kicad-source/libs/kimath/src/geometry/shape_poly_set.cpp

/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2015-2019 CERN
 * Copyright (C) 2021-2022 KiCad Developers, see AUTHORS.txt for contributors.
 *
 * @author Tomasz Wlostowski <tomasz.wlostowski@cern.ch>
 * @author Alejandro García Montoro <alejandro.garciamontoro@gmail.com>
 *
 * Point in polygon algorithm adapted from Clipper Library (C) Angus Johnson,
 * subject to Clipper library license.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, you may find one here:
 * http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
 * or you may search the http://www.gnu.org website for the version 2 license,
 * or you may write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
 */

#include <algorithm>
#include <assert.h>                          // for assert
#include <cmath>                             // for sqrt, cos, hypot, isinf
#include <cstdio>
#include <istream>                           // for operator<<, operator>>
#include <limits>                            // for numeric_limits
#include <map>
#include <memory>
#include <set>
#include <string>                            // for char_traits, operator!=
#include <type_traits>                       // for swap, move
#include <unordered_set>
#include <vector>

#include <clipper.hpp>                       // for Clipper, PolyNode, Clipp...
#include <geometry/geometry_utils.h>
#include <geometry/polygon_triangulation.h>
#include <geometry/seg.h>                    // for SEG, OPT_VECTOR2I
#include <geometry/shape.h>
#include <geometry/shape_line_chain.h>
#include <geometry/shape_poly_set.h>
#include <math/box2.h>                       // for BOX2I
#include <math/util.h>                       // for KiROUND, rescale
#include <math/vector2d.h>                   // for VECTOR2I, VECTOR2D, VECTOR2
#include <md5_hash.h>
#include <geometry/shape_segment.h>
#include <geometry/shape_circle.h>

#include <wx/log.h>


SHAPE_POLY_SET::SHAPE_POLY_SET() :
    SHAPE( SH_POLY_SET )
{
}


SHAPE_POLY_SET::SHAPE_POLY_SET( const BOX2D& aRect ) :
    SHAPE( SH_POLY_SET )
{
    NewOutline();
    Append( VECTOR2I( aRect.GetLeft(),  aRect.GetTop() ) );
    Append( VECTOR2I( aRect.GetRight(), aRect.GetTop() ) );
    Append( VECTOR2I( aRect.GetRight(), aRect.GetBottom() ) );
    Append( VECTOR2I( aRect.GetLeft(),  aRect.GetBottom() ) );
    Outline( 0 ).SetClosed( true );
}


SHAPE_POLY_SET::SHAPE_POLY_SET( const SHAPE_LINE_CHAIN& aOutline ) :
    SHAPE( SH_POLY_SET )
{
    AddOutline( aOutline );
}


SHAPE_POLY_SET::SHAPE_POLY_SET( const SHAPE_POLY_SET& aOther ) :
    SHAPE( aOther ),
    m_polys( aOther.m_polys )
{
    if( aOther.IsTriangulationUpToDate() )
    {
        for( unsigned i = 0; i < aOther.TriangulatedPolyCount(); i++ )
        {
            const TRIANGULATED_POLYGON* poly = aOther.TriangulatedPolygon( i );
            m_triangulatedPolys.push_back( std::make_unique<TRIANGULATED_POLYGON>( *poly ) );
        }

        m_hash = aOther.GetHash();
        m_triangulationValid = true;
    }
    else
    {
        m_triangulationValid = false;
        m_hash = MD5_HASH();
        m_triangulatedPolys.clear();
    }
}


SHAPE_POLY_SET::~SHAPE_POLY_SET()
{
}


SHAPE* SHAPE_POLY_SET::Clone() const
{
    return new SHAPE_POLY_SET( *this );
}


bool SHAPE_POLY_SET::GetRelativeIndices( int aGlobalIdx,
                                         SHAPE_POLY_SET::VERTEX_INDEX* aRelativeIndices ) const
{
    int polygonIdx = 0;
    unsigned int contourIdx = 0;
    int vertexIdx = 0;

    int currentGlobalIdx = 0;

    for( polygonIdx = 0; polygonIdx < OutlineCount(); polygonIdx++ )
    {
        const POLYGON& currentPolygon = CPolygon( polygonIdx );

        for( contourIdx = 0; contourIdx < currentPolygon.size(); contourIdx++ )
        {
            const SHAPE_LINE_CHAIN& currentContour = currentPolygon[contourIdx];
            int totalPoints = currentContour.PointCount();

            for( vertexIdx = 0; vertexIdx < totalPoints; vertexIdx++ )
            {
                // Check if the current vertex is the globally indexed as aGlobalIdx
                if( currentGlobalIdx == aGlobalIdx )
                {
                    aRelativeIndices->m_polygon = polygonIdx;
                    aRelativeIndices->m_contour = contourIdx;
                    aRelativeIndices->m_vertex  = vertexIdx;

                    return true;
                }

                // Advance
                currentGlobalIdx++;
            }
        }
    }

    return false;
}


bool SHAPE_POLY_SET::GetGlobalIndex( SHAPE_POLY_SET::VERTEX_INDEX aRelativeIndices,
                                     int& aGlobalIdx ) const
{
    int          selectedVertex = aRelativeIndices.m_vertex;
    unsigned int selectedContour = aRelativeIndices.m_contour;
    unsigned int selectedPolygon = aRelativeIndices.m_polygon;

    // Check whether the vertex indices make sense in this poly set
    if( selectedPolygon < m_polys.size() && selectedContour < m_polys[selectedPolygon].size()
        && selectedVertex < m_polys[selectedPolygon][selectedContour].PointCount() )
    {
        POLYGON currentPolygon;

        aGlobalIdx = 0;

        for( unsigned int polygonIdx = 0; polygonIdx < selectedPolygon; polygonIdx++ )
        {
            currentPolygon = Polygon( polygonIdx );

            for( unsigned int contourIdx = 0; contourIdx < currentPolygon.size(); contourIdx++ )
                aGlobalIdx += currentPolygon[contourIdx].PointCount();
        }

        currentPolygon = Polygon( selectedPolygon );

        for( unsigned int contourIdx = 0; contourIdx < selectedContour; contourIdx++ )
            aGlobalIdx += currentPolygon[contourIdx].PointCount();

        aGlobalIdx += selectedVertex;

        return true;
    }
    else
    {
        return false;
    }
}


int SHAPE_POLY_SET::NewOutline()
{
    SHAPE_LINE_CHAIN empty_path;
    POLYGON poly;

    empty_path.SetClosed( true );
    poly.push_back( empty_path );
    m_polys.push_back( poly );
    return m_polys.size() - 1;
}


int SHAPE_POLY_SET::NewHole( int aOutline )
{
    SHAPE_LINE_CHAIN empty_path;

    empty_path.SetClosed( true );

    // Default outline is the last one
    if( aOutline < 0 )
        aOutline += m_polys.size();

    // Add hole to the selected outline
    m_polys[aOutline].push_back( empty_path );

    return m_polys.back().size() - 2;
}


int SHAPE_POLY_SET::Append( int x, int y, int aOutline, int aHole, bool aAllowDuplication )
{
    assert( m_polys.size() );

    if( aOutline < 0 )
        aOutline += m_polys.size();

    int idx;

    if( aHole < 0 )
        idx = 0;
    else
        idx = aHole + 1;

    assert( aOutline < (int) m_polys.size() );
    assert( idx < (int) m_polys[aOutline].size() );

    m_polys[aOutline][idx].Append( x, y, aAllowDuplication );

    return m_polys[aOutline][idx].PointCount();
}


int SHAPE_POLY_SET::Append( SHAPE_ARC& aArc, int aOutline, int aHole )
{
    assert( m_polys.size() );

    if( aOutline < 0 )
        aOutline += m_polys.size();

    int idx;

    if( aHole < 0 )
        idx = 0;
    else
        idx = aHole + 1;

    assert( aOutline < (int) m_polys.size() );
    assert( idx < (int) m_polys[aOutline].size() );

    m_polys[aOutline][idx].Append( aArc );

    return m_polys[aOutline][idx].PointCount();
}


void SHAPE_POLY_SET::InsertVertex( int aGlobalIndex, const VECTOR2I& aNewVertex )
{
    VERTEX_INDEX index;

    if( aGlobalIndex < 0 )
        aGlobalIndex = 0;

    if( aGlobalIndex >= TotalVertices() )
    {
        Append( aNewVertex );
    }
    else
    {
        // Assure the position to be inserted exists; throw an exception otherwise
        if( GetRelativeIndices( aGlobalIndex, &index ) )
            m_polys[index.m_polygon][index.m_contour].Insert( index.m_vertex, aNewVertex );
        else
            throw( std::out_of_range( "aGlobalIndex-th vertex does not exist" ) );
    }
}


int SHAPE_POLY_SET::VertexCount( int aOutline, int aHole  ) const
{
    if( m_polys.size() == 0 ) // Empty poly set
        return 0;

    if( aOutline < 0 ) // Use last outline
        aOutline += m_polys.size();

    int idx;

    if( aHole < 0 )
        idx = 0;
    else
        idx = aHole + 1;

    if( aOutline >= (int) m_polys.size() ) // not existing outline
        return 0;

    if( idx >= (int) m_polys[aOutline].size() ) // not existing hole
        return 0;

    return m_polys[aOutline][idx].PointCount();
}


int SHAPE_POLY_SET::FullPointCount() const
{
    int full_count = 0;

    if( m_polys.size() == 0 ) // Empty poly set
        return full_count;

    for( int ii = 0; ii < OutlineCount(); ii++ )
    {
        // the first polygon in m_polys[ii] is the main contour,
        // only others are holes:
        for( int idx = 0; idx <= HoleCount( ii ); idx++ )
        {
            full_count += m_polys[ii][idx].PointCount();
        }
    }

    return full_count;
}


SHAPE_POLY_SET SHAPE_POLY_SET::Subset( int aFirstPolygon, int aLastPolygon )
{
    assert( aFirstPolygon >= 0 && aLastPolygon <= OutlineCount() );

