kicad/thirdparty/clipper/clipper.cpp

/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.4.2                                                           *
* Date      :  27 February 2017                                                *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2017                                         *
*                                                                              *
* License:                                                                     *
* Use, modification & distribution is subject to Boost Software License Ver 1. *
* http://www.boost.org/LICENSE_1_0.txt                                         *
*                                                                              *
* Attributions:                                                                *
* The code in this library is an extension of Bala Vatti's clipping algorithm: *
* "A generic solution to polygon clipping"                                     *
* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
* http://portal.acm.org/citation.cfm?id=129906                                 *
*                                                                              *
* Computer graphics and geometric modeling: implementation and algorithms      *
* By Max K. Agoston                                                            *
* Springer; 1 edition (January 4, 2005)                                        *
* http://books.google.com/books?q=vatti+clipping+agoston                       *
*                                                                              *
* See also:                                                                    *
* "Polygon Offsetting by Computing Winding Numbers"                            *
* Paper no. DETC2005-85513 pp. 565-575                                         *
* ASME 2005 International Design Engineering Technical Conferences             *
* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
* September 24-28, 2005 , Long Beach, California, USA                          *
* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
*                                                                              *
*******************************************************************************/

/*******************************************************************************
*                                                                              *
* This is a translation of the Delphi Clipper library and the naming style     *
* used has retained a Delphi flavour.                                          *
*                                                                              *
*******************************************************************************/

#include "clipper.hpp"
#include <cmath>
#include <vector>
#include <algorithm>
#include <stdexcept>
#include <cstring>
#include <cstdlib>
#include <ostream>
#include <functional>

namespace ClipperLib {
static double const pi = 3.141592653589793238;
static double const two_pi = pi * 2;
static double const def_arc_tolerance = 0.25;

enum Direction
{
    dRightToLeft, dLeftToRight
};

static int const Unassigned = -1;   // edge not currently 'owning' a solution
static int const Skip = -2;         // edge that would otherwise close a path

#define HORIZONTAL  (-1.0E+40)
#define TOLERANCE   (1.0e-20)
#define NEAR_ZERO( val ) ( ( (val) > -TOLERANCE ) && ( (val) < TOLERANCE ) )

struct TEdge
{
    IntPoint Bot;
    IntPoint Curr; // current (updated for every new scanbeam)
    IntPoint Top;
    double Dx;
    PolyType PolyTyp;
    EdgeSide Side;  // side only refers to current side of solution poly
    int WindDelta;  // 1 or -1 depending on winding direction
    int WindCnt;
    int WindCnt2;   // winding count of the opposite polytype
    int OutIdx;
    TEdge* Next;
    TEdge* Prev;
    TEdge* NextInLML;
    TEdge* NextInAEL;
    TEdge* PrevInAEL;
    TEdge* NextInSEL;
    TEdge* PrevInSEL;
};

struct IntersectNode
{
    TEdge* Edge1;
    TEdge* Edge2;
    IntPoint Pt;
};

struct LocalMinimum
{
    cInt Y;
    TEdge* LeftBound;
    TEdge* RightBound;
};

struct OutPt;

// OutRec: contains a path in the clipping solution. Edges in the AEL will
// carry a pointer to an OutRec when they are part of the clipping solution.
struct OutRec
{
    int Idx;
    bool IsHole;
    bool IsOpen;
    OutRec* FirstLeft;  // see comments in clipper.pas
    PolyNode*   PolyNd;
    OutPt*  Pts;
    OutPt*  BottomPt;
};

struct OutPt
{
    int Idx;
    IntPoint Pt;
    OutPt* Next;
    OutPt* Prev;
};

struct Join
{
    OutPt* OutPt1;
    OutPt* OutPt2;
    IntPoint OffPt;
};

struct LocMinSorter
{
    inline bool operator()( const LocalMinimum& locMin1, const LocalMinimum& locMin2 )
    {
        return locMin2.Y < locMin1.Y;
    }
};

// ------------------------------------------------------------------------------
// ------------------------------------------------------------------------------

inline cInt Round( double val )
{
    if( (val < 0) )
        return static_cast<cInt>(val - 0.5);
    else
        return static_cast<cInt>(val + 0.5);
}


// ------------------------------------------------------------------------------

inline cInt Abs( cInt val )
{
    return val < 0 ? -val : val;
}


// ------------------------------------------------------------------------------
// PolyTree methods ...
// ------------------------------------------------------------------------------

void PolyTree::Clear()
{
    for( PolyNodes::size_type i = 0; i < AllNodes.size(); ++i )
        delete AllNodes[i];

    AllNodes.resize( 0 );
    Childs.resize( 0 );
}


// ------------------------------------------------------------------------------

PolyNode* PolyTree::GetFirst() const
{
    if( !Childs.empty() )
        return Childs[0];
    else
        return 0;
}


// ------------------------------------------------------------------------------

int PolyTree::Total() const
{
    int result = (int) AllNodes.size();

    // with negative offsets, ignore the hidden outer polygon ...
    if( result > 0 && Childs[0] != AllNodes[0] )
        result--;

    return result;
}


// ------------------------------------------------------------------------------
// PolyNode methods ...
// ------------------------------------------------------------------------------

PolyNode::PolyNode() : Parent( 0 ), Index( 0 ), m_IsOpen( false ),
        m_jointype( jtSquare ), m_endtype( etClosedPolygon )
{
}


// ------------------------------------------------------------------------------

int PolyNode::ChildCount() const
{
    return (int) Childs.size();
}


// ------------------------------------------------------------------------------

void PolyNode::AddChild( PolyNode& child )
{
    unsigned cnt = (unsigned) Childs.size();

    Childs.push_back( &child );
    child.Parent = this;
    child.Index = cnt;
}


// ------------------------------------------------------------------------------

PolyNode* PolyNode::GetNext() const
{
    if( !Childs.empty() )
        return Childs[0];
    else
        return GetNextSiblingUp();
}


// ------------------------------------------------------------------------------

PolyNode* PolyNode::GetNextSiblingUp() const
{
    if( !Parent ) // protects against PolyTree.GetNextSiblingUp()
        return 0;
    else if( Index == Parent->Childs.size() - 1 )
        return Parent->GetNextSiblingUp();
    else
        return Parent->Childs[Index + 1];
}


// ------------------------------------------------------------------------------

bool PolyNode::IsHole() const
{
    bool result = true;
    PolyNode* node = Parent;

    while( node )
    {
        result = !result;
        node = node->Parent;
    }

    return result;
}


// ------------------------------------------------------------------------------

bool PolyNode::IsOpen() const
{
    return m_IsOpen;
}


// ------------------------------------------------------------------------------

#ifndef use_int32

// ------------------------------------------------------------------------------
// Int128 class (enables safe math on signed 64bit integers)
// eg Int128 val1((long64)9223372036854775807); //ie 2^63 -1
// Int128 val2((long64)9223372036854775807);
// Int128 val3 = val1 * val2;
// val3.AsString => "85070591730234615847396907784232501249" (8.5e+37)
// ------------------------------------------------------------------------------

class Int128
{
public:
    ulong64 lo;
    long64  hi;

    Int128( long64 _lo = 0 )
    {
        lo = (ulong64) _lo;

        if( _lo < 0 )  hi = -1; else hi = 0;
    }

    Int128( const Int128& val ) : lo( val.lo ), hi( val.hi ) {}

    Int128( const long64& _hi, const ulong64& _lo ) : lo( _lo ), hi( _hi ) {}

    Int128& operator =( const long64& val )
    {
        lo = (ulong64) val;

        if( val < 0 ) hi = -1; else hi = 0;

        return *this;
    }

    bool operator ==( const Int128& val ) const
    { return hi == val.hi && lo == val.lo; }

    bool operator !=( const Int128& val ) const
    { return !(*this == val); }

    bool operator >( const Int128& val ) const
    {
        if( hi != val.hi )
            return hi > val.hi;
        else
            return lo > val.lo;
    }

    bool operator <( const Int128& val ) const
    {
        if( hi != val.hi )
            return hi < val.hi;
        else
            return lo < val.lo;
    }

    bool operator >=( const Int128& val ) const
    { return !(*this < val); }

    bool operator <=( const Int128& val ) const
    { return !(*this > val); }

    Int128& operator +=( const Int128& rhs )
    {
        hi  += rhs.hi;
        lo  += rhs.lo;

        if( lo < rhs.lo ) hi++;

        return *this;
    }

    Int128 operator +( const Int128& rhs ) const
    {
        Int128 result( *this );

        result += rhs;
        return result;
    }

    Int128& operator -=( const Int128& rhs )
    {
        *this += -rhs;
        return *this;
    }

    Int128 operator -( const Int128& rhs ) const
    {
        Int128 result( *this );

        result -= rhs;
        return result;
    }

    Int128 operator-() const    // unary negation
    {
        if( lo == 0 )
            return Int128( -hi, 0 );
        else
            return Int128( ~hi, ~lo + 1 );
    }

    operator double() const
    {
        const double shift64 = 18446744073709551616.0; // 2^64

        if( hi < 0 )
        {
            if( lo == 0 ) return (double) hi * shift64;
            else return -(double) (~lo + ~hi * shift64);
        }
        else
            return (double) (lo + hi * shift64);
    }
};
// ------------------------------------------------------------------------------

