path: root/basegfx/source/polygon/b2dpolypolygoncutter.cxx

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

#include <basegfx/numeric/ftools.hxx>
#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
#include <basegfx/point/b2dpoint.hxx>
#include <basegfx/vector/b2dvector.hxx>
#include <basegfx/polygon/b2dpolygon.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
#include <basegfx/range/b2drange.hxx>
#include <basegfx/polygon/b2dpolypolygontools.hxx>
#include <basegfx/curve/b2dcubicbezier.hxx>
#include <sal/log.hxx>
#include <utility>
#include <vector>
#include <algorithm>
#include <numeric>

namespace basegfx
{
    namespace
    {

        struct StripHelper
        {
            B2DRange                                maRange;
            sal_Int32                               mnDepth;
            B2VectorOrientation                     meOrinetation;
        };

        struct PN
        {
        public:
            B2DPoint                maPoint;
            sal_uInt32              mnI;
            sal_uInt32              mnIP;
            sal_uInt32              mnIN;
        };

        struct VN
        {
        public:
            B2DVector               maPrev;
            B2DVector               maNext;

            // to have the correct curve segments in the crossover checks,
            // it is necessary to keep the original next vectors, too. Else,
            // it may happen to use an already switched next vector which
            // would interpolate the wrong comparison point
            B2DVector               maOriginalNext;
        };

        struct SN
        {
        public:
            PN*                     mpPN;

            bool operator<(const SN& rComp) const
            {
                if(fTools::equal(mpPN->maPoint.getX(), rComp.mpPN->maPoint.getX()))
                {
                    if(fTools::equal(mpPN->maPoint.getY(), rComp.mpPN->maPoint.getY()))
                    {
                        return (mpPN->mnI < rComp.mpPN->mnI);
                    }
                    else
                    {
                        return fTools::less(mpPN->maPoint.getY(), rComp.mpPN->maPoint.getY());
                    }
                }
                else
                {
                    return fTools::less(mpPN->maPoint.getX(), rComp.mpPN->maPoint.getX());
                }
            }
        };

        typedef std::vector< PN > PNV;
        typedef std::vector< VN > VNV;
        typedef std::vector< SN > SNV;
        typedef std::pair< basegfx::B2DPoint /*orig*/, basegfx::B2DPoint /*repl*/ > CorrectionPair;

        class solver
        {
        private:
            const B2DPolyPolygon    maOriginal;
            PNV                     maPNV;
            VNV                     maVNV;
            SNV                     maSNV;
            std::vector< CorrectionPair >
                                    maCorrectionTable;

            bool                    mbIsCurve : 1;
            bool                    mbChanged : 1;

            void impAddPolygon(const sal_uInt32 aPos, const B2DPolygon& rGeometry)
            {
                const sal_uInt32 nCount(rGeometry.count());
                PN aNewPN;
                VN aNewVN;
                SN aNewSN;

                for(sal_uInt32 a(0); a < nCount; a++)
                {
                    const B2DPoint aPoint(rGeometry.getB2DPoint(a));
                    aNewPN.maPoint = aPoint;
                    aNewPN.mnI = aPos + a;
                    aNewPN.mnIP = aPos + ((a != 0) ? a - 1 : nCount - 1);
                    aNewPN.mnIN = aPos + ((a + 1 == nCount) ? 0 : a + 1);
                    maPNV.push_back(aNewPN);

                    if(mbIsCurve)
                    {
                        aNewVN.maPrev = rGeometry.getPrevControlPoint(a) - aPoint;
                        aNewVN.maNext = rGeometry.getNextControlPoint(a) - aPoint;
                        aNewVN.maOriginalNext = aNewVN.maNext;
                        maVNV.push_back(aNewVN);
                    }

                    aNewSN.mpPN = &maPNV[maPNV.size() - 1];
                    maSNV.push_back(aNewSN);
                }
            }

            static bool impLeftOfEdges(const B2DVector& rVecA, const B2DVector& rVecB, const B2DVector& rTest)
            {
                // tests if rTest is left of both directed line segments along the line -rVecA, rVecB. Test is
                // with border.
                if(rVecA.cross(rVecB) > 0.0)
                {
                    // b is left turn seen from a, test if Test is left of both and so inside (left is seen as inside)
                    const bool bBoolA(rVecA.cross(rTest) >= 0.0);
                    const bool bBoolB(rVecB.cross(rTest) <= 0.0);

                    return (bBoolA && bBoolB);
                }
                else
                {
                    // b is right turn seen from a, test if Test is right of both and so outside (left is seen as inside)
                    const bool bBoolA(rVecA.cross(rTest) <= 0.0);
                    const bool bBoolB(rVecB.cross(rTest) >= 0.0);

                    return (!(bBoolA && bBoolB));
                }
            }

            void impSwitchNext(PN& rPNa, PN& rPNb)
            {
                std::swap(rPNa.mnIN, rPNb.mnIN);

                if(mbIsCurve)
                {
                    VN& rVNa = maVNV[rPNa.mnI];
                    VN& rVNb = maVNV[rPNb.mnI];

                    std::swap(rVNa.maNext, rVNb.maNext);
                }

                if(!mbChanged)
                {
                    mbChanged = true;
                }
            }