    SHAPE_POLY_SET newPolySet;

    for( int index = aFirstPolygon; index < aLastPolygon; index++ )
        newPolySet.m_polys.push_back( Polygon( index ) );

    return newPolySet;
}


const VECTOR2I& SHAPE_POLY_SET::CVertex( int aIndex, int aOutline, int aHole ) const
{
    if( aOutline < 0 )
        aOutline += m_polys.size();

    int idx;

    if( aHole < 0 )
        idx = 0;
    else
        idx = aHole + 1;

    assert( aOutline < (int) m_polys.size() );
    assert( idx < (int) m_polys[aOutline].size() );

    return m_polys[aOutline][idx].CPoint( aIndex );
}


const VECTOR2I& SHAPE_POLY_SET::CVertex( int aGlobalIndex ) const
{
    SHAPE_POLY_SET::VERTEX_INDEX index;

    // Assure the passed index references a legal position; abort otherwise
    if( !GetRelativeIndices( aGlobalIndex, &index ) )
        throw( std::out_of_range( "aGlobalIndex-th vertex does not exist" ) );

    return m_polys[index.m_polygon][index.m_contour].CPoint( index.m_vertex );
}


const VECTOR2I& SHAPE_POLY_SET::CVertex( SHAPE_POLY_SET::VERTEX_INDEX index ) const
{
    return CVertex( index.m_vertex, index.m_polygon, index.m_contour - 1 );
}


bool SHAPE_POLY_SET::GetNeighbourIndexes( int aGlobalIndex, int* aPrevious, int* aNext )
{
    SHAPE_POLY_SET::VERTEX_INDEX index;

    // If the edge does not exist, throw an exception, it is an illegal access memory error
    if( !GetRelativeIndices( aGlobalIndex, &index ) )
        return false;

    // Calculate the previous and next index of aGlobalIndex, corresponding to
    // the same contour;
    VERTEX_INDEX inext = index;
    int lastpoint = m_polys[index.m_polygon][index.m_contour].SegmentCount();

    if( index.m_vertex == 0 )
    {
        index.m_vertex  = lastpoint;
        inext.m_vertex  = 1;
    }
    else if( index.m_vertex == lastpoint )
    {
        index.m_vertex--;
        inext.m_vertex = 0;
    }
    else
    {
        inext.m_vertex++;
        index.m_vertex--;
    }

    if( aPrevious )
    {
        int previous;
        GetGlobalIndex( index, previous );
        *aPrevious = previous;
    }

    if( aNext )
    {
        int next;
        GetGlobalIndex( inext, next );
        *aNext = next;
    }

    return true;
}


bool SHAPE_POLY_SET::IsPolygonSelfIntersecting( int aPolygonIndex ) const
{
    CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles( aPolygonIndex );
    CONST_SEGMENT_ITERATOR innerIterator;

    for( iterator = CIterateSegmentsWithHoles( aPolygonIndex ); iterator; iterator++ )
    {
        SEG firstSegment = *iterator;

        // Iterate through all remaining segments.
        innerIterator = iterator;

        // Start in the next segment, we don't want to check collision between a segment and itself
        for( innerIterator++; innerIterator; innerIterator++ )
        {
            SEG secondSegment = *innerIterator;

            // Check whether the two segments built collide, only when they are not adjacent.
            if( !iterator.IsAdjacent( innerIterator ) && firstSegment.Collide( secondSegment, 0 ) )
                return true;
        }
    }

    return false;
}


bool SHAPE_POLY_SET::IsSelfIntersecting() const
{
    for( unsigned int polygon = 0; polygon < m_polys.size(); polygon++ )
    {
        if( IsPolygonSelfIntersecting( polygon ) )
            return true;
    }

    return false;
}


int SHAPE_POLY_SET::AddOutline( const SHAPE_LINE_CHAIN& aOutline )
{
    assert( aOutline.IsClosed() );

    POLYGON poly;

    poly.push_back( aOutline );

    m_polys.push_back( poly );

    return m_polys.size() - 1;
}


int SHAPE_POLY_SET::AddHole( const SHAPE_LINE_CHAIN& aHole, int aOutline )
{
    assert( m_polys.size() );

    if( aOutline < 0 )
        aOutline += m_polys.size();

    assert( aOutline < (int)m_polys.size() );

    POLYGON& poly = m_polys[aOutline];

    assert( poly.size() );

    poly.push_back( aHole );

    return poly.size() - 2;
}


double SHAPE_POLY_SET::Area()
{
    double area = 0.0;

    for( int i = 0; i < OutlineCount(); i++ )
    {
        area += Outline( i ).Area();

        for( int j = 0; j < HoleCount( i ); j++ )
            area -= Hole( i, j ).Area();
    }

    return area;
}


int SHAPE_POLY_SET::ArcCount() const
{
    int retval = 0;

    for( const POLYGON& poly : m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
            retval += poly[i].ArcCount();
    }

    return retval;
}


void SHAPE_POLY_SET::GetArcs( std::vector<SHAPE_ARC>& aArcBuffer ) const
{
    for( const POLYGON& poly : m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
        {
            for( SHAPE_ARC arc : poly[i].m_arcs )
                aArcBuffer.push_back( arc );
        }
    }
}


void SHAPE_POLY_SET::ClearArcs()
{
    for( POLYGON& poly : m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
            poly[i].ClearArcs();
    }
}


void SHAPE_POLY_SET::booleanOp( ClipperLib::ClipType aType, const SHAPE_POLY_SET& aOtherShape,
                                POLYGON_MODE aFastMode )
{
    booleanOp( aType, *this, aOtherShape, aFastMode );
}


void SHAPE_POLY_SET::booleanOp( ClipperLib::ClipType aType, const SHAPE_POLY_SET& aShape,
                                const SHAPE_POLY_SET& aOtherShape, POLYGON_MODE aFastMode )
{
    if( ( aShape.OutlineCount() > 1 || aOtherShape.OutlineCount() > 0 )
        && ( aShape.ArcCount() > 0 || aOtherShape.ArcCount() > 0 ) )
    {
        wxFAIL_MSG( wxT( "Boolean ops on curved polygons are not supported. You should call "
                         "ClearArcs() before carrying out the boolean operation." ) );
    }

    ClipperLib::Clipper c;

    c.StrictlySimple( aFastMode == PM_STRICTLY_SIMPLE );

    std::vector<CLIPPER_Z_VALUE> zValues;
    std::vector<SHAPE_ARC> arcBuffer;
    std::map<VECTOR2I, CLIPPER_Z_VALUE> newIntersectPoints;

    for( const POLYGON& poly : aShape.m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
        {
            c.AddPath( poly[i].convertToClipper( i == 0, zValues, arcBuffer ),
                       ClipperLib::ptSubject, true );
        }
    }

    for( const POLYGON& poly : aOtherShape.m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
        {
            c.AddPath( poly[i].convertToClipper( i == 0, zValues, arcBuffer ),
                       ClipperLib::ptClip, true );
        }
    }

    ClipperLib::PolyTree solution;

    ClipperLib::ZFillCallback callback =
            [&]( ClipperLib::IntPoint & e1bot, ClipperLib::IntPoint & e1top,
                ClipperLib::IntPoint & e2bot, ClipperLib::IntPoint & e2top,
                ClipperLib::IntPoint & pt )
            {
                auto arcIndex =
                    [&]( const ssize_t& aZvalue, const ssize_t& aCompareVal = -1 ) -> ssize_t
                    {
                        ssize_t retval;

                        retval = zValues.at( aZvalue ).m_SecondArcIdx;

                        if( retval == -1 || ( aCompareVal > 0 && retval != aCompareVal ) )
                            retval = zValues.at( aZvalue ).m_FirstArcIdx;

                        return retval;
                    };

                auto arcSegment =
                    [&]( const ssize_t& aBottomZ, const ssize_t aTopZ ) -> ssize_t
                    {
                        ssize_t retval = arcIndex( aBottomZ );

                        if( retval != -1 )
                        {
                            if( retval != arcIndex( aTopZ, retval ) )
                                retval = -1; // Not an arc segment as the two indices do not match
                        }

                        return retval;
                    };

                ssize_t e1ArcSegmentIndex = arcSegment( e1bot.Z, e1top.Z );
                ssize_t e2ArcSegmentIndex = arcSegment( e2bot.Z, e2top.Z );