Int128 Int128Mul( long64 lhs, long64 rhs )
{
    bool negate = (lhs < 0) != (rhs < 0);

    if( lhs < 0 )
        lhs = -lhs;

    ulong64 int1Hi  = ulong64( lhs ) >> 32;
    ulong64 int1Lo  = ulong64( lhs & 0xFFFFFFFF );

    if( rhs < 0 )
        rhs = -rhs;

    ulong64 int2Hi  = ulong64( rhs ) >> 32;
    ulong64 int2Lo  = ulong64( rhs & 0xFFFFFFFF );

    // nb: see comments in clipper.pas
    ulong64 a = int1Hi * int2Hi;
    ulong64 b = int1Lo * int2Lo;
    ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;

    Int128 tmp;
    tmp.hi  = long64( a + (c >> 32) );
    tmp.lo  = long64( c << 32 );
    tmp.lo  += long64( b );

    if( tmp.lo < b )
        tmp.hi++;

    if( negate )
        tmp = -tmp;

    return tmp;
}
#endif

// ------------------------------------------------------------------------------
// Miscellaneous global functions
// ------------------------------------------------------------------------------

bool Orientation( const Path& poly )
{
    return Area( poly ) >= 0;
}


// ------------------------------------------------------------------------------

double Area( const Path& poly )
{
    int size = (int) poly.size();

    if( size < 3 )
        return 0;

    double a = 0;

    for( int i = 0, j = size - 1; i < size; ++i )
    {
        a += ( (double) poly[j].X + poly[i].X ) * ( (double) poly[j].Y - poly[i].Y );
        j = i;
    }

    return -a * 0.5;
}


// ------------------------------------------------------------------------------

double Area( const OutPt* op )
{
    const OutPt* startOp = op;

    if( !op )
        return 0;

    double a = 0;

    do {
        a += (double) (op->Prev->Pt.X + op->Pt.X) * (double) (op->Prev->Pt.Y - op->Pt.Y);
        op = op->Next;
    } while( op != startOp );

    return a * 0.5;
}


// ------------------------------------------------------------------------------

double Area( const OutRec& outRec )
{
    return Area( outRec.Pts );
}


// ------------------------------------------------------------------------------

bool PointIsVertex( const IntPoint& Pt, OutPt* pp )
{
    OutPt* pp2 = pp;

    do
    {
        if( pp2->Pt == Pt )
            return true;

        pp2 = pp2->Next;
    } while( pp2 != pp );

    return false;
}


// ------------------------------------------------------------------------------

// See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
// http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
int PointInPolygon( const IntPoint& pt, const Path& path )
{
    // returns 0 if false, +1 if true, -1 if pt ON polygon boundary
    int result  = 0;
    size_t cnt  = path.size();

    if( cnt < 3 )
        return 0;

    IntPoint ip = path[0];

    for( size_t i = 1; i <= cnt; ++i )
    {
        IntPoint ipNext = (i == cnt ? path[0] : path[i]);

        if( ipNext.Y == pt.Y )
        {
            if( (ipNext.X == pt.X) || ( ip.Y == pt.Y
                                        && ( (ipNext.X > pt.X) == (ip.X < pt.X) ) ) )
                return -1;
        }

        if( (ip.Y < pt.Y) != (ipNext.Y < pt.Y) )
        {
            if( ip.X >= pt.X )
            {
                if( ipNext.X > pt.X )
                    result = 1 - result;
                else
                {
                    double d = (double) (ip.X - pt.X) * (ipNext.Y - pt.Y) -
                               (double) (ipNext.X - pt.X) * (ip.Y - pt.Y);

                    if( !d )
                        return -1;

                    if( (d > 0) == (ipNext.Y > ip.Y) )
                        result = 1 - result;
                }
            }
            else
            {
                if( ipNext.X > pt.X )
                {
                    double d = (double) (ip.X - pt.X) * (ipNext.Y - pt.Y) -
                               (double) (ipNext.X - pt.X) * (ip.Y - pt.Y);

                    if( !d )
                        return -1;

                    if( (d > 0) == (ipNext.Y > ip.Y) )
                        result = 1 - result;
                }
            }
        }

        ip = ipNext;
    }

    return result;
}


// ------------------------------------------------------------------------------

int PointInPolygon( const IntPoint& pt, OutPt* op )
{
    // returns 0 if false, +1 if true, -1 if pt ON polygon boundary
    int result = 0;
    OutPt* startOp = op;

    for( ; ; )
    {
        if( op->Next->Pt.Y == pt.Y )
        {
            if( (op->Next->Pt.X == pt.X) || ( op->Pt.Y == pt.Y
                                              && ( (op->Next->Pt.X > pt.X) ==
                                                   (op->Pt.X < pt.X) ) ) )
                return -1;
        }

        if( (op->Pt.Y < pt.Y) != (op->Next->Pt.Y < pt.Y) )
        {
            if( op->Pt.X >= pt.X )
            {
                if( op->Next->Pt.X > pt.X )
                    result = 1 - result;
                else
                {
                    double d = (double) (op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
                               (double) (op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);

                    if( !d )
                        return -1;

                    if( (d > 0) == (op->Next->Pt.Y > op->Pt.Y) )
                        result = 1 - result;
                }
            }
            else
            {
                if( op->Next->Pt.X > pt.X )
                {
                    double d = (double) (op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
                               (double) (op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);

                    if( !d )
                        return -1;

                    if( (d > 0) == (op->Next->Pt.Y > op->Pt.Y) )
                        result = 1 - result;
                }
            }
        }

        op = op->Next;

        if( startOp == op )
            break;
    }

    return result;
}


// ------------------------------------------------------------------------------

bool Poly2ContainsPoly1( OutPt* OutPt1, OutPt* OutPt2 )
{
    OutPt* op = OutPt1;

    do
    {
        // nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
        int res = PointInPolygon( op->Pt, OutPt2 );

        if( res >= 0 )
            return res > 0;

        op = op->Next;
    } while( op != OutPt1 );

    return true;
}


// ----------------------------------------------------------------------

bool SlopesEqual( const TEdge& e1, const TEdge& e2, bool UseFullInt64Range )
{
#ifndef use_int32

    if( UseFullInt64Range )
        return Int128Mul( e1.Top.Y - e1.Bot.Y, e2.Top.X - e2.Bot.X ) ==
               Int128Mul( e1.Top.X - e1.Bot.X, e2.Top.Y - e2.Bot.Y );
    else
#endif
    return (e1.Top.Y - e1.Bot.Y) * (e2.Top.X - e2.Bot.X) ==
           (e1.Top.X - e1.Bot.X) * (e2.Top.Y - e2.Bot.Y);
}


// ------------------------------------------------------------------------------

bool SlopesEqual( const IntPoint pt1, const IntPoint pt2,
        const IntPoint pt3, bool UseFullInt64Range )
{
#ifndef use_int32

    if( UseFullInt64Range )
        return Int128Mul( pt1.Y - pt2.Y,
                pt2.X - pt3.X ) == Int128Mul( pt1.X - pt2.X, pt2.Y - pt3.Y );
    else
#endif
    return (pt1.Y - pt2.Y) * (pt2.X - pt3.X) == (pt1.X - pt2.X) * (pt2.Y - pt3.Y);
}


// ------------------------------------------------------------------------------

bool SlopesEqual( const IntPoint pt1, const IntPoint pt2,
        const IntPoint pt3, const IntPoint pt4, bool UseFullInt64Range )
{
#ifndef use_int32

    if( UseFullInt64Range )
        return Int128Mul( pt1.Y - pt2.Y,
                pt3.X - pt4.X ) == Int128Mul( pt1.X - pt2.X, pt3.Y - pt4.Y );
    else
#endif
    return (pt1.Y - pt2.Y) * (pt3.X - pt4.X) == (pt1.X - pt2.X) * (pt3.Y - pt4.Y);
}


// ------------------------------------------------------------------------------

inline bool IsHorizontal( TEdge& e )
{
    return e.Dx == HORIZONTAL;
}


// ------------------------------------------------------------------------------

inline double GetDx( const IntPoint pt1, const IntPoint pt2 )
{
    return (pt1.Y == pt2.Y) ?
           HORIZONTAL : (double) (pt2.X - pt1.X) / (pt2.Y - pt1.Y);
}


// ---------------------------------------------------------------------------

inline void SetDx( TEdge& e )
{
    cInt dy = (e.Top.Y - e.Bot.Y);

    if( dy == 0 )
        e.Dx = HORIZONTAL;
    else
        e.Dx = (double) (e.Top.X - e.Bot.X) / dy;
}


// ---------------------------------------------------------------------------

inline void SwapSides( TEdge& Edge1, TEdge& Edge2 )
{
    EdgeSide Side = Edge1.Side;

    Edge1.Side  = Edge2.Side;
    Edge2.Side  = Side;
}


// ------------------------------------------------------------------------------

inline void SwapPolyIndexes( TEdge& Edge1, TEdge& Edge2 )
{
    int OutIdx = Edge1.OutIdx;