            B2DCubicBezier createSegment(const PN& rPN, bool bPrev) const
            {
                const B2DPoint& rStart(rPN.maPoint);
                const B2DPoint& rEnd(maPNV[bPrev ? rPN.mnIP : rPN.mnIN].maPoint);
                const B2DVector& rCPA(bPrev ? maVNV[rPN.mnI].maPrev : maVNV[rPN.mnI].maNext);
                // Use maOriginalNext, not maNext to create the original (yet unchanged)
                // curve segment. Otherwise, this segment would NOT ne correct.
                const B2DVector& rCPB(bPrev ? maVNV[maPNV[rPN.mnIP].mnI].maOriginalNext : maVNV[maPNV[rPN.mnIN].mnI].maPrev);

                return B2DCubicBezier(rStart, rStart + rCPA, rEnd + rCPB, rEnd);
            }

            void impHandleCommon(PN& rPNa, PN& rPNb)
            {
                if(mbIsCurve)
                {
                    const B2DCubicBezier aNextA(createSegment(rPNa, false));
                    const B2DCubicBezier aPrevA(createSegment(rPNa, true));

                    if(aNextA.equal(aPrevA))
                    {
                        // deadend on A (identical edge)
                        return;
                    }

                    const B2DCubicBezier aNextB(createSegment(rPNb, false));
                    const B2DCubicBezier aPrevB(createSegment(rPNb, true));

                    if(aNextB.equal(aPrevB))
                    {
                        // deadend on B (identical edge)
                        return;
                    }

                    if(aPrevA.equal(aPrevB))
                    {
                        // common edge in same direction
                        return;
                    }
                    else if(aPrevA.equal(aNextB))
                    {
                        // common edge in opposite direction
                        if(aNextA.equal(aPrevB))
                        {
                            // common edge in opposite direction continues
                            return;
                        }
                        else
                        {
                            // common edge in opposite direction leave
                            impSwitchNext(rPNa, rPNb);
                        }
                    }
                    else if(aNextA.equal(aNextB))
                    {
                        // common edge in same direction enter
                        // search leave edge
                        PN* pPNa2 = &maPNV[rPNa.mnIN];
                        PN* pPNb2 = &maPNV[rPNb.mnIN];
                        bool bOnEdge(true);

                        do
                        {
                            const B2DCubicBezier aNextA2(createSegment(*pPNa2, false));
                            const B2DCubicBezier aNextB2(createSegment(*pPNb2, false));

                            if(aNextA2.equal(aNextB2))
                            {
                                pPNa2 = &maPNV[pPNa2->mnIN];
                                pPNb2 = &maPNV[pPNb2->mnIN];
                            }
                            else
                            {
                                bOnEdge = false;
                            }
                        }
                        while(bOnEdge && pPNa2 != &rPNa && pPNb2 != &rPNb);

                        if(bOnEdge)
                        {
                            // loop over two identical polygon paths
                            return;
                        }
                        else
                        {
                            // enter at rPNa, rPNb; leave at pPNa2, pPNb2. No common edges
                            // at enter/leave. Check for crossover.
                            const B2DVector aPrevCA(aPrevA.interpolatePoint(0.5) - aPrevA.getStartPoint());
                            const B2DVector aNextCA(aNextA.interpolatePoint(0.5) - aNextA.getStartPoint());
                            const B2DVector aPrevCB(aPrevB.interpolatePoint(0.5) - aPrevB.getStartPoint());
                            const bool bEnter(impLeftOfEdges(aPrevCA, aNextCA, aPrevCB));

                            const B2DCubicBezier aNextA2(createSegment(*pPNa2, false));
                            const B2DCubicBezier aPrevA2(createSegment(*pPNa2, true));
                            const B2DCubicBezier aNextB2(createSegment(*pPNb2, false));
                            const B2DVector aPrevCA2(aPrevA2.interpolatePoint(0.5) - aPrevA2.getStartPoint());
                            const B2DVector aNextCA2(aNextA2.interpolatePoint(0.5) - aNextA2.getStartPoint());
                            const B2DVector aNextCB2(aNextB2.interpolatePoint(0.5) - aNextB2.getStartPoint());
                            const bool bLeave(impLeftOfEdges(aPrevCA2, aNextCA2, aNextCB2));