                CLIPPER_Z_VALUE newZval;

                if( e1ArcSegmentIndex != -1 )
                {
                    newZval.m_FirstArcIdx = e1ArcSegmentIndex;
                    newZval.m_SecondArcIdx = e2ArcSegmentIndex;
                }
                else
                {
                    newZval.m_FirstArcIdx = e2ArcSegmentIndex;
                    newZval.m_SecondArcIdx = -1;
                }

                size_t z_value_ptr = zValues.size();
                zValues.push_back( newZval );

                // Only worry about arc segments for later processing
                if( newZval.m_FirstArcIdx != -1 )
                    newIntersectPoints.insert( { VECTOR2I( pt.X, pt.Y ), newZval } );

                pt.Z = z_value_ptr;
                //@todo amend X,Y values to true intersection between arcs or arc and segment
            };

    c.ZFillFunction( callback ); // register callback

    c.Execute( aType, solution, ClipperLib::pftNonZero, ClipperLib::pftNonZero );

    importTree( &solution, zValues, arcBuffer );
}


void SHAPE_POLY_SET::BooleanAdd( const SHAPE_POLY_SET& b, POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctUnion, b, aFastMode );
}


void SHAPE_POLY_SET::BooleanSubtract( const SHAPE_POLY_SET& b, POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctDifference, b, aFastMode );
}


void SHAPE_POLY_SET::BooleanIntersection( const SHAPE_POLY_SET& b, POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctIntersection, b, aFastMode );
}


void SHAPE_POLY_SET::BooleanAdd( const SHAPE_POLY_SET& a, const SHAPE_POLY_SET& b,
                                 POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctUnion, a, b, aFastMode );
}


void SHAPE_POLY_SET::BooleanSubtract( const SHAPE_POLY_SET& a, const SHAPE_POLY_SET& b,
                                      POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctDifference, a, b, aFastMode );
}


void SHAPE_POLY_SET::BooleanIntersection( const SHAPE_POLY_SET& a, const SHAPE_POLY_SET& b,
                                          POLYGON_MODE aFastMode )
{
    booleanOp( ClipperLib::ctIntersection, a, b, aFastMode );
}


void SHAPE_POLY_SET::InflateWithLinkedHoles( int aFactor, int aCircleSegmentsCount,
                                             POLYGON_MODE aFastMode )
{
    Simplify( aFastMode );
    Inflate( aFactor, aCircleSegmentsCount );
    Fracture( aFastMode );
}


void SHAPE_POLY_SET::Inflate( int aAmount, int aCircleSegCount, CORNER_STRATEGY aCornerStrategy )
{
    using namespace ClipperLib;
    // A static table to avoid repetitive calculations of the coefficient
    // 1.0 - cos( M_PI / aCircleSegCount )
    // aCircleSegCount is most of time <= 64 and usually 8, 12, 16, 32
    #define SEG_CNT_MAX 64
    static double arc_tolerance_factor[SEG_CNT_MAX + 1];

    ClipperOffset c;

    // N.B. see the Clipper documentation for jtSquare/jtMiter/jtRound.  They are poorly named
    // and are not what you'd think they are.
    // http://www.angusj.com/delphi/clipper/documentation/Docs/Units/ClipperLib/Types/JoinType.htm
    JoinType joinType = jtRound;    // The way corners are offsetted
    double   miterLimit = 2.0;      // Smaller value when using jtMiter for joinType
    JoinType miterFallback = jtSquare;

    switch( aCornerStrategy )
    {
    case ALLOW_ACUTE_CORNERS:
        joinType = jtMiter;
        miterLimit = 10;        // Allows large spikes
        miterFallback = jtSquare;
        break;

    case CHAMFER_ACUTE_CORNERS: // Acute angles are chamfered
        joinType = jtMiter;
        miterFallback = jtRound;
        break;

    case ROUND_ACUTE_CORNERS:   // Acute angles are rounded
        joinType = jtMiter;
        miterFallback = jtSquare;
        break;

    case CHAMFER_ALL_CORNERS:   // All angles are chamfered.
        joinType = jtSquare;
        miterFallback = jtSquare;
        break;

    case ROUND_ALL_CORNERS:     // All angles are rounded.
        joinType = jtRound;
        miterFallback = jtSquare;
        break;
    }

    std::vector<CLIPPER_Z_VALUE> zValues;
    std::vector<SHAPE_ARC>       arcBuffer;

    for( const POLYGON& poly : m_polys )
    {
        for( size_t i = 0; i < poly.size(); i++ )
        {
            c.AddPath( poly[i].convertToClipper( i == 0, zValues, arcBuffer ),
                       joinType, etClosedPolygon );
        }
    }

    PolyTree solution;

    // Calculate the arc tolerance (arc error) from the seg count by circle. The seg count is
    // nn = M_PI / acos(1.0 - c.ArcTolerance / abs(aAmount))
    // http://www.angusj.com/delphi/clipper/documentation/Docs/Units/ClipperLib/Classes/ClipperOffset/Properties/ArcTolerance.htm

    if( aCircleSegCount < 6 ) // avoid incorrect aCircleSegCount values
        aCircleSegCount = 6;

    double coeff;

    if( aCircleSegCount > SEG_CNT_MAX || arc_tolerance_factor[aCircleSegCount] == 0 )
    {
        coeff = 1.0 - cos( M_PI / aCircleSegCount );

        if( aCircleSegCount <= SEG_CNT_MAX )
            arc_tolerance_factor[aCircleSegCount] = coeff;
    }
    else
    {
        coeff = arc_tolerance_factor[aCircleSegCount];
    }

    c.ArcTolerance = std::abs( aAmount ) * coeff;
    c.MiterLimit = miterLimit;
    c.MiterFallback = miterFallback;
    c.Execute( solution, aAmount );

    importTree( &solution, zValues, arcBuffer );
}


void SHAPE_POLY_SET::importTree( ClipperLib::PolyTree*               tree,
                                 const std::vector<CLIPPER_Z_VALUE>& aZValueBuffer,
                                 const std::vector<SHAPE_ARC>&       aArcBuffer )
{
    m_polys.clear();

    for( ClipperLib::PolyNode* n = tree->GetFirst(); n; n = n->GetNext() )
    {
        if( !n->IsHole() )
        {
            POLYGON paths;
            paths.reserve( n->Childs.size() + 1 );

            paths.emplace_back( n->Contour, aZValueBuffer, aArcBuffer );

            for( unsigned int i = 0; i < n->Childs.size(); i++ )
                paths.emplace_back( n->Childs[i]->Contour, aZValueBuffer, aArcBuffer );

            m_polys.push_back( paths );
        }
    }
}


struct FractureEdge
{
    FractureEdge( int y = 0 ) :
        m_connected( false ),
        m_next( nullptr )
    {
        m_p1.x = m_p2.y = y;
    }

    FractureEdge( bool connected, const VECTOR2I& p1, const VECTOR2I& p2 ) :
        m_connected( connected ),
        m_p1( p1 ),
        m_p2( p2 ),
        m_next( nullptr )
    {
    }

    bool matches( int y ) const
    {
        return ( y >= m_p1.y || y >= m_p2.y ) && ( y <= m_p1.y || y <= m_p2.y );
    }

    bool          m_connected;
    VECTOR2I      m_p1;
    VECTOR2I      m_p2;
    FractureEdge* m_next;
};


typedef std::vector<FractureEdge*> FractureEdgeSet;


static int processEdge( FractureEdgeSet& edges, FractureEdge* edge )
{
    int x   = edge->m_p1.x;
    int y   = edge->m_p1.y;
    int min_dist    = std::numeric_limits<int>::max();
    int x_nearest   = 0;

    FractureEdge* e_nearest = nullptr;

    for( FractureEdge* e : edges )
    {
        if( !e->matches( y ) )
            continue;

        int x_intersect;

        if( e->m_p1.y == e->m_p2.y ) // horizontal edge
        {
            x_intersect = std::max( e->m_p1.x, e->m_p2.x );
        }
        else
        {
            x_intersect = e->m_p1.x + rescale( e->m_p2.x - e->m_p1.x, y - e->m_p1.y,
                                               e->m_p2.y - e->m_p1.y );
        }

        int dist = ( x - x_intersect );

        if( dist >= 0 && dist < min_dist && e->m_connected )
        {
            min_dist    = dist;
            x_nearest   = x_intersect;
            e_nearest   = e;
        }
    }

    if( e_nearest && e_nearest->m_connected )
    {
        int count = 0;

        FractureEdge* lead1 = new FractureEdge( true, VECTOR2I( x_nearest, y ), VECTOR2I( x, y ) );
        FractureEdge* lead2 = new FractureEdge( true, VECTOR2I( x, y ), VECTOR2I( x_nearest, y ) );
        FractureEdge* split_2 = new FractureEdge( true, VECTOR2I( x_nearest, y ), e_nearest->m_p2 );

        edges.push_back( split_2 );
        edges.push_back( lead1 );
        edges.push_back( lead2 );

        FractureEdge* link = e_nearest->m_next;

        e_nearest->m_p2 = VECTOR2I( x_nearest, y );
        e_nearest->m_next = lead1;
        lead1->m_next = edge;