    Edge1.OutIdx = Edge2.OutIdx;
    Edge2.OutIdx = OutIdx;
}


// ------------------------------------------------------------------------------

inline cInt TopX( TEdge& edge, const cInt currentY )
{
    return ( currentY == edge.Top.Y ) ?
           edge.Top.X : edge.Bot.X + Round( edge.Dx * (currentY - edge.Bot.Y) );
}


// ------------------------------------------------------------------------------

void IntersectPoint( TEdge& Edge1, TEdge& Edge2, IntPoint& ip )
{
#ifdef use_xyz
    ip.Z = 0;
#endif

    double b1, b2;

    if( Edge1.Dx == Edge2.Dx )
    {
        ip.Y = Edge1.Curr.Y;
        ip.X = TopX( Edge1, ip.Y );
        return;
    }
    else if( Edge1.Dx == 0 )
    {
        ip.X = Edge1.Bot.X;

        if( IsHorizontal( Edge2 ) )
            ip.Y = Edge2.Bot.Y;
        else
        {
            b2 = Edge2.Bot.Y - (Edge2.Bot.X / Edge2.Dx);
            ip.Y = Round( ip.X / Edge2.Dx + b2 );
        }
    }
    else if( Edge2.Dx == 0 )
    {
        ip.X = Edge2.Bot.X;

        if( IsHorizontal( Edge1 ) )
            ip.Y = Edge1.Bot.Y;
        else
        {
            b1 = Edge1.Bot.Y - (Edge1.Bot.X / Edge1.Dx);
            ip.Y = Round( ip.X / Edge1.Dx + b1 );
        }
    }
    else
    {
        b1  = Edge1.Bot.X - Edge1.Bot.Y * Edge1.Dx;
        b2  = Edge2.Bot.X - Edge2.Bot.Y * Edge2.Dx;
        double q = (b2 - b1) / (Edge1.Dx - Edge2.Dx);
        ip.Y = Round( q );

        if( std::fabs( Edge1.Dx ) < std::fabs( Edge2.Dx ) )
            ip.X = Round( Edge1.Dx * q + b1 );
        else
            ip.X = Round( Edge2.Dx * q + b2 );
    }

    if( ip.Y < Edge1.Top.Y || ip.Y < Edge2.Top.Y )
    {
        if( Edge1.Top.Y > Edge2.Top.Y )
            ip.Y = Edge1.Top.Y;
        else
            ip.Y = Edge2.Top.Y;

        if( std::fabs( Edge1.Dx ) < std::fabs( Edge2.Dx ) )
            ip.X = TopX( Edge1, ip.Y );
        else
            ip.X = TopX( Edge2, ip.Y );
    }

    // finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
    if( ip.Y > Edge1.Curr.Y )
    {
        ip.Y = Edge1.Curr.Y;

        // use the more vertical edge to derive X ...
        if( std::fabs( Edge1.Dx ) > std::fabs( Edge2.Dx ) )
            ip.X = TopX( Edge2, ip.Y );
        else
            ip.X = TopX( Edge1, ip.Y );
    }
}


// ------------------------------------------------------------------------------

void ReversePolyPtLinks( OutPt* pp )
{
    if( !pp )
        return;

    OutPt* pp1, * pp2;
    pp1 = pp;

    do {
        pp2 = pp1->Next;
        pp1->Next = pp1->Prev;
        pp1->Prev = pp2;
        pp1 = pp2;
    } while( pp1 != pp );
}


// ------------------------------------------------------------------------------

void DisposeOutPts( OutPt*& pp )
{
    if( pp == 0 )
        return;

    pp->Prev->Next = 0;

    while( pp )
    {
        OutPt* tmpPp = pp;
        pp = pp->Next;
        delete tmpPp;
    }
}


// ------------------------------------------------------------------------------

inline void InitEdge( TEdge* e, TEdge* eNext, TEdge* ePrev, const IntPoint& Pt )
{
    // This clears the C++ way
    *e = TEdge( { 0 } );

    e->Next = eNext;
    e->Prev = ePrev;
    e->Curr = Pt;
    e->OutIdx = Unassigned;
}


// ------------------------------------------------------------------------------

void InitEdge2( TEdge& e, PolyType Pt )
{
    if( e.Curr.Y >= e.Next->Curr.Y )
    {
        e.Bot = e.Curr;
        e.Top = e.Next->Curr;
    }
    else
    {
        e.Top = e.Curr;
        e.Bot = e.Next->Curr;
    }

    SetDx( e );
    e.PolyTyp = Pt;
}


// ------------------------------------------------------------------------------

TEdge* RemoveEdge( TEdge* e )
{
    // removes e from double_linked_list (but without removing from memory)
    e->Prev->Next = e->Next;
    e->Next->Prev = e->Prev;
    TEdge* result = e->Next;
    e->Prev = 0; // flag as removed (see ClipperBase.Clear)
    return result;
}


// ------------------------------------------------------------------------------

inline void ReverseHorizontal( TEdge& e )
{
    // swap horizontal edges' Top and Bottom x's so they follow the natural
    // progression of the bounds - ie so their xbots will align with the
    // adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
    std::swap( e.Top.X, e.Bot.X );

#ifdef use_xyz
    std::swap( e.Top.Z, e.Bot.Z );
#endif
}


// ------------------------------------------------------------------------------

void SwapPoints( IntPoint& pt1, IntPoint& pt2 )
{
    IntPoint tmp = pt1;

    pt1 = pt2;
    pt2 = tmp;
}


// ------------------------------------------------------------------------------

bool GetOverlapSegment( IntPoint pt1a, IntPoint pt1b, IntPoint pt2a,
        IntPoint pt2b, IntPoint& pt1, IntPoint& pt2 )
{
    // precondition: segments are Collinear.
    if( Abs( pt1a.X - pt1b.X ) > Abs( pt1a.Y - pt1b.Y ) )
    {
        if( pt1a.X > pt1b.X )
            SwapPoints( pt1a, pt1b );

        if( pt2a.X > pt2b.X )
            SwapPoints( pt2a, pt2b );

        if( pt1a.X > pt2a.X )
            pt1 = pt1a;
        else
            pt1 = pt2a;

        if( pt1b.X < pt2b.X )
            pt2 = pt1b;
        else
            pt2 = pt2b;

        return pt1.X < pt2.X;
    }
    else
    {
        if( pt1a.Y < pt1b.Y )
            SwapPoints( pt1a, pt1b );

        if( pt2a.Y < pt2b.Y )
            SwapPoints( pt2a, pt2b );

        if( pt1a.Y < pt2a.Y )
            pt1 = pt1a;
        else
            pt1 = pt2a;

        if( pt1b.Y > pt2b.Y )
            pt2 = pt1b;
        else
            pt2 = pt2b;

        return pt1.Y > pt2.Y;
    }
}


// ------------------------------------------------------------------------------

bool FirstIsBottomPt( const OutPt* btmPt1, const OutPt* btmPt2 )
{
    OutPt* p = btmPt1->Prev;

    while( (p->Pt == btmPt1->Pt) && (p != btmPt1) )
        p = p->Prev;

    double dx1p = std::fabs( GetDx( btmPt1->Pt, p->Pt ) );
    p = btmPt1->Next;

    while( (p->Pt == btmPt1->Pt) && (p != btmPt1) )
        p = p->Next;

    double dx1n = std::fabs( GetDx( btmPt1->Pt, p->Pt ) );

    p = btmPt2->Prev;

    while( (p->Pt == btmPt2->Pt) && (p != btmPt2) )
        p = p->Prev;

    double dx2p = std::fabs( GetDx( btmPt2->Pt, p->Pt ) );
    p = btmPt2->Next;

    while( (p->Pt == btmPt2->Pt) && (p != btmPt2) )
        p = p->Next;

    double dx2n = std::fabs( GetDx( btmPt2->Pt, p->Pt ) );

    if( std::max( dx1p, dx1n ) == std::max( dx2p, dx2n )
        && std::min( dx1p, dx1n ) == std::min( dx2p, dx2n ) )
        return Area( btmPt1 ) > 0; // if otherwise identical use orientation
    else
        return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
}


// ------------------------------------------------------------------------------

OutPt* GetBottomPt( OutPt* pp )
{
    OutPt* dups = 0;
    OutPt* p = pp->Next;

    while( p != pp )
    {
        if( p->Pt.Y > pp->Pt.Y )
        {
            pp = p;
            dups = 0;
        }
        else if( p->Pt.Y == pp->Pt.Y && p->Pt.X <= pp->Pt.X )
        {
            if( p->Pt.X < pp->Pt.X )
            {
                dups = 0;
                pp = p;
            }
            else
            {
                if( p->Next != pp && p->Prev != pp )
                    dups = p;
            }
        }

        p = p->Next;
    }

    if( dups )
    {
        // there appears to be at least 2 vertices at BottomPt so ...
        while( dups != p )
        {
            if( !FirstIsBottomPt( p, dups ) )
                pp = dups;

            dups = dups->Next;

            while( dups->Pt != pp->Pt )
                dups = dups->Next;
        }
    }

    return pp;
}


// ------------------------------------------------------------------------------

bool Pt2IsBetweenPt1AndPt3( const IntPoint pt1,
        const IntPoint pt2, const IntPoint pt3 )
{
    if( (pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2) )
        return false;
    else if( pt1.X != pt3.X )
        return (pt2.X > pt1.X) == (pt2.X < pt3.X);
    else
        return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
}