                            if(bEnter != bLeave)
                            {
                                // crossover
                                impSwitchNext(rPNa, rPNb);
                            }
                        }
                    }
                    else if(aNextA.equal(aPrevB))
                    {
                        // common edge in opposite direction enter
                        impSwitchNext(rPNa, rPNb);
                    }
                    else
                    {
                        // no common edges, check for crossover
                        const B2DVector aPrevCA(aPrevA.interpolatePoint(0.5) - aPrevA.getStartPoint());
                        const B2DVector aNextCA(aNextA.interpolatePoint(0.5) - aNextA.getStartPoint());
                        const B2DVector aPrevCB(aPrevB.interpolatePoint(0.5) - aPrevB.getStartPoint());
                        const B2DVector aNextCB(aNextB.interpolatePoint(0.5) - aNextB.getStartPoint());

                        const bool bEnter(impLeftOfEdges(aPrevCA, aNextCA, aPrevCB));
                        const bool bLeave(impLeftOfEdges(aPrevCA, aNextCA, aNextCB));

                        if(bEnter != bLeave)
                        {
                            // crossover
                            impSwitchNext(rPNa, rPNb);
                        }
                    }
                }
                else
                {
                    const B2DPoint& rNextA(maPNV[rPNa.mnIN].maPoint);
                    const B2DPoint& rPrevA(maPNV[rPNa.mnIP].maPoint);

                    if(rNextA.equal(rPrevA))
                    {
                        // deadend on A
                        return;
                    }

                    const B2DPoint& rNextB(maPNV[rPNb.mnIN].maPoint);
                    const B2DPoint& rPrevB(maPNV[rPNb.mnIP].maPoint);

                    if(rNextB.equal(rPrevB))
                    {
                        // deadend on B
                        return;
                    }

                    if(rPrevA.equal(rPrevB))
                    {
                        // common edge in same direction
                        return;
                    }
                    else if(rPrevA.equal(rNextB))
                    {
                        // common edge in opposite direction
                        if(rNextA.equal(rPrevB))
                        {
                            // common edge in opposite direction continues
                            return;
                        }
                        else
                        {
                            // common edge in opposite direction leave
                            impSwitchNext(rPNa, rPNb);
                        }
                    }
                    else if(rNextA.equal(rNextB))
                    {
                        // common edge in same direction enter
                        // search leave edge
                        PN* pPNa2 = &maPNV[rPNa.mnIN];
                        PN* pPNb2 = &maPNV[rPNb.mnIN];
                        bool bOnEdge(true);

                        do
                        {
                            const B2DPoint& rNextA2(maPNV[pPNa2->mnIN].maPoint);
                            const B2DPoint& rNextB2(maPNV[pPNb2->mnIN].maPoint);

                            if(rNextA2.equal(rNextB2))
                            {
                                pPNa2 = &maPNV[pPNa2->mnIN];
                                pPNb2 = &maPNV[pPNb2->mnIN];
                            }
                            else
                            {
                                bOnEdge = false;
                            }
                        }
                        while(bOnEdge && pPNa2 != &rPNa && pPNb2 != &rPNb);

                        if(bOnEdge)
                        {
                            // loop over two identical polygon paths
                            return;
                        }
                        else
                        {
                            // enter at rPNa, rPNb; leave at pPNa2, pPNb2. No common edges
                            // at enter/leave. Check for crossover.
                            const B2DPoint& aPointE(rPNa.maPoint);
                            const B2DVector aPrevAE(rPrevA - aPointE);
                            const B2DVector aNextAE(rNextA - aPointE);
                            const B2DVector aPrevBE(rPrevB - aPointE);

                            const B2DPoint& aPointL(pPNa2->maPoint);
                            const B2DVector aPrevAL(maPNV[pPNa2->mnIP].maPoint - aPointL);
                            const B2DVector aNextAL(maPNV[pPNa2->mnIN].maPoint - aPointL);
                            const B2DVector aNextBL(maPNV[pPNb2->mnIN].maPoint - aPointL);

                            const bool bEnter(impLeftOfEdges(aPrevAE, aNextAE, aPrevBE));
                            const bool bLeave(impLeftOfEdges(aPrevAL, aNextAL, aNextBL));

                            if(bEnter != bLeave)
                            {
                                // crossover; switch start or end
                                impSwitchNext(rPNa, rPNb);
                            }
                        }
                    }
                    else if(rNextA.equal(rPrevB))
                    {
                        // common edge in opposite direction enter
                        impSwitchNext(rPNa, rPNb);
                    }
                    else
                    {
                        // no common edges, check for crossover
                        const B2DPoint& aPoint(rPNa.maPoint);
                        const B2DVector aPrevA(rPrevA - aPoint);
                        const B2DVector aNextA(rNextA - aPoint);
                        const B2DVector aPrevB(rPrevB - aPoint);
                        const B2DVector aNextB(rNextB - aPoint);

