getX()) + M_PI_2,
                                rEdge.getStartPoint().getX(), rEdge.getStartPoint().getY()));
                        aBezierPolygon.append(aStartPolygon);
                    }
                    else // bStartSquare
                    {
                        const basegfx::B2DPoint aStart(rEdge.getStartPoint() - (aTangentA * fHalfLineWidth));
 
                        if(bCutB)
                        {
                            aBezierPolygon.append(rEdge.getStartPoint() + aPerpendStartB);
                        }
 
                        aBezierPolygon.append(aStart + aPerpendStartB);
                        aBezierPolygon.append(aStart + aPerpendStartA);
 
                        if(bCutA)
                        {
                            aBezierPolygon.append(rEdge.getStartPoint() + aPerpendStartA);
                        }
                    }
                }
                else
                {
                    // append original in-between point
                    aBezierPolygon.append(rEdge.getStartPoint());
                }
 
                // create upper edge.
                {
                    if(bCutA)
                    {
                        // calculate cut point and add
                        aCutPoint = rEdge.getStartPoint() + (aPerpendStartA * fCutA);
                        aBezierPolygon.append(aCutPoint);
                    }
                    else
                    {
                        // create scaled bezier segment
                        const B2DPoint aStart(rEdge.getStartPoint() + aPerpendStartA);
                        const B2DPoint aEnd(rEdge.getEndPoint() + aPerpendEndA);
                        const B2DVector aEdge(aEnd - aStart);
                        const double fLength(aEdge.getLength());
                        const double fScale(bIsEdgeLengthZero ? 1.0 : fLength / fEdgeLength);
                        const B2DVector fRelNext(rEdge.getControlPointA() - rEdge.getStartPoint());
                        const B2DVector fRelPrev(rEdge.getControlPointB() - rEdge.getEndPoint());
 
                        aBezierPolygon.append(aStart);
                        aBezierPolygon.appendBezierSegment(aStart + (fRelNext * fScale), aEnd + (fRelPrev * fScale), aEnd);
                    }
                }
 
                // create right edge
                if(bEndRound || bEndSquare)
                {
                    if(bEndRound)
                    {
                        basegfx::B2DPolygon aEndPolygon(utils::createHalfUnitCircle());
 
                        aEndPolygon.transform(
                            utils::createScaleShearXRotateTranslateB2DHomMatrix(
                                fHalfLineWidth, fHalfLineWidth,
                                0.0,
                                atan2(aTangentB.getY(), aTangentB.getX()) - M_PI_2,
                                rEdge.getEndPoint().getX(), rEdge.getEndPoint().getY()));
                        aBezierPolygon.append(aEndPolygon);
                    }
                    else // bEndSquare
                    {
                        const basegfx::B2DPoint aEnd(rEdge.getEndPoint() + (aTangentB * fHalfLineWidth));
 
                        if(bCutA)
                        {
                            aBezierPolygon.append(rEdge.getEndPoint() + aPerpendEndA);
                        }
 
                        aBezierPolygon.append(aEnd + aPerpendEndA);
                        aBezierPolygon.append(aEnd + aPerpendEndB);
 
                        if(bCutB)
                        {
                            aBezierPolygon.append(rEdge.getEndPoint() + aPerpendEndB);
                        }
                    }
                }
                else
                {
                    // append original in-between point
                    aBezierPolygon.append(rEdge.getEndPoint());
                }
 
                // create lower edge.
                {
                    if(bCutB)
                    {
                        // calculate cut point and add
                        aCutPoint = rEdge.getEndPoint() + (aPerpendEndB * fCutB);
                        aBezierPolygon.append(aCutPoint);
                    }
                    else
                    {
                        // create scaled bezier segment
                        const B2DPoint aStart(rEdge.getEndPoint() + aPerpendEndB);
                        const B2DPoint aEnd(rEdge.getStartPoint() + aPerpendStartB);
                        const B2DVector aEdge(aEnd - aStart);
                        const double fLength(aEdge.getLength());
                        const double fScale(bIsEdgeLengthZero ? 1.0 : fLength / fEdgeLength);
                        const B2DVector fRelNext(rEdge.getControlPointB() - rEdge.getEndPoint());
                        const B2DVector fRelPrev(rEdge.getControlPointA() - rEdge.getStartPoint());
 
                        aBezierPolygon.append(aStart);
                        aBezierPolygon.appendBezierSegment(aStart + (fRelNext * fScale), aEnd + (fRelPrev * fScale), aEnd);
                    }
                }
 