// ------------------------------------------------------------------------------

bool HorzSegmentsOverlap( cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b )
{
    if( seg1a > seg1b )
        std::swap( seg1a, seg1b );

    if( seg2a > seg2b )
        std::swap( seg2a, seg2b );

    return (seg1a < seg2b) && (seg2a < seg1b);
}


// ------------------------------------------------------------------------------
// ClipperBase class methods ...
// ------------------------------------------------------------------------------

ClipperBase::ClipperBase()              // constructor
{
    m_CurrentLM = m_MinimaList.begin(); // begin() == end() here
    m_UseFullRange = false;

    // Avoid uninitialized vars:
    m_PreserveCollinear = false;
    m_HasOpenPaths = false;
    m_ActiveEdges = nullptr;
}


// ------------------------------------------------------------------------------

ClipperBase::~ClipperBase()    // destructor
{
    Clear();
}


// ------------------------------------------------------------------------------

void RangeTest( const IntPoint& Pt, bool& useFullRange )
{
    if( useFullRange )
    {
        if( Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange )
            throw clipperException( "Coordinate outside allowed range" );
    }
    else if( Pt.X > loRange|| Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange )
    {
        useFullRange = true;
        RangeTest( Pt, useFullRange );
    }
}


// ------------------------------------------------------------------------------

TEdge* FindNextLocMin( TEdge* E )
{
    for( ; ; )
    {
        while( E->Bot != E->Prev->Bot || E->Curr == E->Top )
            E = E->Next;

        if( !IsHorizontal( *E ) && !IsHorizontal( *E->Prev ) )
            break;

        while( IsHorizontal( *E->Prev ) )
            E = E->Prev;

        TEdge* E2 = E;

        while( IsHorizontal( *E ) )
            E = E->Next;

        if( E->Top.Y == E->Prev->Bot.Y )
            continue;                         // ie just an intermediate horz.

        if( E2->Prev->Bot.X < E->Bot.X )
            E = E2;

        break;
    }

    return E;
}


// ------------------------------------------------------------------------------

TEdge* ClipperBase::ProcessBound( TEdge* E, bool NextIsForward )
{
    TEdge* Result = E;
    TEdge* Horz = 0;

    if( E->OutIdx == Skip )
    {
        // if edges still remain in the current bound beyond the skip edge then
        // create another LocMin and call ProcessBound once more
        if( NextIsForward )
        {
            while( E->Top.Y == E->Next->Bot.Y )
                E = E->Next;

            // don't include top horizontals when parsing a bound a second time,
            // they will be contained in the opposite bound ...
            while( E != Result && IsHorizontal( *E ) )
                E = E->Prev;
        }
        else
        {
            while( E->Top.Y == E->Prev->Bot.Y )
                E = E->Prev;

            while( E != Result && IsHorizontal( *E ) )
                E = E->Next;
        }

        if( E == Result )
        {
            if( NextIsForward )
                Result = E->Next;
            else
                Result = E->Prev;
        }
        else
        {
            // there are more edges in the bound beyond result starting with E
            if( NextIsForward )
                E = Result->Next;
            else
                E = Result->Prev;

            MinimaList::value_type locMin;
            locMin.Y = E->Bot.Y;
            locMin.LeftBound = 0;
            locMin.RightBound = E;
            E->WindDelta = 0;
            Result = ProcessBound( E, NextIsForward );
            m_MinimaList.push_back( locMin );
        }

        return Result;
    }

    TEdge* EStart;

    if( IsHorizontal( *E ) )
    {
        // We need to be careful with open paths because this may not be a
        // true local minima (ie E may be following a skip edge).
        // Also, consecutive horz. edges may start heading left before going right.
        if( NextIsForward )
            EStart = E->Prev;
        else
            EStart = E->Next;

        if( IsHorizontal( *EStart ) ) // ie an adjoining horizontal skip edge
        {
            if( EStart->Bot.X != E->Bot.X && EStart->Top.X != E->Bot.X )
                ReverseHorizontal( *E );
        }
        else if( EStart->Bot.X != E->Bot.X )
            ReverseHorizontal( *E );
    }

    EStart = E;

    if( NextIsForward )
    {
        while( Result->Top.Y == Result->Next->Bot.Y && Result->Next->OutIdx != Skip )
            Result = Result->Next;

        if( IsHorizontal( *Result ) && Result->Next->OutIdx != Skip )
        {
            // nb: at the top of a bound, horizontals are added to the bound
            // only when the preceding edge attaches to the horizontal's left vertex
            // unless a Skip edge is encountered when that becomes the top divide
            Horz = Result;

            while( IsHorizontal( *Horz->Prev ) )
                Horz = Horz->Prev;

            if( Horz->Prev->Top.X > Result->Next->Top.X )
                Result = Horz->Prev;
        }

        while( E != Result )
        {
            E->NextInLML = E->Next;

            if( IsHorizontal( *E ) && E != EStart
                && E->Bot.X != E->Prev->Top.X )
                ReverseHorizontal( *E );

            E = E->Next;
        }

        if( IsHorizontal( *E ) && E != EStart && E->Bot.X != E->Prev->Top.X )
            ReverseHorizontal( *E );

        Result = Result->Next; // move to the edge just beyond current bound
    }
    else
    {
        while( Result->Top.Y == Result->Prev->Bot.Y && Result->Prev->OutIdx != Skip )
            Result = Result->Prev;

        if( IsHorizontal( *Result ) && Result->Prev->OutIdx != Skip )
        {
            Horz = Result;

            while( IsHorizontal( *Horz->Next ) )
                Horz = Horz->Next;

            if( Horz->Next->Top.X == Result->Prev->Top.X
                || Horz->Next->Top.X > Result->Prev->Top.X )
                Result = Horz->Next;
        }

        while( E != Result )
        {
            E->NextInLML = E->Prev;

            if( IsHorizontal( *E ) && E != EStart && E->Bot.X != E->Next->Top.X )
                ReverseHorizontal( *E );

            E = E->Prev;
        }

        if( IsHorizontal( *E ) && E != EStart && E->Bot.X != E->Next->Top.X )
            ReverseHorizontal( *E );

        Result = Result->Prev; // move to the edge just beyond current bound
    }

    return Result;
}


// ------------------------------------------------------------------------------

bool ClipperBase::AddPath( const Path& pg, PolyType PolyTyp, bool Closed )
{
#ifdef use_lines

    if( !Closed && PolyTyp == ptClip )
        throw clipperException( "AddPath: Open paths must be subject." );

#else

    if( !Closed )
        throw clipperException( "AddPath: Open paths have been disabled." );

#endif

    int highI = (int) pg.size() - 1;

    if( Closed )
        while( highI > 0 && (pg[highI] == pg[0]) )
            --highI;


    while( highI > 0 && (pg[highI] == pg[highI - 1]) )
        --highI;

    if( (Closed && highI < 2) || (!Closed && highI < 1) )
        return false;

    // create a new edge array ...
    TEdge* edges = new TEdge[highI + 1];

    bool IsFlat = true;
    // 1. Basic (first) edge initialization ...
    try
    {
        edges[1].Curr = pg[1];
        RangeTest( pg[0], m_UseFullRange );
        RangeTest( pg[highI], m_UseFullRange );
        InitEdge( &edges[0], &edges[1], &edges[highI], pg[0] );
        InitEdge( &edges[highI], &edges[0], &edges[highI - 1], pg[highI] );

        for( int i = highI - 1; i >= 1; --i )
        {
            RangeTest( pg[i], m_UseFullRange );
            InitEdge( &edges[i], &edges[i + 1], &edges[i - 1], pg[i] );
        }
    }
    catch( ... )
    {
        delete [] edges;
        throw; // range test fails
    }
    TEdge* eStart = &edges[0];

    // 2. Remove duplicate vertices, and (when closed) collinear edges ...
    TEdge* E = eStart, * eLoopStop = eStart;

    for( ; ; )
    {
        // nb: allows matching start and end points when not Closed ...
        if( E->Curr == E->Next->Curr && (Closed || E->Next != eStart) )
        {
            if( E == E->Next )
                break;

            if( E == eStart )
                eStart = E->Next;

            E = RemoveEdge( E );
            eLoopStop = E;
            continue;
        }

        if( E->Prev == E->Next )
            break; // only two vertices
        else if( Closed
                 && SlopesEqual( E->Prev->Curr, E->Curr, E->Next->Curr, m_UseFullRange )
                 && ( !m_PreserveCollinear
                      || !Pt2IsBetweenPt1AndPt3( E->Prev->Curr, E->Curr, E->Next->Curr ) ) )
        {
            // Collinear edges are allowed for open paths but in closed paths
            // the default is to merge adjacent collinear edges into a single edge.
            // However, if the PreserveCollinear property is enabled, only overlapping
            // collinear edges (ie spikes) will be removed from closed paths.
            if( E == eStart )
                eStart = E->Next;

            E = RemoveEdge( E );
            E = E->Prev;
            eLoopStop = E;
            continue;
        }

        E = E->Next;

        if( (E == eLoopStop) || (!Closed && E->Next == eStart) )
            break;
    }

    if( ( !Closed && (E == E->Next) ) || ( Closed && (E->Prev == E->Next) ) )
    {
        delete [] edges;
        return false;
    }

    if( !Closed )
    {
        m_HasOpenPaths = true;
        eStart->Prev->OutIdx = Skip;
    }

    // 3. Do second stage of edge initialization ...
    E = eStart;

    do
    {
        InitEdge2( *E, PolyTyp );
        E = E->Next;

        if( IsFlat && E->Curr.Y != eStart->Curr.Y )
            IsFlat = false;
    } while( E != eStart );

    // 4. Finally, add edge bounds to LocalMinima list ...