                        const bool bEnter(impLeftOfEdges(aPrevA, aNextA, aPrevB));
                        const bool bLeave(impLeftOfEdges(aPrevA, aNextA, aNextB));

                        if(bEnter != bLeave)
                        {
                            // crossover
                            impSwitchNext(rPNa, rPNb);
                        }
                    }
                }
            }

            void impSolve()
            {
                // sort by point to identify common nodes easier
                std::sort(maSNV.begin(), maSNV.end());

                // handle common nodes
                const sal_uInt32 nNodeCount(maSNV.size());

                // snap unsharp-equal points
                if(nNodeCount)
                {
                    basegfx::B2DPoint* pLast(&maSNV[0].mpPN->maPoint);

                    for(const auto& rSN : maSNV)
                    {
                        basegfx::B2DPoint* pCurrent(&rSN.mpPN->maPoint);

                        if(pLast->equal(*pCurrent) && (pLast->getX() != pCurrent->getX() || pLast->getY() != pCurrent->getY()))
                        {
                            const basegfx::B2DPoint aMiddle((*pLast + *pCurrent) * 0.5);

                            if(pLast->getX() != aMiddle.getX() || pLast->getY() != aMiddle.getY())
                            {
                                maCorrectionTable.emplace_back(*pLast, aMiddle);
                                *pLast = aMiddle;
                            }

                            if(pCurrent->getX() != aMiddle.getX() || pCurrent->getY() != aMiddle.getY())
                            {
                                maCorrectionTable.emplace_back(*pCurrent, aMiddle);
                                *pCurrent = aMiddle;
                            }
                        }

                        pLast = pCurrent;
                    }

                    for (sal_uInt32 a = 0; a < nNodeCount - 1; a++)
                    {
                        // test a before using it, not after. Also use nPointCount instead of aSortNodes.size()
                        PN& rPNb = *(maSNV[a].mpPN);

                        for(sal_uInt32 b(a + 1); b < nNodeCount && rPNb.maPoint.equal(maSNV[b].mpPN->maPoint); b++)
                        {
                            impHandleCommon(rPNb, *maSNV[b].mpPN);
                        }
                    }
                }
            }

        public:
            explicit solver(const B2DPolygon& rOriginal)
            :   maOriginal(B2DPolyPolygon(rOriginal)),
                mbIsCurve(false),
                mbChanged(false)
            {
                const sal_uInt32 nOriginalCount(rOriginal.count());

                if(!nOriginalCount)
                    return;

                B2DPolygon aGeometry(utils::addPointsAtCutsAndTouches(rOriginal));
                aGeometry.removeDoublePoints();
                aGeometry = utils::simplifyCurveSegments(aGeometry);
                mbIsCurve = aGeometry.areControlPointsUsed();

                const sal_uInt32 nPointCount(aGeometry.count());

                // If it's not a bezier polygon, at least four points are needed to create
                // a self-intersection. If it's a bezier polygon, the minimum point number
                // is two, since with a single point You get a curve, but no self-intersection
                if(!(nPointCount > 3 || (nPointCount > 1 && mbIsCurve)))
                    return;

                // reserve space in point, control and sort vector.
                maSNV.reserve(nPointCount);
                maPNV.reserve(nPointCount);
                maVNV.reserve(mbIsCurve ? nPointCount : 0);

                // fill data
                impAddPolygon(0, aGeometry);

                // solve common nodes
                impSolve();
            }

            explicit solver(B2DPolyPolygon aOriginal, size_t* pPointLimit = nullptr)
            :   maOriginal(std::move(aOriginal)),
                mbIsCurve(false),
                mbChanged(false)
            {
                sal_uInt32 nOriginalCount(maOriginal.count());

                if(!nOriginalCount)
                    return;

                B2DPolyPolygon aGeometry(utils::addPointsAtCutsAndTouches(maOriginal, pPointLimit));
                aGeometry.removeDoublePoints();
                aGeometry = utils::simplifyCurveSegments(aGeometry);
                mbIsCurve = aGeometry.areControlPointsUsed();
                nOriginalCount = aGeometry.count();

                if(!nOriginalCount)
                    return;