        FractureEdge* last;

        for( last = edge; last->m_next != edge; last = last->m_next )
        {
            last->m_connected = true;
            count++;
        }

        last->m_connected = true;
        last->m_next    = lead2;
        lead2->m_next   = split_2;
        split_2->m_next = link;

        return count + 1;
    }

    return 0;
}


void SHAPE_POLY_SET::fractureSingle( POLYGON& paths )
{
    FractureEdgeSet edges;
    FractureEdgeSet border_edges;
    FractureEdge*   root = nullptr;

    bool first = true;

    if( paths.size() == 1 )
        return;

    int num_unconnected = 0;

    for( const SHAPE_LINE_CHAIN& path : paths )
    {
        const std::vector<VECTOR2I>& points = path.CPoints();
        int pointCount = points.size();

        FractureEdge* prev = nullptr, * first_edge = nullptr;

        int x_min = std::numeric_limits<int>::max();

        for( int i = 0; i < pointCount; i++ )
        {
            if( points[i].x < x_min )
                x_min = points[i].x;

            // Do not use path.CPoint() here; open-coding it using the local variables "points"
            // and "pointCount" gives a non-trivial performance boost to zone fill times.
            FractureEdge* fe = new FractureEdge( first, points[ i ],
                                                 points[ i+1 == pointCount ? 0 : i+1 ] );

            if( !root )
                root = fe;

            if( !first_edge )
                first_edge = fe;

            if( prev )
                prev->m_next = fe;

            if( i == pointCount - 1 )
                fe->m_next = first_edge;

            prev = fe;
            edges.push_back( fe );

            if( !first )
            {
                if( fe->m_p1.x == x_min )
                    border_edges.push_back( fe );
            }

            if( !fe->m_connected )
                num_unconnected++;
        }

        first = false;    // first path is always the outline
    }

    // keep connecting holes to the main outline, until there's no holes left...
    while( num_unconnected > 0 )
    {
        int x_min = std::numeric_limits<int>::max();
        auto it = border_edges.begin();

        FractureEdge* smallestX = nullptr;

        // find the left-most hole edge and merge with the outline
        for( ; it != border_edges.end(); ++it )
        {
            FractureEdge* border_edge = *it;
            int xt = border_edge->m_p1.x;

            if( ( xt <= x_min ) && !border_edge->m_connected )
            {
                x_min = xt;
                smallestX = border_edge;
            }
        }

        int num_processed = processEdge( edges, smallestX );

        // If we can't handle the edge, the zone is broken (maybe)
        if( !num_processed )
        {
            wxLogWarning( wxT( "Broken polygon, dropping path" ) );

            for( FractureEdge* edge : edges )
                delete edge;

            return;
        }

        num_unconnected -= num_processed;
    }

    paths.clear();
    SHAPE_LINE_CHAIN newPath;

    newPath.SetClosed( true );

    FractureEdge* e;

    for( e = root; e->m_next != root; e = e->m_next )
        newPath.Append( e->m_p1 );

    newPath.Append( e->m_p1 );

    for( FractureEdge* edge : edges )
        delete edge;

    paths.push_back( std::move( newPath ) );
}


void SHAPE_POLY_SET::Fracture( POLYGON_MODE aFastMode )
{
    Simplify( aFastMode );    // remove overlapping holes/degeneracy

    for( POLYGON& paths : m_polys )
        fractureSingle( paths );
}


void SHAPE_POLY_SET::unfractureSingle( SHAPE_POLY_SET::POLYGON& aPoly )
{
    assert( aPoly.size() == 1 );

    struct EDGE
    {
        int m_index = 0;
        SHAPE_LINE_CHAIN* m_poly = nullptr;
        bool m_duplicate = false;

        EDGE( SHAPE_LINE_CHAIN* aPolygon, int aIndex ) :
            m_index( aIndex ),
            m_poly( aPolygon )
        {}

        bool compareSegs( const SEG& s1, const SEG& s2 ) const
        {
            return (s1.A == s2.B && s1.B == s2.A);
        }

        bool operator==( const EDGE& aOther ) const
        {
            return compareSegs( m_poly->CSegment( m_index ),
                                aOther.m_poly->CSegment( aOther.m_index ) );
        }

        bool operator!=( const EDGE& aOther ) const
        {
            return !compareSegs( m_poly->CSegment( m_index ),
                                 aOther.m_poly->CSegment( aOther.m_index ) );
        }

        struct HASH
        {
            std::size_t operator()(  const EDGE& aEdge ) const
            {
                const SEG& a = aEdge.m_poly->CSegment( aEdge.m_index );

                return (std::size_t) ( a.A.x + a.B.x + a.A.y + a.B.y );
            }
        };
    };

    struct EDGE_LIST_ENTRY
    {
        int              index;
        EDGE_LIST_ENTRY* next;
    };

    std::unordered_set<EDGE, EDGE::HASH> uniqueEdges;

    SHAPE_LINE_CHAIN lc = aPoly[0];
    lc.Simplify();

    auto edgeList = std::make_unique<EDGE_LIST_ENTRY[]>( lc.SegmentCount() );

    for( int i = 0; i < lc.SegmentCount(); i++ )
    {
        edgeList[i].index   = i;
        edgeList[i].next    = &edgeList[ (i != lc.SegmentCount() - 1) ? i + 1 : 0 ];
    }

    std::unordered_set<EDGE_LIST_ENTRY*> queue;

    for( int i = 0; i < lc.SegmentCount(); i++ )
    {
        EDGE e( &lc, i );
        uniqueEdges.insert( e );
    }

    for( int i = 0; i < lc.SegmentCount(); i++ )
    {
        EDGE    e( &lc, i );
        auto    it = uniqueEdges.find( e );

        if( it != uniqueEdges.end() && it->m_index != i )
        {
            int e1  = it->m_index;
            int e2  = i;

            if( e1 > e2 )
                std::swap( e1, e2 );

            int e1_prev = e1 - 1;

            if( e1_prev < 0 )
                e1_prev = lc.SegmentCount() - 1;

            int e2_prev = e2 - 1;

            if( e2_prev < 0 )
                e2_prev = lc.SegmentCount() - 1;

            int e1_next = e1 + 1;

            if( e1_next == lc.SegmentCount() )
                e1_next = 0;

            int e2_next = e2 + 1;

            if( e2_next == lc.SegmentCount() )
                e2_next = 0;

            edgeList[e1_prev].next  = &edgeList[ e2_next ];
            edgeList[e2_prev].next  = &edgeList[ e1_next ];
            edgeList[i].next = nullptr;
            edgeList[it->m_index].next = nullptr;
        }
    }

    for( int i = 0; i < lc.SegmentCount(); i++ )
    {
        if( edgeList[i].next )
            queue.insert( &edgeList[i] );
    }

    auto edgeBuf = std::make_unique<EDGE_LIST_ENTRY* []>( lc.SegmentCount() );

    int n = 0;
    int outline = -1;

    POLYGON result;

    while( queue.size() )
    {
        EDGE_LIST_ENTRY* e_first = *queue.begin();
        EDGE_LIST_ENTRY* e = e_first;
        int              cnt = 0;

        do
        {
            edgeBuf[cnt++] = e;
            e = e->next;
        } while( e && e != e_first );

        SHAPE_LINE_CHAIN outl;

        for( int i = 0; i < cnt; i++ )
        {
            VECTOR2I p = lc.CPoint( edgeBuf[i]->index );
            outl.Append( p );
            queue.erase( edgeBuf[i] );
        }

        outl.SetClosed( true );

        bool cw = outl.Area() > 0.0;

        if( cw )
            outline = n;

        result.push_back( outl );
        n++;
    }

    if( outline > 0 )
        std::swap( result[0], result[outline] );

    aPoly = result;
}


bool SHAPE_POLY_SET::HasHoles() const
{
    // Iterate through all the polygons on the set
    for( const POLYGON& paths : m_polys )
    {
        // If any of them has more than one contour, it is a hole.
        if( paths.size() > 1 )
            return true;
    }

    // Return false if and only if every polygon has just one outline, without holes.
    return false;
}


void SHAPE_POLY_SET::Unfracture( POLYGON_MODE aFastMode )
{
    for( POLYGON& path : m_polys )
        unfractureSingle( path );

    Simplify( aFastMode );    // remove overlapping holes/degeneracy
}


void SHAPE_POLY_SET::Simplify( POLYGON_MODE aFastMode )
{
    SHAPE_POLY_SET empty;

    booleanOp( ClipperLib::ctUnion, empty, aFastMode );
}


int SHAPE_POLY_SET::NormalizeAreaOutlines()
{
    // We are expecting only one main outline, but this main outline can have holes
    // if holes: combine holes and remove them from the main outline.
    // Note also we are using SHAPE_POLY_SET::PM_STRICTLY_SIMPLE in polygon
    // calculations, but it is not mandatory. It is used mainly
    // because there is usually only very few vertices in area outlines
    SHAPE_POLY_SET::POLYGON& outline = Polygon( 0 );
    SHAPE_POLY_SET holesBuffer;

    // Move holes stored in outline to holesBuffer:
    // The first SHAPE_LINE_CHAIN is the main outline, others are holes
    while( outline.size() > 1 )
    {
        holesBuffer.AddOutline( outline.back() );
        outline.pop_back();
    }

    Simplify( SHAPE_POLY_SET::PM_STRICTLY_SIMPLE );