    // Totally flat paths must be handled differently when adding them
    // to LocalMinima list to avoid endless loops etc ...
    if( IsFlat )
    {
        if( Closed )
        {
            delete [] edges;
            return false;
        }

        E->Prev->OutIdx = Skip;
        MinimaList::value_type locMin;
        locMin.Y = E->Bot.Y;
        locMin.LeftBound = 0;
        locMin.RightBound = E;
        locMin.RightBound->Side = esRight;
        locMin.RightBound->WindDelta = 0;

        for( ; ; )
        {
            if( E->Bot.X != E->Prev->Top.X )
                ReverseHorizontal( *E );

            if( E->Next->OutIdx == Skip )
                break;

            E->NextInLML = E->Next;
            E = E->Next;
        }

        m_MinimaList.push_back( locMin );
        m_edges.push_back( edges );
        return true;
    }

    m_edges.push_back( edges );
    bool leftBoundIsForward;
    TEdge* EMin = 0;

    // workaround to avoid an endless loop in the while loop below when
    // open paths have matching start and end points ...
    if( E->Prev->Bot == E->Prev->Top )
        E = E->Next;

    for( ; ; )
    {
        E = FindNextLocMin( E );

        if( E == EMin )
            break;
        else if( !EMin )
            EMin = E;

        // E and E.Prev now share a local minima (left aligned if horizontal).
        // Compare their slopes to find which starts which bound ...
        MinimaList::value_type locMin;
        locMin.Y = E->Bot.Y;

        if( E->Dx < E->Prev->Dx )
        {
            locMin.LeftBound = E->Prev;
            locMin.RightBound = E;
            leftBoundIsForward = false; // Q.nextInLML = Q.prev
        }
        else
        {
            locMin.LeftBound = E;
            locMin.RightBound = E->Prev;
            leftBoundIsForward = true; // Q.nextInLML = Q.next
        }

        if( !Closed )
            locMin.LeftBound->WindDelta = 0;
        else if( locMin.LeftBound->Next == locMin.RightBound )
            locMin.LeftBound->WindDelta = -1;
        else
            locMin.LeftBound->WindDelta = 1;

        locMin.RightBound->WindDelta = -locMin.LeftBound->WindDelta;

        E = ProcessBound( locMin.LeftBound, leftBoundIsForward );

        if( E->OutIdx == Skip )
            E = ProcessBound( E, leftBoundIsForward );

        TEdge* E2 = ProcessBound( locMin.RightBound, !leftBoundIsForward );

        if( E2->OutIdx == Skip )
            E2 = ProcessBound( E2, !leftBoundIsForward );

        if( locMin.LeftBound->OutIdx == Skip )
            locMin.LeftBound = 0;
        else if( locMin.RightBound->OutIdx == Skip )
            locMin.RightBound = 0;

        m_MinimaList.push_back( locMin );

        if( !leftBoundIsForward )
            E = E2;
    }

    return true;
}


// ------------------------------------------------------------------------------

bool ClipperBase::AddPaths( const Paths& ppg, PolyType PolyTyp, bool Closed )
{
    bool result = false;

    for( Paths::size_type i = 0; i < ppg.size(); ++i )
        if( AddPath( ppg[i], PolyTyp, Closed ) )
            result = true;


    return result;
}


// ------------------------------------------------------------------------------

void ClipperBase::Clear()
{
    DisposeLocalMinimaList();

    for( EdgeList::size_type i = 0; i < m_edges.size(); ++i )
    {
        TEdge* edges = m_edges[i];
        delete [] edges;
    }

    m_edges.clear();
    m_UseFullRange  = false;
    m_HasOpenPaths  = false;
}


// ------------------------------------------------------------------------------

void ClipperBase::Reset()
{
    m_CurrentLM = m_MinimaList.begin();

    if( m_CurrentLM == m_MinimaList.end() )
        return;                                  // ie nothing to process

    std::sort( m_MinimaList.begin(), m_MinimaList.end(), LocMinSorter() );

    m_Scanbeam = ScanbeamList(); // clears/resets priority_queue

    // reset all edges ...
    for( MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm )
    {
        InsertScanbeam( lm->Y );
        TEdge* e = lm->LeftBound;

        if( e )
        {
            e->Curr = e->Bot;
            e->Side = esLeft;
            e->OutIdx = Unassigned;
        }

        e = lm->RightBound;

        if( e )
        {
            e->Curr = e->Bot;
            e->Side = esRight;
            e->OutIdx = Unassigned;
        }
    }

    m_ActiveEdges = 0;
    m_CurrentLM = m_MinimaList.begin();
}


// ------------------------------------------------------------------------------

void ClipperBase::DisposeLocalMinimaList()
{
    m_MinimaList.clear();
    m_CurrentLM = m_MinimaList.begin();
}


// ------------------------------------------------------------------------------

bool ClipperBase::PopLocalMinima( cInt Y, const LocalMinimum*& locMin )
{
    if( m_CurrentLM == m_MinimaList.end() || (*m_CurrentLM).Y != Y )
        return false;

    locMin = &(*m_CurrentLM);
    ++m_CurrentLM;
    return true;
}


// ------------------------------------------------------------------------------

IntRect ClipperBase::GetBounds()
{
    IntRect result;
    MinimaList::iterator lm = m_MinimaList.begin();

    if( lm == m_MinimaList.end() )
    {
        result.left = result.top = result.right = result.bottom = 0;
        return result;
    }

    result.left = lm->LeftBound->Bot.X;
    result.top = lm->LeftBound->Bot.Y;
    result.right = lm->LeftBound->Bot.X;
    result.bottom = lm->LeftBound->Bot.Y;

    while( lm != m_MinimaList.end() )
    {
        // todo - needs fixing for open paths
        result.bottom = std::max( result.bottom, lm->LeftBound->Bot.Y );
        TEdge* e = lm->LeftBound;

        for( ; ; )
        {
            TEdge* bottomE = e;

            while( e->NextInLML )
            {
                if( e->Bot.X < result.left )
                    result.left = e->Bot.X;

                if( e->Bot.X > result.right )
                    result.right = e->Bot.X;

                e = e->NextInLML;
            }

            result.left = std::min( result.left, e->Bot.X );
            result.right = std::max( result.right, e->Bot.X );
            result.left = std::min( result.left, e->Top.X );
            result.right = std::max( result.right, e->Top.X );
            result.top = std::min( result.top, e->Top.Y );

            if( bottomE == lm->LeftBound )
                e = lm->RightBound;
            else
                break;
        }

        ++lm;
    }

    return result;
}


// ------------------------------------------------------------------------------

void ClipperBase::InsertScanbeam( const cInt Y )
{
    m_Scanbeam.push( Y );
}


// ------------------------------------------------------------------------------

bool ClipperBase::PopScanbeam( cInt& Y )
{
    if( m_Scanbeam.empty() )
        return false;

    Y = m_Scanbeam.top();
    m_Scanbeam.pop();

    while( !m_Scanbeam.empty() && Y == m_Scanbeam.top() )
    {
        m_Scanbeam.pop();
    }                                                                        // Pop duplicates.

    return true;
}


// ------------------------------------------------------------------------------

void ClipperBase::DisposeAllOutRecs()
{
    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
        DisposeOutRec( i );

    m_PolyOuts.clear();
}


// ------------------------------------------------------------------------------

void ClipperBase::DisposeOutRec( PolyOutList::size_type index )
{
    OutRec* outRec = m_PolyOuts[index];

    if( outRec->Pts )
        DisposeOutPts( outRec->Pts );

    delete outRec;
    m_PolyOuts[index] = 0;
}


// ------------------------------------------------------------------------------

void ClipperBase::DeleteFromAEL( TEdge* e )
{
    TEdge* AelPrev  = e->PrevInAEL;
    TEdge* AelNext  = e->NextInAEL;

    if( !AelPrev &&  !AelNext && (e != m_ActiveEdges) )
        return;                                              // already deleted

    if( AelPrev )
        AelPrev->NextInAEL = AelNext;
    else
        m_ActiveEdges = AelNext;

    if( AelNext )
        AelNext->PrevInAEL = AelPrev;

    e->NextInAEL = 0;
    e->PrevInAEL = 0;
}


// ------------------------------------------------------------------------------