                // If it's not a bezier curve, at least three points would be needed to have a
                // topological relevant (not empty) polygon. Since it's not known here if trivial
                // edges (dead ends) will be kept or sorted out, add non-bezier polygons with
                // more than one point.
                // For bezier curves, the minimum for defining an area is also one.
                sal_uInt32 nPointCount = std::accumulate( aGeometry.begin(), aGeometry.end(), sal_uInt32(0),
                    [](sal_uInt32 a, const basegfx::B2DPolygon& b){return a + b.count();});

                if(!nPointCount)
                    return;

                // reserve space in point, control and sort vector.
                maSNV.reserve(nPointCount);
                maPNV.reserve(nPointCount);
                maVNV.reserve(mbIsCurve ? nPointCount : 0);

                // fill data
                sal_uInt32 nInsertIndex(0);

                for(const auto& rCandidate : aGeometry )
                {
                    const sal_uInt32 nCandCount(rCandidate.count());

                    // use same condition as above, the data vector is
                    // pre-allocated
                    if(nCandCount)
                    {
                        impAddPolygon(nInsertIndex, rCandidate);
                        nInsertIndex += nCandCount;
                    }
                }

                // solve common nodes
                impSolve();
            }

            B2DPolyPolygon getB2DPolyPolygon()
            {
                if(mbChanged)
                {
                    B2DPolyPolygon aRetval;
                    const sal_uInt32 nCount(maPNV.size());
                    sal_uInt32 nCountdown(nCount);

                    for(sal_uInt32 a(0); nCountdown && a < nCount; a++)
                    {
                        PN& rPN = maPNV[a];

                        if(rPN.mnI != SAL_MAX_UINT32)
                        {
                            // unused node, start new part polygon
                            B2DPolygon aNewPart;
                            PN* pPNCurr = &rPN;

                            do
                            {
                                const B2DPoint& rPoint = pPNCurr->maPoint;
                                aNewPart.append(rPoint);

                                if(mbIsCurve)
                                {
                                    const VN& rVNCurr = maVNV[pPNCurr->mnI];

                                    if(!rVNCurr.maPrev.equalZero())
                                    {
                                        aNewPart.setPrevControlPoint(aNewPart.count() - 1, rPoint + rVNCurr.maPrev);
                                    }

                                    if(!rVNCurr.maNext.equalZero())
                                    {
                                        aNewPart.setNextControlPoint(aNewPart.count() - 1, rPoint + rVNCurr.maNext);
                                    }
                                }

                                pPNCurr->mnI = SAL_MAX_UINT32;
                                nCountdown--;
                                pPNCurr = &(maPNV[pPNCurr->mnIN]);
                            }
                            while(pPNCurr != &rPN && pPNCurr->mnI != SAL_MAX_UINT32);

                            // close and add
                            aNewPart.setClosed(true);
                            aRetval.append(aNewPart);
                        }
                    }

                    return aRetval;
                }
                else
                {
                    const sal_uInt32 nCorrectionSize(maCorrectionTable.size());

                    // no change, return original
                    if(!nCorrectionSize)
                    {
                        return maOriginal;
                    }

                    // apply coordinate corrections to ensure inside/outside correctness after solving
                    const sal_uInt32 nPolygonCount(maOriginal.count());
                    basegfx::B2DPolyPolygon aRetval(maOriginal);

                    for(sal_uInt32 a(0); a < nPolygonCount; a++)
                    {
                        basegfx::B2DPolygon aTemp(aRetval.getB2DPolygon(a));
                        const sal_uInt32 nPointCount(aTemp.count());
                        bool bChanged(false);

                        for(sal_uInt32 b(0); b < nPointCount; b++)
                        {
                            const basegfx::B2DPoint aCandidate(aTemp.getB2DPoint(b));

                            for(sal_uInt32 c(0); c < nCorrectionSize; c++)
                            {
                                if(maCorrectionTable[c].first.getX() == aCandidate.getX() && maCorrectionTable[c].first.getY() == aCandidate.getY())
                                {
                                    aTemp.setB2DPoint(b, maCorrectionTable[c].second);
                                    bChanged = true;
                                }
                            }
                        }

                        if(bChanged)
                        {
                            aRetval.setB2DPolygon(a, aTemp);
                        }
                    }

                    return aRetval;
                }
            }
        };

    } // end of anonymous namespace
} // end of namespace basegfx

namespace basegfx::utils
{

        B2DPolyPolygon solveCrossovers(const B2DPolyPolygon& rCandidate, size_t* pPointLimit)
        {
            if(rCandidate.count() > 0)
            {
                solver aSolver(rCandidate, pPointLimit);
                return aSolver.getB2DPolyPolygon();
            }
            else
            {
                return rCandidate;
            }
        }

        B2DPolyPolygon solveCrossovers(const B2DPolygon& rCandidate)
        {
            solver aSolver(rCandidate);
            return aSolver.getB2DPolyPolygon();
        }