    // If any hole, subtract it to main outline
    if( holesBuffer.OutlineCount() )
    {
        holesBuffer.Simplify( SHAPE_POLY_SET::PM_FAST );
        BooleanSubtract( holesBuffer, SHAPE_POLY_SET::PM_STRICTLY_SIMPLE );
    }

    RemoveNullSegments();

    return OutlineCount();
}


const std::string SHAPE_POLY_SET::Format() const
{
    std::stringstream ss;

    ss << "SHAPE_LINE_CHAIN poly; \n";

    for( unsigned i = 0; i < m_polys.size(); i++ )
    {
        for( unsigned j = 0; j < m_polys[i].size(); j++ )
        {

            ss << "{ auto tmp = " << m_polys[i][j].Format() << ";\n";

            SHAPE_POLY_SET poly;

            if( j == 0 )
            {
                ss << " poly.AddOutline(tmp); } \n";
            }
            else
            {
                ss << " poly.AddHole(tmp); } \n";
            }

        }
    }

    return ss.str();
}


bool SHAPE_POLY_SET::Parse( std::stringstream& aStream )
{
    std::string tmp;

    aStream >> tmp;

    if( tmp != "polyset" )
        return false;

    aStream >> tmp;

    int n_polys = atoi( tmp.c_str() );

    if( n_polys < 0 )
        return false;

    for( int i = 0; i < n_polys; i++ )
    {
        POLYGON paths;

        aStream >> tmp;

        if( tmp != "poly" )
            return false;

        aStream >> tmp;
        int n_outlines = atoi( tmp.c_str() );

        if( n_outlines < 0 )
            return false;

        for( int j = 0; j < n_outlines; j++ )
        {
            SHAPE_LINE_CHAIN outline;

            outline.SetClosed( true );

            aStream >> tmp;
            int n_vertices = atoi( tmp.c_str() );

            for( int v = 0; v < n_vertices; v++ )
            {
                VECTOR2I p;

                aStream >> tmp; p.x = atoi( tmp.c_str() );
                aStream >> tmp; p.y = atoi( tmp.c_str() );
                outline.Append( p );
            }

            paths.push_back( outline );
        }

        m_polys.push_back( paths );
    }

    return true;
}


const BOX2I SHAPE_POLY_SET::BBox( int aClearance ) const
{
    BOX2I bb;

    for( unsigned i = 0; i < m_polys.size(); i++ )
    {
        if( i == 0 )
            bb = m_polys[i][0].BBox();
        else
            bb.Merge( m_polys[i][0].BBox() );
    }

    bb.Inflate( aClearance );
    return bb;
}


const BOX2I SHAPE_POLY_SET::BBoxFromCaches() const
{
    BOX2I bb;

    for( unsigned i = 0; i < m_polys.size(); i++ )
    {
        if( i == 0 )
            bb = *m_polys[i][0].GetCachedBBox();
        else
            bb.Merge( *m_polys[i][0].GetCachedBBox() );
    }

    return bb;
}


bool SHAPE_POLY_SET::PointOnEdge( const VECTOR2I& aP ) const
{
    // Iterate through all the polygons in the set
    for( const POLYGON& polygon : m_polys )
    {
        // Iterate through all the line chains in the polygon
        for( const SHAPE_LINE_CHAIN& lineChain : polygon )
        {
            if( lineChain.PointOnEdge( aP ) )
                return true;
        }
    }

    return false;
}


bool SHAPE_POLY_SET::Collide( const SEG& aSeg, int aClearance, int* aActual,
                              VECTOR2I* aLocation ) const
{
    VECTOR2I nearest;
    ecoord dist_sq = SquaredDistance( aSeg, aLocation ? &nearest : nullptr );

    if( dist_sq == 0 || dist_sq < SEG::Square( aClearance ) )
    {
        if( aLocation )
            *aLocation = nearest;

        if( aActual )
            *aActual = sqrt( dist_sq );

        return true;
    }

    return false;
}


bool SHAPE_POLY_SET::Collide( const VECTOR2I& aP, int aClearance, int* aActual,
                              VECTOR2I* aLocation ) const
{
    if( IsEmpty() || VertexCount() == 0 )
        return false;

    VECTOR2I nearest;
    ecoord dist_sq = SquaredDistance( aP, aLocation ? &nearest : nullptr );

    if( dist_sq == 0 || dist_sq < SEG::Square( aClearance ) )
    {
        if( aLocation )
            *aLocation = nearest;

        if( aActual )
            *aActual = sqrt( dist_sq );

        return true;
    }

    return false;
}


bool SHAPE_POLY_SET::Collide( const SHAPE* aShape, int aClearance, int* aActual,
                              VECTOR2I* aLocation ) const
{
    // A couple of simple cases are worth trying before we fall back on triangulation.

    if( aShape->Type() == SH_SEGMENT )
    {
        const SHAPE_SEGMENT* segment = static_cast<const SHAPE_SEGMENT*>( aShape );
        int                  extra = segment->GetWidth() / 2;

        if( Collide( segment->GetSeg(), aClearance + extra, aActual, aLocation ) )
        {
            if( aActual )
                *aActual = std::max( 0, *aActual - extra );

            return true;
        }

        return false;
    }

    if( aShape->Type() == SH_CIRCLE )
    {
        const SHAPE_CIRCLE* circle = static_cast<const SHAPE_CIRCLE*>( aShape );
        int                 extra = circle->GetRadius();

        if( Collide( circle->GetCenter(), aClearance + extra, aActual, aLocation ) )
        {
            if( aActual )
                *aActual = std::max( 0, *aActual - extra );

            return true;
        }

        return false;
    }

    const_cast<SHAPE_POLY_SET*>( this )->CacheTriangulation( true );

    int      actual = INT_MAX;
    VECTOR2I location;

    for( const std::unique_ptr<TRIANGULATED_POLYGON>& tpoly : m_triangulatedPolys )
    {
        for( const TRIANGULATED_POLYGON::TRI& tri : tpoly->Triangles() )
        {
            if( aActual || aLocation )
            {
                int      triActual;
                VECTOR2I triLocation;

                if( aShape->Collide( &tri, aClearance, &triActual, &triLocation ) )
                {
                    if( triActual < actual )
                    {
                        actual = triActual;
                        location = triLocation;
                    }
                }
            }
            else    // A much faster version of above
            {
                if( aShape->Collide( &tri, aClearance ) )
                    return true;
            }
        }
    }

    if( actual < INT_MAX )
    {
        if( aActual )
            *aActual = std::max( 0, actual );

        if( aLocation )
            *aLocation = location;

        return true;
    }

    return false;
}


void SHAPE_POLY_SET::RemoveAllContours()
{
    m_polys.clear();
}


void SHAPE_POLY_SET::RemoveContour( int aContourIdx, int aPolygonIdx )
{
    // Default polygon is the last one
    if( aPolygonIdx < 0 )
        aPolygonIdx += m_polys.size();

    m_polys[aPolygonIdx].erase( m_polys[aPolygonIdx].begin() + aContourIdx );
}


int SHAPE_POLY_SET::RemoveNullSegments()
{
    int removed = 0;

    ITERATOR iterator = IterateWithHoles();

    VECTOR2I    contourStart = *iterator;
    VECTOR2I    segmentStart, segmentEnd;

    VERTEX_INDEX indexStart;

    while( iterator )
    {
        // Obtain first point and its index
        segmentStart = *iterator;
        indexStart = iterator.GetIndex();

        // Obtain last point
        if( iterator.IsEndContour() )
        {
            segmentEnd = contourStart;

            // Advance
            iterator++;

            if( iterator )
                contourStart = *iterator;
        }
        else
        {
            // Advance
            iterator++;

            if( iterator )
                segmentEnd = *iterator;
        }

        // Remove segment start if both points are equal
        if( segmentStart == segmentEnd )
        {
            RemoveVertex( indexStart );
            removed++;

            // Advance the iterator one position, as there is one vertex less.
            if( iterator )
                iterator++;
        }
    }

    return removed;
}


void SHAPE_POLY_SET::DeletePolygon( int aIdx )
{
    m_polys.erase( m_polys.begin() + aIdx );
}


void SHAPE_POLY_SET::Append( const SHAPE_POLY_SET& aSet )
{
    m_polys.insert( m_polys.end(), aSet.m_polys.begin(), aSet.m_polys.end() );
}


void SHAPE_POLY_SET::Append( const VECTOR2I& aP, int aOutline, int aHole )
{
    Append( aP.x, aP.y, aOutline, aHole );
}


bool SHAPE_POLY_SET::CollideVertex( const VECTOR2I& aPoint,
                                    SHAPE_POLY_SET::VERTEX_INDEX& aClosestVertex,
                                    int aClearance ) const
{
    // Shows whether there was a collision
    bool collision = false;

    // Difference vector between each vertex and aPoint.
    VECTOR2D    delta;
    double      distance, clearance;

    // Convert clearance to double for precision when comparing distances
    clearance = aClearance;

    for( CONST_ITERATOR iterator = CIterateWithHoles(); iterator; iterator++ )
    {
        // Get the difference vector between current vertex and aPoint
        delta = *iterator - aPoint;

        // Compute distance
        distance = delta.EuclideanNorm();

        // Check for collisions
        if( distance <= clearance )
        {
            collision = true;