OutRec* ClipperBase::CreateOutRec()
{
    OutRec* result = new OutRec;

    result->IsHole  = false;
    result->IsOpen  = false;
    result->FirstLeft = 0;
    result->Pts = 0;
    result->BottomPt = 0;
    result->PolyNd = 0;
    m_PolyOuts.push_back( result );
    result->Idx = (int) m_PolyOuts.size() - 1;
    return result;
}


// ------------------------------------------------------------------------------

void ClipperBase::SwapPositionsInAEL( TEdge* Edge1, TEdge* Edge2 )
{
    // check that one or other edge hasn't already been removed from AEL ...
    if( Edge1->NextInAEL == Edge1->PrevInAEL
        || Edge2->NextInAEL == Edge2->PrevInAEL )
        return;

    if( Edge1->NextInAEL == Edge2 )
    {
        TEdge* Next = Edge2->NextInAEL;

        if( Next )
            Next->PrevInAEL = Edge1;

        TEdge* Prev = Edge1->PrevInAEL;

        if( Prev )
            Prev->NextInAEL = Edge2;

        Edge2->PrevInAEL = Prev;
        Edge2->NextInAEL = Edge1;
        Edge1->PrevInAEL = Edge2;
        Edge1->NextInAEL = Next;
    }
    else if( Edge2->NextInAEL == Edge1 )
    {
        TEdge* Next = Edge1->NextInAEL;

        if( Next )
            Next->PrevInAEL = Edge2;

        TEdge* Prev = Edge2->PrevInAEL;

        if( Prev )
            Prev->NextInAEL = Edge1;

        Edge1->PrevInAEL = Prev;
        Edge1->NextInAEL = Edge2;
        Edge2->PrevInAEL = Edge1;
        Edge2->NextInAEL = Next;
    }
    else
    {
        TEdge* Next = Edge1->NextInAEL;
        TEdge* Prev = Edge1->PrevInAEL;
        Edge1->NextInAEL = Edge2->NextInAEL;

        if( Edge1->NextInAEL )
            Edge1->NextInAEL->PrevInAEL = Edge1;

        Edge1->PrevInAEL = Edge2->PrevInAEL;

        if( Edge1->PrevInAEL )
            Edge1->PrevInAEL->NextInAEL = Edge1;

        Edge2->NextInAEL = Next;

        if( Edge2->NextInAEL )
            Edge2->NextInAEL->PrevInAEL = Edge2;

        Edge2->PrevInAEL = Prev;

        if( Edge2->PrevInAEL )
            Edge2->PrevInAEL->NextInAEL = Edge2;
    }

    if( !Edge1->PrevInAEL )
        m_ActiveEdges = Edge1;
    else if( !Edge2->PrevInAEL )
        m_ActiveEdges = Edge2;
}


// ------------------------------------------------------------------------------

void ClipperBase::UpdateEdgeIntoAEL( TEdge*& e )
{
    if( !e->NextInLML )
        throw clipperException( "UpdateEdgeIntoAEL: invalid call" );

    e->NextInLML->OutIdx = e->OutIdx;
    TEdge* AelPrev  = e->PrevInAEL;
    TEdge* AelNext  = e->NextInAEL;

    if( AelPrev )
        AelPrev->NextInAEL = e->NextInLML;
    else
        m_ActiveEdges = e->NextInLML;

    if( AelNext )
        AelNext->PrevInAEL = e->NextInLML;

    e->NextInLML->Side = e->Side;
    e->NextInLML->WindDelta = e->WindDelta;
    e->NextInLML->WindCnt   = e->WindCnt;
    e->NextInLML->WindCnt2  = e->WindCnt2;
    e = e->NextInLML;
    e->Curr = e->Bot;
    e->PrevInAEL = AelPrev;
    e->NextInAEL = AelNext;

    if( !IsHorizontal( *e ) )
        InsertScanbeam( e->Top.Y );
}


// ------------------------------------------------------------------------------

bool ClipperBase::LocalMinimaPending()
{
    return m_CurrentLM != m_MinimaList.end();
}


// ------------------------------------------------------------------------------
// TClipper methods ...
// ------------------------------------------------------------------------------

Clipper::Clipper( int initOptions ) : ClipperBase()    // constructor
{
    m_ExecuteLocked = false;
    m_UseFullRange  = false;
    m_ReverseOutput = ( (initOptions & ioReverseSolution) != 0 );
    m_StrictSimple  = ( (initOptions & ioStrictlySimple) != 0 );
    m_PreserveCollinear = ( (initOptions & ioPreserveCollinear) != 0 );
    m_HasOpenPaths = false;

    // Avoid uninitialized vars
    m_ClipType = ctIntersection;
    m_SortedEdges = nullptr;
    m_ClipFillType = pftEvenOdd;
    m_SubjFillType = pftEvenOdd;
    m_UsingPolyTree = false;
#ifdef use_xyz
    m_ZFill = 0;
#endif
}


// ------------------------------------------------------------------------------

#ifdef use_xyz
void Clipper::ZFillFunction( ZFillCallback zFillFunc )
{
    m_ZFill = zFillFunc;
}


// ------------------------------------------------------------------------------
#endif

bool Clipper::Execute( ClipType clipType, Paths& solution, PolyFillType fillType )
{
    return Execute( clipType, solution, fillType, fillType );
}


// ------------------------------------------------------------------------------

bool Clipper::Execute( ClipType clipType, PolyTree& polytree, PolyFillType fillType )
{
    return Execute( clipType, polytree, fillType, fillType );
}


// ------------------------------------------------------------------------------

bool Clipper::Execute( ClipType clipType, Paths& solution,
        PolyFillType subjFillType, PolyFillType clipFillType )
{
    if( m_ExecuteLocked )
        return false;

    if( m_HasOpenPaths )
        throw clipperException( "Error: PolyTree struct is needed for open path clipping." );

    m_ExecuteLocked = true;
    solution.resize( 0 );
    m_SubjFillType  = subjFillType;
    m_ClipFillType  = clipFillType;
    m_ClipType = clipType;
    m_UsingPolyTree = false;
    bool succeeded = ExecuteInternal();

    if( succeeded )
        BuildResult( solution );

    DisposeAllOutRecs();
    m_ExecuteLocked = false;
    return succeeded;
}


// ------------------------------------------------------------------------------

bool Clipper::Execute( ClipType clipType, PolyTree& polytree,
        PolyFillType subjFillType, PolyFillType clipFillType )
{
    if( m_ExecuteLocked )
        return false;

    m_ExecuteLocked = true;
    m_SubjFillType  = subjFillType;
    m_ClipFillType  = clipFillType;
    m_ClipType = clipType;
    m_UsingPolyTree = true;
    bool succeeded = ExecuteInternal();

    if( succeeded )
        BuildResult2( polytree );

    DisposeAllOutRecs();
    m_ExecuteLocked = false;
    return succeeded;
}


// ------------------------------------------------------------------------------

void Clipper::FixHoleLinkage( OutRec& outrec )
{
    // skip OutRecs that (a) contain outermost polygons or
    // (b) already have the correct owner/child linkage ...
    if( !outrec.FirstLeft
        || (outrec.IsHole != outrec.FirstLeft->IsHole
            && outrec.FirstLeft->Pts) )
        return;

    OutRec* orfl = outrec.FirstLeft;

    while( orfl && ( (orfl->IsHole == outrec.IsHole) || !orfl->Pts ) )
        orfl = orfl->FirstLeft;

    outrec.FirstLeft = orfl;
}


// ------------------------------------------------------------------------------

bool Clipper::ExecuteInternal()
{
    bool succeeded = true;

    try
    {
        Reset();
        m_Maxima = MaximaList();
        m_SortedEdges = 0;

        succeeded = true;
        cInt botY, topY;

        if( !PopScanbeam( botY ) )
            return false;

        InsertLocalMinimaIntoAEL( botY );

        while( PopScanbeam( topY ) || LocalMinimaPending() )
        {
            ProcessHorizontals();
            ClearGhostJoins();

            if( !ProcessIntersections( topY ) )
            {
                succeeded = false;
                break;
            }

            ProcessEdgesAtTopOfScanbeam( topY );
            botY = topY;
            InsertLocalMinimaIntoAEL( botY );
        }
    }
    catch( ... )
    {
        succeeded = false;
    }

    if( succeeded )
    {
        // fix orientations ...
        for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
        {
            OutRec* outRec = m_PolyOuts[i];

            if( !outRec->Pts || outRec->IsOpen )
                continue;

            if( (outRec->IsHole ^ m_ReverseOutput) == (Area( *outRec ) > 0) )
                ReversePolyPtLinks( outRec->Pts );
        }

        if( !m_Joins.empty() )
            JoinCommonEdges();

        // unfortunately FixupOutPolygon() must be done after JoinCommonEdges()
        for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
        {
            OutRec* outRec = m_PolyOuts[i];

            if( !outRec->Pts )
                continue;

            if( outRec->IsOpen )
                FixupOutPolyline( *outRec );
            else
                FixupOutPolygon( *outRec );
        }

        if( m_StrictSimple )
            DoSimplePolygons();
    }

    ClearJoins();
    ClearGhostJoins();
    return succeeded;
}


// ------------------------------------------------------------------------------

void Clipper::SetWindingCount( TEdge& edge )
{
    TEdge* e = edge.PrevInAEL;