        B2DPolyPolygon stripNeutralPolygons(const B2DPolyPolygon& rCandidate)
        {
            B2DPolyPolygon aRetval;

            for(const auto& rPolygon : rCandidate)
            {
                if(utils::getOrientation(rPolygon) != B2VectorOrientation::Neutral)
                {
                    aRetval.append(rPolygon);
                }
            }

            return aRetval;
        }

        B2DPolyPolygon createNonzeroConform(const B2DPolyPolygon& rCandidate)
        {
            if (rCandidate.count() > 1000)
            {
                SAL_WARN("basegfx", "this poly is too large, " << rCandidate.count() << " elements, to be able to process timeously, falling back to ignoring the winding rule, which is likely to cause rendering artifacts");
                return rCandidate;
            }

            B2DPolyPolygon aCandidate;

            // remove all self-intersections and intersections
            if(rCandidate.count() == 1)
            {
                aCandidate = basegfx::utils::solveCrossovers(rCandidate.getB2DPolygon(0));
            }
            else
            {
                aCandidate = basegfx::utils::solveCrossovers(rCandidate);
            }

            // cleanup evtl. neutral polygons
            aCandidate = basegfx::utils::stripNeutralPolygons(aCandidate);

            // remove all polygons which have the same orientation as the polygon they are directly contained in
            const sal_uInt32 nCount(aCandidate.count());

            if(nCount > 1)
            {
                sal_uInt32 a, b;
                std::vector< StripHelper > aHelpers;
                aHelpers.resize(nCount);

                for(a = 0; a < nCount; a++)
                {
                    const B2DPolygon& aCand(aCandidate.getB2DPolygon(a));
                    StripHelper* pNewHelper = &(aHelpers[a]);
                    pNewHelper->maRange = utils::getRange(aCand);
                    pNewHelper->meOrinetation = utils::getOrientation(aCand);

                    // initialize with own orientation
                    pNewHelper->mnDepth = (pNewHelper->meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
                }

                for(a = 0; a < nCount - 1; a++)
                {
                    const B2DPolygon& aCandA(aCandidate.getB2DPolygon(a));
                    StripHelper& rHelperA = aHelpers[a];

                    for(b = a + 1; b < nCount; b++)
                    {
                        const B2DPolygon& aCandB(aCandidate.getB2DPolygon(b));
                        StripHelper& rHelperB = aHelpers[b];
                        const bool bAInB(rHelperB.maRange.isInside(rHelperA.maRange) && utils::isInside(aCandB, aCandA, true));

                        if(bAInB)
                        {
                            // A is inside B, add orientation of B to A
                            rHelperA.mnDepth += (rHelperB.meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
                        }

                        const bool bBInA(rHelperA.maRange.isInside(rHelperB.maRange) && utils::isInside(aCandA, aCandB, true));

                        if(bBInA)
                        {
                            // B is inside A, add orientation of A to B
                            rHelperB.mnDepth += (rHelperA.meOrinetation == B2VectorOrientation::Negative ? -1 : 1);
                        }
                    }
                }

                const B2DPolyPolygon aSource(aCandidate);
                aCandidate.clear();

                for(a = 0; a < nCount; a++)
                {
                    const StripHelper& rHelper = aHelpers[a];
                    // for contained unequal oriented polygons sum will be 0
                    // for contained equal it will be >=2 or <=-2
                    // for free polygons (not contained) it will be 1 or -1
                    // -> accept all which are >=-1 && <= 1
                    bool bAcceptEntry(rHelper.mnDepth >= -1 && rHelper.mnDepth <= 1);

                    if(bAcceptEntry)
                    {
                        aCandidate.append(aSource.getB2DPolygon(a));
                    }
                }
            }

            return aCandidate;
        }

        B2DPolyPolygon stripDispensablePolygons(const B2DPolyPolygon& rCandidate, bool bKeepAboveZero)
        {
            const sal_uInt32 nCount(rCandidate.count());
            B2DPolyPolygon aRetval;

            if(nCount)
            {
                if(nCount == 1)
                {
                    if(!bKeepAboveZero && utils::getOrientation(rCandidate.getB2DPolygon(0)) == B2VectorOrientation::Positive)
                    {
                        aRetval = rCandidate;
                    }
                }
                else
                {
                    sal_uInt32 a, b;
                    std::vector< StripHelper > aHelpers;
                    aHelpers.resize(nCount);

                    for(a = 0; a < nCount; a++)
                    {
                        const B2DPolygon& aCandidate(rCandidate.getB2DPolygon(a));
                        StripHelper* pNewHelper = &(aHelpers[a]);
                        pNewHelper->maRange = utils::getRange(aCandidate);
                        pNewHelper->meOrinetation = utils::getOrientation(aCandidate);
                        pNewHelper->mnDepth = (pNewHelper->meOrinetation == B2VectorOrientation::Negative ? -1 : 0);
                    }

                    for(a = 0; a < nCount - 1; a++)
                    {
                        const B2DPolygon& aCandA(rCandidate.getB2DPolygon(a));
                        StripHelper& rHelperA = aHelpers[a];