                // close
                aBezierPolygon.setClosed(true);
 
                if(bStartRound || bEndRound)
                {
                    // double points possible when round caps are used at start or end
                    aBezierPolygon.removeDoublePoints();
                }
 
                if(bCut && ((bStartRound || bStartSquare) && (bEndRound || bEndSquare)))
                {
                    // When cut exists and both ends are extended with caps, a self-intersecting polygon
                    // is created; one cut point is known, but there is a 2nd one in the caps geometry.
                    // Solve by using tooling.
                    // Remark: This nearly never happens due to curve preparations to extreme points
                    // and maximum angle turning, but I constructed a test case and checked that it is
                    // working properly.
                    const B2DPolyPolygon aTemp(utils::solveCrossovers(aBezierPolygon));
                    const sal_uInt32 nTempCount(aTemp.count());
 
                    if(nTempCount)
                    {
                        if(nTempCount > 1)
                        {
                            // as expected, multiple polygons (with same orientation). Remove
                            // the one which contains aCutPoint, or better take the one without
                            for (sal_uInt32 a(0); a < nTempCount; a++)
                            {
                                aBezierPolygon = aTemp.getB2DPolygon(a);
 
                                const sal_uInt32 nCandCount(aBezierPolygon.count());
 
                                for(sal_uInt32 b(0); b < nCandCount; b++)
                                {
                                    if(aCutPoint.equal(aBezierPolygon.getB2DPoint(b)))
                                    {
                                        aBezierPolygon.clear();
                                        break;
                                    }
                                }
 
                                if(aBezierPolygon.count())
                                {
                                    break;
                                }
                            }
 
                            OSL_ENSURE(aBezierPolygon.count(), "Error in line geometry creation, could not solve self-intersection (!)");
                        }
                        else
                        {
                            // none found, use result
                            aBezierPolygon = aTemp.getB2DPolygon(0);
                        }
                    }
                    else
                    {
                        OSL_ENSURE(false, "Error in line geometry creation, could not solve self-intersection (!)");
                    }
                }
 
                if(nullptr != pTriangles)
                {
                    const basegfx::triangulator::B2DTriangleVector aResult(
                        basegfx::triangulator::triangulate(
                            aBezierPolygon));
                    pTriangles->insert(pTriangles->end(), aResult.begin(), aResult.end());
                    aBezierPolygon.clear();
                }
 
                // return
                return aBezierPolygon;
            }
            else
            {
                // Get start and  end point, create tangent and set to needed length
                B2DVector aTangent(rEdge.getEndPoint() - rEdge.getStartPoint());
                aTangent.setLength(fHalfLineWidth);
 
                // prepare return value
                B2DPolygon aEdgePolygon;
 
                // buffered angle
                double fAngle(0.0);
                bool bAngle(false);
 
                // buffered perpendicular
                B2DVector aPerpend;
                bool bPerpend(false);
 
                // create left vertical
                if(bStartRound)
                {
                    aEdgePolygon = utils::createHalfUnitCircle();
                    fAngle = atan2(aTangent.getY(), aTangent.getX());
                    bAngle = true;
                    aEdgePolygon.transform(
                        utils::createScaleShearXRotateTranslateB2DHomMatrix(
                            fHalfLineWidth, fHalfLineWidth,
                            0.0,
                            fAngle + M_PI_2,
                            rEdge.getStartPoint().getX(), rEdge.getStartPoint().getY()));
                }
                else
                {
                    aPerpend.setX(-aTangent.getY());
                    aPerpend.setY(aTangent.getX());
                    bPerpend = true;
 
                    if(bStartSquare)
                    {
                        const basegfx::B2DPoint aStart(rEdge.getStartPoint() - aTangent);
 
                        aEdgePolygon.append(aStart + aPerpend);
                        aEdgePolygon.append(aStart - aPerpend);
                    }
                    else
                    {
                        aEdgePolygon.append(rEdge.getStartPoint() + aPerpend);
                        aEdgePolygon.append(rEdge.getStartPoint()); // keep the in-between point for numerical reasons
                        aEdgePolygon.append(rEdge.getStartPoint() - aPerpend);
                    }
                }
 
                // create right vertical
                if(bEndRound)
                {
                    basegfx::B2DPolygon aEndPolygon(utils::createHalfUnitCircle());
 
                    if(!bAngle)
                    {
                        fAngle = atan2(aTangent.getY(), aTangent.getX());
                    }
 
                    aEndPolygon.transform(
                        utils::createScaleShearXRotateTranslateB2DHomMatrix(
                            fHalfLineWidth, fHalfLineWidth,
                            0.0,
                            fAngle - M_PI_2,
                            rEdge.getEndPoint().getX(), rEdge.getEndPoint().getY()));
                    aEdgePolygon.append(aEndPolygon);
                }
                else
                {
                    if(!bPerpend)
                    {
                        aPerpend.setX(-aTangent.getY());
                        aPerpend.setY(aTangent.getX());
                    }
 
                    if(bEndSquare)
                    {
                        const basegfx::B2DPoint aEnd(rEdge.getEndPoint() + aTangent);
 