    // find the edge of the same polytype that immediately preceeds 'edge' in AEL
    while( e  && ( (e->PolyTyp != edge.PolyTyp) || (e->WindDelta == 0) ) )
        e = e->PrevInAEL;

    if( !e )
    {
        if( edge.WindDelta == 0 )
        {
            PolyFillType pft = (edge.PolyTyp == ptSubject ? m_SubjFillType : m_ClipFillType);
            edge.WindCnt = (pft == pftNegative ? -1 : 1);
        }
        else
            edge.WindCnt = edge.WindDelta;

        edge.WindCnt2 = 0;
        e = m_ActiveEdges; // ie get ready to calc WindCnt2
    }
    else if( edge.WindDelta == 0 && m_ClipType != ctUnion )
    {
        edge.WindCnt = 1;
        edge.WindCnt2 = e->WindCnt2;
        e = e->NextInAEL; // ie get ready to calc WindCnt2
    }
    else if( IsEvenOddFillType( edge ) )
    {
        // EvenOdd filling ...
        if( edge.WindDelta == 0 )
        {
            // are we inside a subj polygon ...
            bool Inside = true;
            TEdge* e2 = e->PrevInAEL;

            while( e2 )
            {
                if( e2->PolyTyp == e->PolyTyp && e2->WindDelta != 0 )
                    Inside = !Inside;

                e2 = e2->PrevInAEL;
            }

            edge.WindCnt = (Inside ? 0 : 1);
        }
        else
        {
            edge.WindCnt = edge.WindDelta;
        }

        edge.WindCnt2 = e->WindCnt2;
        e = e->NextInAEL; // ie get ready to calc WindCnt2
    }
    else
    {
        // nonZero, Positive or Negative filling ...
        if( e->WindCnt * e->WindDelta < 0 )
        {
            // prev edge is 'decreasing' WindCount (WC) toward zero
            // so we're outside the previous polygon ...
            if( Abs( e->WindCnt ) > 1 )
            {
                // outside prev poly but still inside another.
                // when reversing direction of prev poly use the same WC
                if( e->WindDelta * edge.WindDelta < 0 )
                    edge.WindCnt = e->WindCnt;
                // otherwise continue to 'decrease' WC ...
                else
                    edge.WindCnt = e->WindCnt + edge.WindDelta;
            }
            else
                // now outside all polys of same polytype so set own WC ...
                edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
        }
        else
        {
            // prev edge is 'increasing' WindCount (WC) away from zero
            // so we're inside the previous polygon ...
            if( edge.WindDelta == 0 )
                edge.WindCnt = (e->WindCnt < 0 ? e->WindCnt - 1 : e->WindCnt + 1);
            // if wind direction is reversing prev then use same WC
            else if( e->WindDelta * edge.WindDelta < 0 )
                edge.WindCnt = e->WindCnt;
            // otherwise add to WC ...
            else
                edge.WindCnt = e->WindCnt + edge.WindDelta;
        }

        edge.WindCnt2 = e->WindCnt2;
        e = e->NextInAEL; // ie get ready to calc WindCnt2
    }

    // update WindCnt2 ...
    if( IsEvenOddAltFillType( edge ) )
    {
        // EvenOdd filling ...
        while( e != &edge )
        {
            if( e->WindDelta != 0 )
                edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);

            e = e->NextInAEL;
        }
    }
    else
    {
        // nonZero, Positive or Negative filling ...
        while( e != &edge )
        {
            edge.WindCnt2 += e->WindDelta;
            e = e->NextInAEL;
        }
    }
}


// ------------------------------------------------------------------------------

bool Clipper::IsEvenOddFillType( const TEdge& edge ) const
{
    if( edge.PolyTyp == ptSubject )
        return m_SubjFillType == pftEvenOdd;
    else
        return m_ClipFillType == pftEvenOdd;
}


// ------------------------------------------------------------------------------

bool Clipper::IsEvenOddAltFillType( const TEdge& edge ) const
{
    if( edge.PolyTyp == ptSubject )
        return m_ClipFillType == pftEvenOdd;
    else
        return m_SubjFillType == pftEvenOdd;
}


// ------------------------------------------------------------------------------

bool Clipper::IsContributing( const TEdge& edge ) const
{
    PolyFillType pft, pft2;

    if( edge.PolyTyp == ptSubject )
    {
        pft = m_SubjFillType;
        pft2 = m_ClipFillType;
    }
    else
    {
        pft = m_ClipFillType;
        pft2 = m_SubjFillType;
    }

    switch( pft )
    {
    case pftEvenOdd:

        // return false if a subj line has been flagged as inside a subj polygon
        if( edge.WindDelta == 0 && edge.WindCnt != 1 )
            return false;

        break;

    case pftNonZero:

        if( Abs( edge.WindCnt ) != 1 )
            return false;

        break;

    case pftPositive:

        if( edge.WindCnt != 1 )
            return false;

        break;

    default:    // pftNegative

        if( edge.WindCnt != -1 )
            return false;
    }

    switch( m_ClipType )
    {
    case ctIntersection:

        switch( pft2 )
        {
        case pftEvenOdd:
        case pftNonZero:
            return edge.WindCnt2 != 0;

        case pftPositive:
            return edge.WindCnt2 > 0;

        default:
            return edge.WindCnt2 < 0;
        }

        break;

    case ctUnion:

        switch( pft2 )
        {
        case pftEvenOdd:
        case pftNonZero:
            return edge.WindCnt2 == 0;

        case pftPositive:
            return edge.WindCnt2 <= 0;

        default:
            return edge.WindCnt2 >= 0;
        }

        break;

    case ctDifference:

        if( edge.PolyTyp == ptSubject )
            switch( pft2 )
            {
            case pftEvenOdd:
            case pftNonZero:
                return edge.WindCnt2 == 0;

            case pftPositive:
                return edge.WindCnt2 <= 0;

            default:
                return edge.WindCnt2 >= 0;
            }


        else
            switch( pft2 )
            {
            case pftEvenOdd:
            case pftNonZero:
                return edge.WindCnt2 != 0;

            case pftPositive:
                return edge.WindCnt2 > 0;

            default:
                return edge.WindCnt2 < 0;
            }


        break;

    case ctXor:

        if( edge.WindDelta == 0 ) // XOr always contributing unless open
            switch( pft2 )
            {
            case pftEvenOdd:
            case pftNonZero:
                return edge.WindCnt2 == 0;

            case pftPositive:
                return edge.WindCnt2 <= 0;

            default:
                return edge.WindCnt2 >= 0;
            }


        else
            return true;

        break;

    default:
        return true;
    }
}


// ------------------------------------------------------------------------------

OutPt* Clipper::AddLocalMinPoly( TEdge* e1, TEdge* e2, const IntPoint& Pt )
{
    OutPt* result;
    TEdge* e, * prevE;

    if( IsHorizontal( *e2 ) || ( e1->Dx > e2->Dx ) )
    {
        result = AddOutPt( e1, Pt );
        e2->OutIdx  = e1->OutIdx;
        e1->Side    = esLeft;
        e2->Side    = esRight;
        e = e1;

        if( e->PrevInAEL == e2 )
            prevE = e2->PrevInAEL;
        else
            prevE = e->PrevInAEL;
    }
    else
    {
        result = AddOutPt( e2, Pt );
        e1->OutIdx  = e2->OutIdx;
        e1->Side    = esRight;
        e2->Side    = esLeft;
        e = e2;

        if( e->PrevInAEL == e1 )
            prevE = e1->PrevInAEL;
        else
            prevE = e->PrevInAEL;
    }

    if( prevE && prevE->OutIdx >= 0 && prevE->Top.Y < Pt.Y && e->Top.Y < Pt.Y )
    {
        cInt xPrev = TopX( *prevE, Pt.Y );
        cInt xE = TopX( *e, Pt.Y );

        if( xPrev == xE && (e->WindDelta != 0) && (prevE->WindDelta != 0)
            && SlopesEqual( IntPoint( xPrev, Pt.Y ), prevE->Top, IntPoint( xE, Pt.Y ), e->Top,
                    m_UseFullRange ) )
        {
            OutPt* outPt = AddOutPt( prevE, Pt );
            AddJoin( result, outPt, e->Top );
        }
    }

    return result;
}


// ------------------------------------------------------------------------------

void Clipper::AddLocalMaxPoly( TEdge* e1, TEdge* e2, const IntPoint& Pt )
{
    AddOutPt( e1, Pt );

    if( e2->WindDelta == 0 )
        AddOutPt( e2, Pt );

    if( e1->OutIdx == e2->OutIdx )
    {
        e1->OutIdx  = Unassigned;
        e2->OutIdx  = Unassigned;
    }
    else if( e1->OutIdx < e2->OutIdx )
        AppendPolygon( e1, e2 );
    else
        AppendPolygon( e2, e1 );
}