                        for(b = a + 1; b < nCount; b++)
                        {
                            const B2DPolygon& aCandB(rCandidate.getB2DPolygon(b));
                            StripHelper& rHelperB = aHelpers[b];
                            const bool bAInB(rHelperB.maRange.isInside(rHelperA.maRange) && utils::isInside(aCandB, aCandA, true));
                            const bool bBInA(rHelperA.maRange.isInside(rHelperB.maRange) && utils::isInside(aCandA, aCandB, true));

                            if(bAInB && bBInA)
                            {
                                // congruent
                                if(rHelperA.meOrinetation == rHelperB.meOrinetation)
                                {
                                    // two polys or two holes. Lower one of them to get one of them out of the way.
                                    // Since each will be contained in the other one, both will be increased, too.
                                    // So, for lowering, increase only one of them
                                    rHelperA.mnDepth++;
                                }
                                else
                                {
                                    // poly and hole. They neutralize, so get rid of both. Move securely below zero.
                                    rHelperA.mnDepth = - static_cast<sal_Int32>(nCount);
                                    rHelperB.mnDepth = - static_cast<sal_Int32>(nCount);
                                }
                            }
                            else
                            {
                                if(bAInB)
                                {
                                    if(rHelperB.meOrinetation == B2VectorOrientation::Negative)
                                    {
                                        rHelperA.mnDepth--;
                                    }
                                    else
                                    {
                                        rHelperA.mnDepth++;
                                    }
                                }
                                else if(bBInA)
                                {
                                    if(rHelperA.meOrinetation == B2VectorOrientation::Negative)
                                    {
                                        rHelperB.mnDepth--;
                                    }
                                    else
                                    {
                                        rHelperB.mnDepth++;
                                    }
                                }
                            }
                        }
                    }

                    for(a = 0; a < nCount; a++)
                    {
                        const StripHelper& rHelper = aHelpers[a];
                        bool bAcceptEntry(bKeepAboveZero ? 1 <= rHelper.mnDepth : rHelper.mnDepth == 0);

                        if(bAcceptEntry)
                        {
                            aRetval.append(rCandidate.getB2DPolygon(a));
                        }
                    }
                }
            }

            return aRetval;
        }

        B2DPolyPolygon prepareForPolygonOperation(const B2DPolygon& rCandidate)
        {
            solver aSolver(rCandidate);
            B2DPolyPolygon aRetval(stripNeutralPolygons(aSolver.getB2DPolyPolygon()));

            return correctOrientations(aRetval);
        }

        B2DPolyPolygon prepareForPolygonOperation(const B2DPolyPolygon& rCandidate)
        {
            solver aSolver(rCandidate);
            B2DPolyPolygon aRetval(stripNeutralPolygons(aSolver.getB2DPolyPolygon()));

            return correctOrientations(aRetval);
        }

        B2DPolyPolygon solvePolygonOperationOr(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
        {
            if(!rCandidateA.count())
            {
                return rCandidateB;
            }
            else if(!rCandidateB.count())
            {
                return rCandidateA;
            }
            else
            {
                // concatenate polygons, solve crossovers and throw away all sub-polygons
                // which have a depth other than 0.
                B2DPolyPolygon aRetval(rCandidateA);

                aRetval.append(rCandidateB);
                aRetval = solveCrossovers(aRetval);
                aRetval = stripNeutralPolygons(aRetval);

                return stripDispensablePolygons(aRetval);
            }
        }

        B2DPolyPolygon solvePolygonOperationXor(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
        {
            if(!rCandidateA.count())
            {
                return rCandidateB;
            }
            else if(!rCandidateB.count())
            {
                return rCandidateA;
            }
            else
            {
                // XOR is pretty simple: By definition it is the simple concatenation of
                // the single polygons since we imply XOR fill rule. Make it intersection-free
                // and correct orientations
                B2DPolyPolygon aRetval(rCandidateA);

                aRetval.append(rCandidateB);
                aRetval = solveCrossovers(aRetval);
                aRetval = stripNeutralPolygons(aRetval);