                        aEdgePolygon.append(aEnd - aPerpend);
                        aEdgePolygon.append(aEnd + aPerpend);
                    }
                    else
                    {
                        aEdgePolygon.append(rEdge.getEndPoint() - aPerpend);
                        aEdgePolygon.append(rEdge.getEndPoint()); // keep the in-between point for numerical reasons
                        aEdgePolygon.append(rEdge.getEndPoint() + aPerpend);
                    }
                }
 
                // close and return
                aEdgePolygon.setClosed(true);
 
                if(nullptr != pTriangles)
                {
                    const basegfx::triangulator::B2DTriangleVector aResult(
                        basegfx::triangulator::triangulate(
                            aEdgePolygon));
                    pTriangles->insert(pTriangles->end(), aResult.begin(), aResult.end());
                    aEdgePolygon.clear();
                }
 
                return aEdgePolygon;
            }
        }
 
        B2DPolygon createAreaGeometryForJoin(
            const B2DVector& rTangentPrev,
            const B2DVector& rTangentEdge,
            const B2DVector& rPerpendPrev,
            const B2DVector& rPerpendEdge,
            const B2DPoint& rPoint,
            double fHalfLineWidth,
            B2DLineJoin eJoin,
            double fMiterMinimumAngle,
            basegfx::triangulator::B2DTriangleVector* pTriangles)
        {
            SAL_WARN_IF(fHalfLineWidth <= 0.0,"basegfx","createAreaGeometryForJoin: LineWidth too small (!)");
            assert((eJoin != B2DLineJoin::NONE) && "createAreaGeometryForJoin: B2DLineJoin::NONE not allowed (!)");
 
            // LineJoin from tangent rPerpendPrev to tangent rPerpendEdge in rPoint
            B2DPolygon aEdgePolygon;
            const B2DPoint aStartPoint(rPoint + rPerpendPrev);
            const B2DPoint aEndPoint(rPoint + rPerpendEdge);
 
            // test if for Miter, the angle is too small and the fallback
            // to bevel needs to be used
            if(eJoin == B2DLineJoin::Miter)
            {
                const double fAngle(fabs(rPerpendPrev.angle(rPerpendEdge)));
 
                if((M_PI - fAngle) < fMiterMinimumAngle)
                {
                    // fallback to bevel
                    eJoin = B2DLineJoin::Bevel;
                }
            }
 
            switch(eJoin)
            {
                case B2DLineJoin::Miter :
                {
                    if(nullptr != pTriangles)
                    {
                        pTriangles->emplace_back(
                            aEndPoint,
                            rPoint,
                            aStartPoint);
                    }
                    else
                    {
                        aEdgePolygon.append(aEndPoint);
                        aEdgePolygon.append(rPoint);
                        aEdgePolygon.append(aStartPoint);
                    }
 
                    // Look for the cut point between start point along rTangentPrev and
                    // end point along rTangentEdge. -rTangentEdge should be used, but since
                    // the cut value is used for interpolating along the first edge, the negation
                    // is not needed since the same fCut will be found on the first edge.
                    // If it exists, insert it to complete the mitered fill polygon.
                    double fCutPos(0.0);
                    utils::findCut(aStartPoint, rTangentPrev, aEndPoint, rTangentEdge, CutFlagValue::ALL, &fCutPos);
 
                    if(fCutPos != 0.0)
                    {
                        const B2DPoint aCutPoint(aStartPoint + (rTangentPrev * fCutPos));
 
                        if(nullptr != pTriangles)
                        {
                            pTriangles->emplace_back(
                                aStartPoint,
                                aCutPoint,
                                aEndPoint);
                        }
                        else
                        {
                            aEdgePolygon.append(aCutPoint);
                        }
                    }
 
                    break;
                }
                case B2DLineJoin::Round :
                {
                    // use tooling to add needed EllipseSegment
                    double fAngleStart(atan2(rPerpendPrev.getY(), rPerpendPrev.getX()));
                    double fAngleEnd(atan2(rPerpendEdge.getY(), rPerpendEdge.getX()));
 