            // Update aClearance to look for closer vertices
            clearance = distance;

            // Store the indices that identify the vertex
            aClosestVertex = iterator.GetIndex();
        }
    }

    return collision;
}


bool SHAPE_POLY_SET::CollideEdge( const VECTOR2I& aPoint,
                                  SHAPE_POLY_SET::VERTEX_INDEX& aClosestVertex,
                                  int aClearance ) const
{
    // Shows whether there was a collision
    bool collision = false;

    for( CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles(); iterator; iterator++ )
    {
        const SEG currentSegment = *iterator;
        int distance = currentSegment.Distance( aPoint );

        // Check for collisions
        if( distance <= aClearance )
        {
            collision = true;

            // Update aClearance to look for closer edges
            aClearance = distance;

            // Store the indices that identify the vertex
            aClosestVertex = iterator.GetIndex();
        }
    }

    return collision;
}


void SHAPE_POLY_SET::BuildBBoxCaches() const
{
    for( int polygonIdx = 0; polygonIdx < OutlineCount(); polygonIdx++ )
    {
        COutline( polygonIdx ).GenerateBBoxCache();

        for( int holeIdx = 0; holeIdx < HoleCount( polygonIdx ); holeIdx++ )
            CHole( polygonIdx, holeIdx ).GenerateBBoxCache();
    }
}


bool SHAPE_POLY_SET::Contains( const VECTOR2I& aP, int aSubpolyIndex, int aAccuracy,
                               bool aUseBBoxCaches ) const
{
    if( m_polys.empty() )
        return false;

    // If there is a polygon specified, check the condition against that polygon
    if( aSubpolyIndex >= 0 )
        return containsSingle( aP, aSubpolyIndex, aAccuracy, aUseBBoxCaches );

    // In any other case, check it against all polygons in the set
    for( int polygonIdx = 0; polygonIdx < OutlineCount(); polygonIdx++ )
    {
        if( containsSingle( aP, polygonIdx, aAccuracy, aUseBBoxCaches ) )
            return true;
    }

    return false;
}


void SHAPE_POLY_SET::RemoveVertex( int aGlobalIndex )
{
    VERTEX_INDEX index;

    // Assure the to be removed vertex exists, abort otherwise
    if( GetRelativeIndices( aGlobalIndex, &index ) )
        RemoveVertex( index );
    else
        throw( std::out_of_range( "aGlobalIndex-th vertex does not exist" ) );
}


void SHAPE_POLY_SET::RemoveVertex( VERTEX_INDEX aIndex )
{
    m_polys[aIndex.m_polygon][aIndex.m_contour].Remove( aIndex.m_vertex );
}


void SHAPE_POLY_SET::SetVertex( int aGlobalIndex, const VECTOR2I& aPos )
{
    VERTEX_INDEX index;

    if( GetRelativeIndices( aGlobalIndex, &index ) )
        SetVertex( index, aPos );
    else
        throw( std::out_of_range( "aGlobalIndex-th vertex does not exist" ) );
}


void SHAPE_POLY_SET::SetVertex( const VERTEX_INDEX& aIndex, const VECTOR2I& aPos )
{
    m_polys[aIndex.m_polygon][aIndex.m_contour].SetPoint( aIndex.m_vertex, aPos );
}


bool SHAPE_POLY_SET::containsSingle( const VECTOR2I& aP, int aSubpolyIndex, int aAccuracy,
                                     bool aUseBBoxCaches ) const
{
    // Check that the point is inside the outline
    if( m_polys[aSubpolyIndex][0].PointInside( aP, aAccuracy ) )
    {
        // Check that the point is not in any of the holes
        for( int holeIdx = 0; holeIdx < HoleCount( aSubpolyIndex ); holeIdx++ )
        {
            const SHAPE_LINE_CHAIN& hole = CHole( aSubpolyIndex, holeIdx );

            // If the point is inside a hole it is outside of the polygon.  Do not use aAccuracy
            // here as it's meaning would be inverted.
            if( hole.PointInside( aP, 1, aUseBBoxCaches ) )
                return false;
        }

        return true;
    }

    return false;
}


void SHAPE_POLY_SET::Move( const VECTOR2I& aVector )
{
    for( POLYGON& poly : m_polys )
    {
        for( SHAPE_LINE_CHAIN& path : poly )
            path.Move( aVector );
    }

    for( std::unique_ptr<TRIANGULATED_POLYGON>& tri : m_triangulatedPolys )
        tri->Move( aVector );

    m_hash = checksum();
}


void SHAPE_POLY_SET::Mirror( bool aX, bool aY, const VECTOR2I& aRef )
{
    for( POLYGON& poly : m_polys )
    {
        for( SHAPE_LINE_CHAIN& path : poly )
            path.Mirror( aX, aY, aRef );
    }

    if( m_triangulationValid )
        CacheTriangulation();
}


void SHAPE_POLY_SET::Rotate( const EDA_ANGLE& aAngle, const VECTOR2I& aCenter )
{
    for( POLYGON& poly : m_polys )
    {
        for( SHAPE_LINE_CHAIN& path : poly )
            path.Rotate( aAngle, aCenter );
    }

    // Don't re-cache if the triangulation is already invalid
    if( m_triangulationValid )
        CacheTriangulation();
}


int SHAPE_POLY_SET::TotalVertices() const
{
    int c = 0;

    for( const POLYGON& poly : m_polys )
    {
        for( const SHAPE_LINE_CHAIN& path : poly )
            c += path.PointCount();
    }

    return c;
}


SHAPE_POLY_SET::POLYGON SHAPE_POLY_SET::ChamferPolygon( unsigned int aDistance, int aIndex )
{
    return chamferFilletPolygon( CHAMFERED, aDistance, aIndex, 0 );
}


SHAPE_POLY_SET::POLYGON SHAPE_POLY_SET::FilletPolygon( unsigned int aRadius, int aErrorMax,
                                                       int aIndex )
{
    return chamferFilletPolygon( FILLETED, aRadius, aIndex, aErrorMax );
}


SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( VECTOR2I aPoint, int aPolygonIndex,
                                                      VECTOR2I* aNearest ) const
{
    // We calculate the min dist between the segment and each outline segment.  However, if the
    // segment to test is inside the outline, and does not cross any edge, it can be seen outside
    // the polygon.  Therefore test if a segment end is inside (testing only one end is enough).
    // Use an accuracy of "1" to say that we don't care if it's exactly on the edge or not.
    if( containsSingle( aPoint, aPolygonIndex, 1 ) )
    {
        if( aNearest )
            *aNearest = aPoint;

        return 0;
    }

    CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles( aPolygonIndex );

    SEG::ecoord minDistance = (*iterator).SquaredDistance( aPoint );

    for( iterator++; iterator && minDistance > 0; iterator++ )
    {
        SEG::ecoord currentDistance = (*iterator).SquaredDistance( aPoint );

        if( currentDistance < minDistance )
        {
            if( aNearest )
                *aNearest = (*iterator).NearestPoint( aPoint );

            minDistance = currentDistance;
        }
    }

    return minDistance;
}


SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( const SEG& aSegment, int aPolygonIndex,
                                                      VECTOR2I* aNearest ) const
{
    // Check if the segment is fully-contained.  If so, its midpoint is a good-enough nearest point.
    if( containsSingle( aSegment.A, aPolygonIndex, 1 ) &&
        containsSingle( aSegment.B, aPolygonIndex, 1 ) )
    {
        if( aNearest )
            *aNearest = ( aSegment.A + aSegment.B ) / 2;

        return 0;
    }

    CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles( aPolygonIndex );
    SEG::ecoord            minDistance = (*iterator).SquaredDistance( aSegment );

    if( aNearest && minDistance == 0 )
        *aNearest = ( *iterator ).NearestPoint( aSegment );

    for( iterator++; iterator && minDistance > 0; iterator++ )
    {
        SEG::ecoord currentDistance = (*iterator).SquaredDistance( aSegment );

        if( currentDistance < minDistance )
        {
            if( aNearest )
                *aNearest = (*iterator).NearestPoint( aSegment );

            minDistance = currentDistance;
        }
    }

    // Return the maximum of minDistance and zero
    return minDistance < 0 ? 0 : minDistance;
}


SEG::ecoord SHAPE_POLY_SET::SquaredDistance( VECTOR2I aPoint, VECTOR2I* aNearest ) const
{
    SEG::ecoord currentDistance_sq;
    SEG::ecoord minDistance_sq = VECTOR2I::ECOORD_MAX;
    VECTOR2I    nearest;

    // Iterate through all the polygons and get the minimum distance.
    for( unsigned int polygonIdx = 0; polygonIdx < m_polys.size(); polygonIdx++ )
    {
        currentDistance_sq = SquaredDistanceToPolygon( aPoint, polygonIdx,
                                                       aNearest ? &nearest : nullptr );

        if( currentDistance_sq < minDistance_sq )
        {
            if( aNearest )
                *aNearest = nearest;

            minDistance_sq = currentDistance_sq;
        }
    }

    return minDistance_sq;
}


SEG::ecoord SHAPE_POLY_SET::SquaredDistance( const SEG& aSegment, VECTOR2I* aNearest ) const
{
    SEG::ecoord currentDistance_sq;
    SEG::ecoord minDistance_sq = VECTOR2I::ECOORD_MAX;
    VECTOR2I    nearest;