                return correctOrientations(aRetval);
            }
        }

        B2DPolyPolygon solvePolygonOperationAnd(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
        {
            if(!rCandidateA.count())
            {
                return B2DPolyPolygon();
            }
            else if(!rCandidateB.count())
            {
                return B2DPolyPolygon();
            }
            else
            {
                // tdf#130150 shortcut & precision: If both are simple ranges,
                // solve based on ranges
                if(basegfx::utils::isRectangle(rCandidateA) && basegfx::utils::isRectangle(rCandidateB))
                {
                    // *if* both are ranges, AND always can be solved
                    const basegfx::B2DRange aRangeA(rCandidateA.getB2DRange());
                    const basegfx::B2DRange aRangeB(rCandidateB.getB2DRange());

                    if(aRangeA.isInside(aRangeB))
                    {
                        // 2nd completely inside 1st -> 2nd is result of AND
                        return rCandidateB;
                    }

                    if(aRangeB.isInside(aRangeA))
                    {
                        // 2nd completely inside 1st -> 2nd is result of AND
                        return rCandidateA;
                    }

                    // solve by intersection
                    basegfx::B2DRange aIntersect(aRangeA);
                    aIntersect.intersect(aRangeB);

                    if(aIntersect.isEmpty())
                    {
                        // no overlap -> empty polygon as result of AND
                        return B2DPolyPolygon();
                    }

                    // create polygon result
                    return B2DPolyPolygon(
                        basegfx::utils::createPolygonFromRect(
                            aIntersect));
                }

                // concatenate polygons, solve crossovers and throw away all sub-polygons
                // with a depth of < 1. This means to keep all polygons where at least two
                // polygons do overlap.
                B2DPolyPolygon aRetval(rCandidateA);

                aRetval.append(rCandidateB);
                aRetval = solveCrossovers(aRetval);
                aRetval = stripNeutralPolygons(aRetval);

                return stripDispensablePolygons(aRetval, true);
            }
        }

        B2DPolyPolygon solvePolygonOperationDiff(const B2DPolyPolygon& rCandidateA, const B2DPolyPolygon& rCandidateB)
        {
            if(!rCandidateA.count())
            {
                return B2DPolyPolygon();
            }
            else if(!rCandidateB.count())
            {
                return rCandidateA;
            }
            else
            {
                // Make B topologically to holes and append to A
                B2DPolyPolygon aRetval(rCandidateB);

                aRetval.flip();
                aRetval.append(rCandidateA);

                // solve crossovers and throw away all sub-polygons which have a
                // depth other than 0.
                aRetval = basegfx::utils::solveCrossovers(aRetval);
                aRetval = basegfx::utils::stripNeutralPolygons(aRetval);

                return basegfx::utils::stripDispensablePolygons(aRetval);
            }
        }

        B2DPolyPolygon mergeToSinglePolyPolygon(const B2DPolyPolygonVector& rInput)
        {
            if(rInput.empty())
                return B2DPolyPolygon();

            // first step: prepareForPolygonOperation and simple merge of non-overlapping
            // PolyPolygons for speedup; this is possible for the wanted OR-operation
            B2DPolyPolygonVector aResult;
            aResult.reserve(rInput.size());

            for(const basegfx::B2DPolyPolygon & a : rInput)
            {
                const basegfx::B2DPolyPolygon aCandidate(prepareForPolygonOperation(a));

                if(!aResult.empty())
                {
                    const B2DRange aCandidateRange(aCandidate.getB2DRange());
                    bool bCouldMergeSimple(false);

                    for(auto & b: aResult)
                    {
                        basegfx::B2DPolyPolygon aTarget(b);
                        const B2DRange aTargetRange(aTarget.getB2DRange());

                        if(!aCandidateRange.overlaps(aTargetRange))
                        {
                            aTarget.append(aCandidate);
                            b = std::move(aTarget);
                            bCouldMergeSimple = true;
                            break;
                        }
                    }

                    if(!bCouldMergeSimple)
                    {
                        aResult.push_back(aCandidate);
                    }
                }
                else
                {
                    aResult.push_back(aCandidate);
                }
            }

            // second step: melt pairwise to a single PolyPolygon
            while(aResult.size() > 1)
            {
                B2DPolyPolygonVector aResult2;
                aResult2.reserve((aResult.size() / 2) + 1);

                for(size_t a(0); a < aResult.size(); a += 2)
                {
                    if(a + 1 < aResult.size())
                    {
                        // a pair for processing
                        aResult2.push_back(solvePolygonOperationOr(aResult[a], aResult[a + 1]));
                    }
                    else
                    {
                        // last single PolyPolygon; copy to target to not lose it
                        aResult2.push_back(aResult[a]);
                    }
                }

                aResult = std::move(aResult2);
            }

            // third step: get result
            if(aResult.size() == 1)
            {
                return aResult[0];
            }

            return B2DPolyPolygon();
        }

} // end of namespace

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