                    // atan2 results are [-PI .. PI], consolidate to [0.0 .. 2PI]
                    if(fAngleStart < 0.0)
                    {
                        fAngleStart += 2 * M_PI;
                    }
 
                    if(fAngleEnd < 0.0)
                    {
                        fAngleEnd += 2 * M_PI;
                    }
 
                    const B2DPolygon aBow(utils::createPolygonFromEllipseSegment(rPoint, fHalfLineWidth, fHalfLineWidth, fAngleStart, fAngleEnd));
 
                    if(aBow.count() > 1)
                    {
                        if(nullptr != pTriangles)
                        {
                            for(sal_uInt32 a(0); a < aBow.count() - 1; a++)
                            {
                                pTriangles->emplace_back(
                                    0 == a ? aStartPoint : aBow.getB2DPoint(a),
                                    rPoint,
                                    aBow.count() - 1 == a + 1 ? aEndPoint : aBow.getB2DPoint(a + 1));
                            }
                        }
                        else
                        {
                            // #i101491#
                            // use the original start/end positions; the ones from bow creation may be numerically
                            // different due to their different creation. To guarantee good merging quality with edges
                            // and edge roundings (and to reduce point count)
                            aEdgePolygon = aBow;
                            aEdgePolygon.setB2DPoint(0, aStartPoint);
                            aEdgePolygon.setB2DPoint(aEdgePolygon.count() - 1, aEndPoint);
                            aEdgePolygon.append(rPoint);
                        }
 
                        break;
                    }
                    else
                    {
                        [[fallthrough]]; // wanted fall-through to default
                    }
                }
                default: // B2DLineJoin::Bevel
                {
                    if(nullptr != pTriangles)
                    {
                        pTriangles->emplace_back(
                            aEndPoint,
                            rPoint,
                            aStartPoint);
                    }
                    else
                    {
                        aEdgePolygon.append(aEndPoint);
                        aEdgePolygon.append(rPoint);
                        aEdgePolygon.append(aStartPoint);
                    }
 
                    break;
                }
            }
 
            // create last polygon part for edge
            aEdgePolygon.setClosed(true);
 
            return aEdgePolygon;
        }
    } // end of anonymous namespace
 
    namespace utils
    {
        B2DPolyPolygon createAreaGeometry(
            const B2DPolygon& rCandidate,
            double fHalfLineWidth,
            B2DLineJoin eJoin,
            css::drawing::LineCap eCap,
            double fMaxAllowedAngle,
            double fMaxPartOfEdge,
            double fMiterMinimumAngle)
        {
            if(fMaxAllowedAngle > M_PI_2)
            {
                fMaxAllowedAngle = M_PI_2;
            }
            else if(fMaxAllowedAngle < 0.01 * M_PI_2)
            {
                fMaxAllowedAngle = 0.01 * M_PI_2;
            }
 
            if(fMaxPartOfEdge > 1.0)
            {
                fMaxPartOfEdge = 1.0;
            }
            else if(fMaxPartOfEdge < 0.01)
            {
                fMaxPartOfEdge = 0.01;
            }
 
            if(fMiterMinimumAngle > M_PI)
            {
                fMiterMinimumAngle = M_PI;
            }
            else if(fMiterMinimumAngle < 0.01 * M_PI)
            {
                fMiterMinimumAngle = 0.01 * M_PI;
            }
 
            B2DPolygon aCandidate(rCandidate);
            const double fMaxCos(cos(fMaxAllowedAngle));
 
            aCandidate.removeDoublePoints();
            aCandidate = subdivideToSimple(aCandidate, fMaxCos * fMaxCos, fMaxPartOfEdge * fMaxPartOfEdge);
 
            const sal_uInt32 nPointCount(aCandidate.count());
 
            if(nPointCount)
            {
                B2DPolyPolygon aRetval;
                const bool bIsClosed(aCandidate.isClosed());
                const sal_uInt32 nEdgeCount(bIsClosed ? nPointCount : nPointCount - 1);
                const bool bLineCap(!bIsClosed && eCap != css::drawing::LineCap_BUTT);
 
                if(nEdgeCount)
                {
                    B2DCubicBezier aEdge;
                    B2DCubicBezier aPrev;
 
                    const bool bEventuallyCreateLineJoin(eJoin != B2DLineJoin::NONE);
                    // prepare edge
                    aEdge.setStartPoint(aCandidate.getB2DPoint(0));
 
                    if(bIsClosed && bEventuallyCreateLineJoin)
                    {
                        // prepare previous edge
                        const sal_uInt32 nPrevIndex(nPointCount - 1);
                        aPrev.setStartPoint(aCandidate.getB2DPoint(nPrevIndex));
                        aPrev.setControlPointA(aCandidate.getNextControlPoint(nPrevIndex));
                        aPrev.setControlPointB(aCandidate.getPrevControlPoint(0));
                        aPrev.setEndPoint(aEdge.getStartPoint());
                    }
 