    // Iterate through all the polygons and get the minimum distance.
    for( unsigned int polygonIdx = 0; polygonIdx < m_polys.size(); polygonIdx++ )
    {
        currentDistance_sq = SquaredDistanceToPolygon( aSegment, polygonIdx,
                                                       aNearest ? &nearest : nullptr );

        if( currentDistance_sq < minDistance_sq )
        {
            if( aNearest )
                *aNearest = nearest;

            minDistance_sq = currentDistance_sq;
        }
    }

    return minDistance_sq;
}


bool SHAPE_POLY_SET::IsVertexInHole( int aGlobalIdx )
{
    VERTEX_INDEX index;

    // Get the polygon and contour where the vertex is. If the vertex does not exist, return false
    if( !GetRelativeIndices( aGlobalIdx, &index ) )
        return false;

    // The contour is a hole if its index is greater than zero
    return index.m_contour > 0;
}


SHAPE_POLY_SET SHAPE_POLY_SET::Chamfer( int aDistance )
{
    SHAPE_POLY_SET chamfered;

    for( unsigned int idx = 0; idx < m_polys.size(); idx++ )
        chamfered.m_polys.push_back( ChamferPolygon( aDistance, idx ) );

    return chamfered;
}


SHAPE_POLY_SET SHAPE_POLY_SET::Fillet( int aRadius, int aErrorMax )
{
    SHAPE_POLY_SET filleted;

    for( size_t idx = 0; idx < m_polys.size(); idx++ )
        filleted.m_polys.push_back( FilletPolygon( aRadius, aErrorMax, idx ) );

    return filleted;
}


SHAPE_POLY_SET::POLYGON SHAPE_POLY_SET::chamferFilletPolygon( CORNER_MODE aMode,
                                                              unsigned int aDistance,
                                                              int aIndex, int aErrorMax )
{
    // Null segments create serious issues in calculations. Remove them:
    RemoveNullSegments();

    SHAPE_POLY_SET::POLYGON currentPoly = Polygon( aIndex );
    SHAPE_POLY_SET::POLYGON newPoly;

    // If the chamfering distance is zero, then the polygon remain intact.
    if( aDistance == 0 )
    {
        return currentPoly;
    }

    // Iterate through all the contours (outline and holes) of the polygon.
    for( SHAPE_LINE_CHAIN& currContour : currentPoly )
    {
        // Generate a new contour in the new polygon
        SHAPE_LINE_CHAIN newContour;

        // Iterate through the vertices of the contour
        for( int currVertex = 0; currVertex < currContour.PointCount(); currVertex++ )
        {
            // Current vertex
            int x1 = currContour.CPoint( currVertex ).x;
            int y1 = currContour.CPoint( currVertex ).y;

            // Indices for previous and next vertices.
            int prevVertex;
            int nextVertex;

            // Previous and next vertices indices computation. Necessary to manage the edge cases.

            // Previous vertex is the last one if the current vertex is the first one
            prevVertex = currVertex == 0 ? currContour.PointCount() - 1 : currVertex - 1;

            // next vertex is the first one if the current vertex is the last one.
            nextVertex = currVertex == currContour.PointCount() - 1 ? 0 : currVertex + 1;

            // Previous vertex computation
            double xa = currContour.CPoint( prevVertex ).x - x1;
            double ya = currContour.CPoint( prevVertex ).y - y1;

            // Next vertex computation
            double xb = currContour.CPoint( nextVertex ).x - x1;
            double yb = currContour.CPoint( nextVertex ).y - y1;

            // Compute the new distances
            double  lena    = hypot( xa, ya );
            double  lenb    = hypot( xb, yb );

            // Make the final computations depending on the mode selected, chamfered or filleted.
            if( aMode == CORNER_MODE::CHAMFERED )
            {
                double distance = aDistance;

                // Chamfer one half of an edge at most
                if( 0.5 * lena < distance )
                    distance = 0.5 * lena;

                if( 0.5 * lenb < distance )
                    distance = 0.5 * lenb;

                int nx1 = KiROUND( distance * xa / lena );
                int ny1 = KiROUND( distance * ya / lena );

                newContour.Append( x1 + nx1, y1 + ny1 );

                int nx2 = KiROUND( distance * xb / lenb );
                int ny2 = KiROUND( distance * yb / lenb );

                newContour.Append( x1 + nx2, y1 + ny2 );
            }
            else    // CORNER_MODE = FILLETED
            {
                double cosine = ( xa * xb + ya * yb ) / ( lena * lenb );

                double  radius  = aDistance;
                double  denom   = sqrt( 2.0 / ( 1 + cosine ) - 1 );

                // Do nothing in case of parallel edges
                if( std::isinf( denom ) )
                    continue;

                // Limit rounding distance to one half of an edge
                if( 0.5 * lena * denom < radius )
                    radius = 0.5 * lena * denom;

                if( 0.5 * lenb * denom < radius )
                    radius = 0.5 * lenb * denom;

                // Calculate fillet arc absolute center point (xc, yx)
                double  k = radius / sqrt( .5 * ( 1 - cosine ) );
                double  lenab = sqrt( ( xa / lena + xb / lenb ) * ( xa / lena + xb / lenb ) +
                        ( ya / lena + yb / lenb ) * ( ya / lena + yb / lenb ) );
                double  xc  = x1 + k * ( xa / lena + xb / lenb ) / lenab;
                double  yc  = y1 + k * ( ya / lena + yb / lenb ) / lenab;

                // Calculate arc start and end vectors
                k = radius / sqrt( 2 / ( 1 + cosine ) - 1 );
                double  xs  = x1 + k * xa / lena - xc;
                double  ys  = y1 + k * ya / lena - yc;
                double  xe  = x1 + k * xb / lenb - xc;
                double  ye  = y1 + k * yb / lenb - yc;

                // Cosine of arc angle
                double argument = ( xs * xe + ys * ye ) / ( radius * radius );

                // Make sure the argument is in [-1,1], interval in which the acos function is
                // defined
                if( argument < -1 )
                    argument = -1;
                else if( argument > 1 )
                    argument = 1;

                double arcAngle = acos( argument );
                int    segments = GetArcToSegmentCount( radius, aErrorMax,
                                                        EDA_ANGLE( arcAngle, RADIANS_T ) );

                double deltaAngle = arcAngle / segments;
                double startAngle = atan2( -ys, xs );

                // Flip arc for inner corners
                if( xa * yb - ya * xb <= 0 )
                    deltaAngle *= -1;

                double  nx  = xc + xs;
                double  ny  = yc + ys;

                newContour.Append( KiROUND( nx ), KiROUND( ny ) );

                // Store the previous added corner to make a sanity check
                int prevX   = KiROUND( nx );
                int prevY   = KiROUND( ny );

                for( int j = 0; j < segments; j++ )
                {
                    nx = xc + cos( startAngle + ( j + 1 ) * deltaAngle ) * radius;
                    ny = yc - sin( startAngle + ( j + 1 ) * deltaAngle ) * radius;

                    // Sanity check: the rounding can produce repeated corners; do not add them.
                    if( KiROUND( nx ) != prevX || KiROUND( ny ) != prevY )
                    {
                        newContour.Append( KiROUND( nx ), KiROUND( ny ) );
                        prevX   = KiROUND( nx );
                        prevY   = KiROUND( ny );
                    }
                }
            }
        }

        // Close the current contour and add it the new polygon
        newContour.SetClosed( true );
        newPoly.push_back( newContour );
    }

    return newPoly;
}


SHAPE_POLY_SET &SHAPE_POLY_SET::operator=( const SHAPE_POLY_SET& aOther )
{
    static_cast<SHAPE&>(*this) = aOther;
    m_polys = aOther.m_polys;
    m_triangulatedPolys.clear();
    m_triangulationValid = false;

    if( aOther.IsTriangulationUpToDate() )
    {
        for( unsigned i = 0; i < aOther.TriangulatedPolyCount(); i++ )
        {
            const TRIANGULATED_POLYGON* poly = aOther.TriangulatedPolygon( i );
            m_triangulatedPolys.push_back( std::make_unique<TRIANGULATED_POLYGON>( *poly ) );
        }

        m_hash = aOther.GetHash();
        m_triangulationValid = true;
    }

    return *this;
}


MD5_HASH SHAPE_POLY_SET::GetHash() const
{
    if( !m_hash.IsValid() )
        return checksum();

    return m_hash;
}


bool SHAPE_POLY_SET::IsTriangulationUpToDate() const
{
    if( !m_triangulationValid )
        return false;

    if( !m_hash.IsValid() )
        return false;

    MD5_HASH hash = checksum();

    return hash == m_hash;
}


static void partitionPolyIntoRegularCellGrid( const SHAPE_POLY_SET& aPoly, int aSize,
                                              SHAPE_POLY_SET& aOut )
{
    BOX2I bb = aPoly.BBox();

    double w = bb.GetWidth();
    double h = bb.GetHeight();

    if( w == 0.0 || h == 0.0 )
        return;

    int n_cells_x, n_cells_y;

    if( w > h )
    {
        n_cells_x = w / aSize;
        n_cells_y = floor( h / w * n_cells_x ) + 1;
    }
    else
    {
        n_cells_y = h / aSize;
        n_cells_x = floor( w / h * n_cells_y ) + 1;
    }

    SHAPE_POLY_SET ps1( aPoly ), ps2( aPoly ), maskSetOdd, maskSetEven;

    for( int yy = 0; yy < n_cells_y; yy++ )
    {
        for( int xx = 0; xx < n_cells_x; xx++ )
        {
            VECTOR2I p;

            p.x = bb.GetX() + w * xx / n_cells_x;
            p.y = bb.GetY() + h * yy / n_cells_y;

            VECTOR2I p2;

            p2.x = bb.GetX() + w * ( xx + 1 ) / n_cells_x;
            p2.y = bb.GetY() + h * ( yy + 1 ) / n_cells_y;


            SHAPE_LINE_CHAIN mask;
            mask.Append( VECTOR2I( p.x, p.y ) );
            mask.Append( VECTOR2I( p2.x, p.y ) );
            mask.Append( VECTOR2I( p2.x, p2.y ) );
            mask.Append( VECTOR2I( p.x, p2.y ) );
            mask.SetClosed( true );

            if( ( xx ^ yy ) & 1 )
                maskSetOdd.AddOutline( mask );
            else
                maskSetEven.AddOutline( mask );
        }
    }

    ps1.BooleanIntersection( maskSetOdd, SHAPE_POLY_SET::PM_FAST );
    ps2.BooleanIntersection( maskSetEven, SHAPE_POLY_SET::PM_FAST );
    ps1.Fracture( SHAPE_POLY_SET::PM_FAST );
    ps2.Fracture( SHAPE_POLY_SET::PM_FAST );

    aOut = ps1;

    for( int i = 0; i < ps2.OutlineCount(); i++ )
        aOut.AddOutline( ps2.COutline( i ) );

    if( !aOut.OutlineCount() )
        aOut = aPoly;
}


void SHAPE_POLY_SET::CacheTriangulation( bool aPartition )
{
    bool recalculate = !m_hash.IsValid();
    MD5_HASH hash;

    if( !m_triangulationValid )
        recalculate = true;

    if( !recalculate )
    {
        hash = checksum();

        if( m_hash != hash )
        {
            m_hash = hash;
            recalculate = true;
        }
    }

    if( !recalculate )
        return;

    SHAPE_POLY_SET tmpSet;

    if( aPartition )
    {
        // This partitions into regularly-sized grids (1cm in Pcbnew)
        SHAPE_POLY_SET flattened( *this );
        flattened.ClearArcs();
        partitionPolyIntoRegularCellGrid( flattened, 1e7, tmpSet );
    }
    else
    {
        tmpSet = *this;

        if( tmpSet.HasHoles() )
            tmpSet.Fracture( PM_FAST );
    }

    m_triangulatedPolys.clear();
    m_triangulationValid = false;

    while( tmpSet.OutlineCount() > 0 )
    {

        if( !m_triangulatedPolys.empty() && m_triangulatedPolys.back()->GetTriangleCount() == 0 )
            m_triangulatedPolys.erase( m_triangulatedPolys.end() - 1 );

        m_triangulatedPolys.push_back( std::make_unique<TRIANGULATED_POLYGON>() );
        PolygonTriangulation tess( *m_triangulatedPolys.back() );

        // If the tessellation fails, we re-fracture the polygon, which will
        // first simplify the system before fracturing and removing the holes
        // This may result in multiple, disjoint polygons.
        if( !tess.TesselatePolygon( tmpSet.Polygon( 0 ).front() ) )
        {
            tmpSet.Fracture( PM_FAST );
            m_triangulationValid = false;
            continue;
        }

        tmpSet.DeletePolygon( 0 );
        m_triangulationValid = true;
    }

    if( m_triangulationValid )
        m_hash = checksum();
}


MD5_HASH SHAPE_POLY_SET::checksum() const
{
    MD5_HASH hash;

    hash.Hash( m_polys.size() );

    for( const POLYGON& outline : m_polys )
    {
        hash.Hash( outline.size() );

        for( const SHAPE_LINE_CHAIN& lc : outline )
        {
            hash.Hash( lc.PointCount() );

            for( int i = 0; i < lc.PointCount(); i++ )
            {
                hash.Hash( lc.CPoint( i ).x );
                hash.Hash( lc.CPoint( i ).y );
            }
        }
    }

    hash.Finalize();

    return hash;
}


bool SHAPE_POLY_SET::HasTouchingHoles() const
{
    for( int i = 0; i < OutlineCount(); i++ )
    {
        if( hasTouchingHoles( CPolygon( i ) ) )
            return true;
    }

    return false;
}


bool SHAPE_POLY_SET::hasTouchingHoles( const POLYGON& aPoly ) const
{
    std::set<long long> ptHashes;

    for( const SHAPE_LINE_CHAIN& lc : aPoly )
    {
        for( const VECTOR2I& pt : lc.CPoints() )
        {
            const long long ptHash = (long long) pt.x << 32 | pt.y;

            if( ptHashes.count( ptHash ) > 0 )
                return true;

            ptHashes.insert( ptHash );
        }
    }

    return false;
}


bool SHAPE_POLY_SET::HasIndexableSubshapes() const
{
    return IsTriangulationUpToDate();
}


size_t SHAPE_POLY_SET::GetIndexableSubshapeCount() const
{
    size_t n = 0;

    for( const std::unique_ptr<TRIANGULATED_POLYGON>& t : m_triangulatedPolys )
        n += t->GetTriangleCount();

    return n;
}


void SHAPE_POLY_SET:: GetIndexableSubshapes( std::vector<SHAPE*>& aSubshapes )
{
    aSubshapes.reserve( GetIndexableSubshapeCount() );

    for( const std::unique_ptr<TRIANGULATED_POLYGON>& tpoly : m_triangulatedPolys )
    {
        for( TRIANGULATED_POLYGON::TRI& tri : tpoly->Triangles() )
            aSubshapes.push_back( &tri );
    }
}


const BOX2I SHAPE_POLY_SET::TRIANGULATED_POLYGON::TRI::BBox( int aClearance ) const
{
    BOX2I bbox( parent->m_vertices[a] );
    bbox.Merge( parent->m_vertices[b] );
    bbox.Merge( parent->m_vertices[c] );

    if( aClearance != 0 )
        bbox.Inflate( aClearance );

    return bbox;
}


void SHAPE_POLY_SET::TRIANGULATED_POLYGON::AddTriangle( int a, int b, int c )
{
    m_triangles.emplace_back( a, b, c, this );
}


SHAPE_POLY_SET::TRIANGULATED_POLYGON::TRIANGULATED_POLYGON( const TRIANGULATED_POLYGON& aOther )
{
    m_vertices = aOther.m_vertices;
    m_triangles = aOther.m_triangles;

    for( TRI& tri : m_triangles )
        tri.parent = this;
}


SHAPE_POLY_SET::TRIANGULATED_POLYGON& SHAPE_POLY_SET::TRIANGULATED_POLYGON::operator=( const TRIANGULATED_POLYGON& aOther )
{
    m_vertices = aOther.m_vertices;
    m_triangles = aOther.m_triangles;

    for( TRI& tri : m_triangles )
        tri.parent = this;

    return *this;
}


SHAPE_POLY_SET::TRIANGULATED_POLYGON::TRIANGULATED_POLYGON()
{
}


SHAPE_POLY_SET::TRIANGULATED_POLYGON::~TRIANGULATED_POLYGON()
{
}


const SHAPE_POLY_SET
SHAPE_POLY_SET::BuildPolysetFromOrientedPaths( const std::vector<SHAPE_LINE_CHAIN>& aPaths,
                                               bool aReverseOrientation, bool aEvenOdd )
{
    ClipperLib::Clipper  clipper;
    ClipperLib::PolyTree tree;

    // fixme: do we need aReverseOrientation?

    for( const SHAPE_LINE_CHAIN& path : aPaths )
    {
        ClipperLib::Path lc;

        for( int i = 0; i < path.PointCount(); i++ )
        {
            lc.emplace_back( path.CPoint( i ).x, path.CPoint( i ).y );
        }

        clipper.AddPath( lc, ClipperLib::ptSubject, true );
    }

    clipper.StrictlySimple( true );
    clipper.Execute( ClipperLib::ctUnion, tree,
                     aEvenOdd ? ClipperLib::pftEvenOdd : ClipperLib::pftNonZero,
                     ClipperLib::pftNonZero );
    SHAPE_POLY_SET result;

    for( ClipperLib::PolyNode* n = tree.GetFirst(); n; n = n->GetNext() )
    {
        if( !n->IsHole() )
        {
            int outl = result.NewOutline();

            for( unsigned int i = 0; i < n->Contour.size(); i++ )
                result.Outline( outl ).Append( n->Contour[i].X, n->Contour[i].Y );

            for( unsigned int i = 0; i < n->Childs.size(); i++ )
            {
                int outh = result.NewHole( outl );
                for( unsigned int j = 0; j < n->Childs[i]->Contour.size(); j++ )
                {
                    result.Hole( outl, outh )
                            .Append( n->Childs[i]->Contour[j].X, n->Childs[i]->Contour[j].Y );
                }
            }
        }
    }

    return result;
}