                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
                    {
                        // fill current Edge
                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                        aEdge.setControlPointA(aCandidate.getNextControlPoint(a));
                        aEdge.setControlPointB(aCandidate.getPrevControlPoint(nNextIndex));
                        aEdge.setEndPoint(aCandidate.getB2DPoint(nNextIndex));
 
                        // check and create linejoin
                        if(bEventuallyCreateLineJoin && (bIsClosed || a != 0))
                        {
                            B2DVector aTangentPrev(aPrev.getTangent(1.0)); aTangentPrev.normalize();
                            B2DVector aTangentEdge(aEdge.getTangent(0.0)); aTangentEdge.normalize();
                            B2VectorOrientation aOrientation(getOrientation(aTangentPrev, aTangentEdge));
 
                            if(aOrientation == B2VectorOrientation::Neutral)
                            {
                                // they are parallel or empty; if they are both not zero and point
                                // in opposite direction, a half-circle is needed
                                if(!aTangentPrev.equalZero() && !aTangentEdge.equalZero())
                                {
                                    const double fAngle(fabs(aTangentPrev.angle(aTangentEdge)));
 
                                    if(fTools::equal(fAngle, M_PI))
                                    {
                                        // for half-circle production, fallback to positive
                                        // orientation
                                        aOrientation = B2VectorOrientation::Positive;
                                    }
                                }
                            }
 
                            if(aOrientation == B2VectorOrientation::Positive)
                            {
                                const B2DVector aPerpendPrev(getPerpendicular(aTangentPrev) * -fHalfLineWidth);
                                const B2DVector aPerpendEdge(getPerpendicular(aTangentEdge) * -fHalfLineWidth);
 
                                aRetval.append(
                                    createAreaGeometryForJoin(
                                        aTangentPrev,
                                        aTangentEdge,
                                        aPerpendPrev,
                                        aPerpendEdge,
                                        aEdge.getStartPoint(),
                                        fHalfLineWidth,
                                        eJoin,
                                        fMiterMinimumAngle,
                                        nullptr));
                            }
                            else if(aOrientation == B2VectorOrientation::Negative)
                            {
                                const B2DVector aPerpendPrev(getPerpendicular(aTangentPrev) * fHalfLineWidth);
                                const B2DVector aPerpendEdge(getPerpendicular(aTangentEdge) * fHalfLineWidth);
 
                                aRetval.append(
                                    createAreaGeometryForJoin(
                                        aTangentEdge,
                                        aTangentPrev,
                                        aPerpendEdge,
                                        aPerpendPrev,
                                        aEdge.getStartPoint(),
                                        fHalfLineWidth,
                                        eJoin,
                                        fMiterMinimumAngle,
                                        nullptr));
                            }
                        }
 
                        // create geometry for edge
                        const bool bLast(a + 1 == nEdgeCount);
 
                        if(bLineCap)
                        {
                            const bool bFirst(!a);
 
                            aRetval.append(
                                createAreaGeometryForEdge(
                                    aEdge,
                                    fHalfLineWidth,
                                    bFirst && eCap == css::drawing::LineCap_ROUND,
                                    bLast && eCap == css::drawing::LineCap_ROUND,
                                    bFirst && eCap == css::drawing::LineCap_SQUARE,
                                    bLast && eCap == css::drawing::LineCap_SQUARE,
                                    nullptr));
                        }
                        else
                        {
                            aRetval.append(
                                createAreaGeometryForEdge(
                                    aEdge,
                                    fHalfLineWidth,
                                    false,
                                    false,
                                    false,
                                    false,
                                    nullptr));
                        }
 
                        // prepare next step
                        if(!bLast)
                        {
                            if(bEventuallyCreateLineJoin)
                            {
                                aPrev = aEdge;
                            }
 
                            aEdge.setStartPoint(aEdge.getEndPoint());
                        }
                    }
                }
                else
                {
                    // point count, but no edge count -> single point
                    const basegfx::B2DPolygon aCircle(
                        createPolygonFromCircle(
                            aCandidate.getB2DPoint(0),
                            fHalfLineWidth));
 
                    aRetval.append(aCircle);
                }
 
                return aRetval;
            }
            else
            {
                return B2DPolyPolygon(rCandidate);
            }
        }
    } // end of namespace utils
} // end of namespace basegfx
 
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