// ------------------------------------------------------------------------------

void Clipper::AddEdgeToSEL( TEdge* edge )
{
    // SEL pointers in PEdge are reused to build a list of horizontal edges.
    // However, we don't need to worry about order with horizontal edge processing.
    if( !m_SortedEdges )
    {
        m_SortedEdges = edge;
        edge->PrevInSEL = 0;
        edge->NextInSEL = 0;
    }
    else
    {
        edge->NextInSEL = m_SortedEdges;
        edge->PrevInSEL = 0;
        m_SortedEdges->PrevInSEL = edge;
        m_SortedEdges = edge;
    }
}


// ------------------------------------------------------------------------------

bool Clipper::PopEdgeFromSEL( TEdge*& edge )
{
    if( !m_SortedEdges )
        return false;

    edge = m_SortedEdges;
    DeleteFromSEL( m_SortedEdges );
    return true;
}


// ------------------------------------------------------------------------------

void Clipper::CopyAELToSEL()
{
    TEdge* e = m_ActiveEdges;

    m_SortedEdges = e;

    while( e )
    {
        e->PrevInSEL = e->PrevInAEL;
        e->NextInSEL = e->NextInAEL;
        e = e->NextInAEL;
    }
}


// ------------------------------------------------------------------------------

void Clipper::AddJoin( OutPt* op1, OutPt* op2, const IntPoint OffPt )
{
    Join* j = new Join;

    j->OutPt1 = op1;
    j->OutPt2 = op2;
    j->OffPt = OffPt;
    m_Joins.push_back( j );
}


// ------------------------------------------------------------------------------

void Clipper::ClearJoins()
{
    for( JoinList::size_type i = 0; i < m_Joins.size(); i++ )
        delete m_Joins[i];

    m_Joins.resize( 0 );
}


// ------------------------------------------------------------------------------

void Clipper::ClearGhostJoins()
{
    for( JoinList::size_type i = 0; i < m_GhostJoins.size(); i++ )
        delete m_GhostJoins[i];

    m_GhostJoins.resize( 0 );
}


// ------------------------------------------------------------------------------

void Clipper::AddGhostJoin( OutPt* op, const IntPoint OffPt )
{
    Join* j = new Join;

    j->OutPt1 = op;
    j->OutPt2 = 0;
    j->OffPt = OffPt;
    m_GhostJoins.push_back( j );
}


// ------------------------------------------------------------------------------

void Clipper::InsertLocalMinimaIntoAEL( const cInt botY )
{
    const LocalMinimum* lm;

    while( PopLocalMinima( botY, lm ) )
    {
        TEdge* lb   = lm->LeftBound;
        TEdge* rb   = lm->RightBound;

        OutPt* Op1 = 0;

        if( !lb )
        {
            // nb: don't insert LB into either AEL or SEL
            InsertEdgeIntoAEL( rb, 0 );
            SetWindingCount( *rb );

            if( IsContributing( *rb ) )
                Op1 = AddOutPt( rb, rb->Bot );
        }
        else if( !rb )
        {
            InsertEdgeIntoAEL( lb, 0 );
            SetWindingCount( *lb );

            if( IsContributing( *lb ) )
                Op1 = AddOutPt( lb, lb->Bot );

            InsertScanbeam( lb->Top.Y );
        }
        else
        {
            InsertEdgeIntoAEL( lb, 0 );
            InsertEdgeIntoAEL( rb, lb );
            SetWindingCount( *lb );
            rb->WindCnt = lb->WindCnt;
            rb->WindCnt2 = lb->WindCnt2;

            if( IsContributing( *lb ) )
                Op1 = AddLocalMinPoly( lb, rb, lb->Bot );

            InsertScanbeam( lb->Top.Y );
        }

        if( rb )
        {
            if( IsHorizontal( *rb ) )
            {
                AddEdgeToSEL( rb );

                if( rb->NextInLML )
                    InsertScanbeam( rb->NextInLML->Top.Y );
            }
            else
                InsertScanbeam( rb->Top.Y );
        }

        if( !lb || !rb )
            continue;

        // if any output polygons share an edge, they'll need joining later ...
        if( Op1 && IsHorizontal( *rb )
            && m_GhostJoins.size() > 0 && (rb->WindDelta != 0) )
        {
            for( JoinList::size_type i = 0; i < m_GhostJoins.size(); ++i )
            {
                Join* jr = m_GhostJoins[i];

                // if the horizontal Rb and a 'ghost' horizontal overlap, then convert
                // the 'ghost' join to a real join ready for later ...
                if( HorzSegmentsOverlap( jr->OutPt1->Pt.X, jr->OffPt.X, rb->Bot.X, rb->Top.X ) )
                    AddJoin( jr->OutPt1, Op1, jr->OffPt );
            }
        }

        if( lb->OutIdx >= 0 && lb->PrevInAEL
            && lb->PrevInAEL->Curr.X == lb->Bot.X
            && lb->PrevInAEL->OutIdx >= 0
            && SlopesEqual( lb->PrevInAEL->Bot, lb->PrevInAEL->Top, lb->Curr, lb->Top,
                    m_UseFullRange )
            && (lb->WindDelta != 0) && (lb->PrevInAEL->WindDelta != 0) )
        {
            OutPt* Op2 = AddOutPt( lb->PrevInAEL, lb->Bot );
            AddJoin( Op1, Op2, lb->Top );
        }

        if( lb->NextInAEL != rb )
        {
            if( rb->OutIdx >= 0 && rb->PrevInAEL->OutIdx >= 0
                && SlopesEqual( rb->PrevInAEL->Curr, rb->PrevInAEL->Top, rb->Curr, rb->Top,
                        m_UseFullRange )
                && (rb->WindDelta != 0) && (rb->PrevInAEL->WindDelta != 0) )
            {
                OutPt* Op2 = AddOutPt( rb->PrevInAEL, rb->Bot );
                AddJoin( Op1, Op2, rb->Top );
            }

            TEdge* e = lb->NextInAEL;

            if( e )
            {
                while( e != rb )
                {
                    // nb: For calculating winding counts etc, IntersectEdges() assumes
                    // that param1 will be to the Right of param2 ABOVE the intersection ...
                    IntersectEdges( rb, e, lb->Curr ); // order important here
                    e = e->NextInAEL;
                }
            }
        }
    }
}


// ------------------------------------------------------------------------------

void Clipper::DeleteFromSEL( TEdge* e )
{
    TEdge* SelPrev  = e->PrevInSEL;
    TEdge* SelNext  = e->NextInSEL;

    if( !SelPrev &&  !SelNext && (e != m_SortedEdges) )
        return;                                               // already deleted

    if( SelPrev )
        SelPrev->NextInSEL = SelNext;
    else
        m_SortedEdges = SelNext;

    if( SelNext )
        SelNext->PrevInSEL = SelPrev;

    e->NextInSEL = 0;
    e->PrevInSEL = 0;
}


// ------------------------------------------------------------------------------

#ifdef use_xyz
void Clipper::SetZ( IntPoint& pt, TEdge& e1, TEdge& e2 )
{
    if( pt.Z != 0 || !m_ZFill )
        return;
    else if( pt == e1.Bot )
        pt.Z = e1.Bot.Z;
    else if( pt == e1.Top )
        pt.Z = e1.Top.Z;
    else if( pt == e2.Bot )
        pt.Z = e2.Bot.Z;
    else if( pt == e2.Top )
        pt.Z = e2.Top.Z;
    else
        m_ZFill( e1.Bot, e1.Top, e2.Bot, e2.Top, pt );
}


// ------------------------------------------------------------------------------
#endif

void Clipper::IntersectEdges( TEdge* e1, TEdge* e2, IntPoint& Pt )
{
    bool e1Contributing = ( e1->OutIdx >= 0 );
    bool e2Contributing = ( e2->OutIdx >= 0 );

#ifdef use_xyz
    SetZ( Pt, *e1, *e2 );
#endif

#ifdef use_lines

    // if either edge is on an OPEN path ...
    if( e1->WindDelta == 0 || e2->WindDelta == 0 )
    {
        // ignore subject-subject open path intersections UNLESS they
        // are both open paths, AND they are both 'contributing maximas' ...
        if( e1->WindDelta == 0 && e2->WindDelta == 0 )
            return;

        // if intersecting a subj line with a subj poly ...
        else if( e1->PolyTyp == e2->PolyTyp
                 && e1->WindDelta != e2->WindDelta && m_ClipType == ctUnion )
        {
            if( e1->WindDelta == 0 )
            {
                if( e2Contributing )
                {
                    AddOutPt( e1, Pt );

                    if( e1Contributing )
                        e1->OutIdx = Unassigned;
                }
            }
            else
            {
                if( e1Contributing )
                {
                    AddOutPt( e2, Pt );

                    if( e2Contributing )
                        e2->OutIdx = Unassigned;
                }
            }
        }
        else if( e1->PolyTyp != e2->PolyTyp )
        {
            // toggle subj open path OutIdx on/off when Abs(clip.WndCnt) == 1 ...
            if( (e1->WindDelta == 0) && abs( e2->WindCnt ) == 1
                && (m_ClipType != ctUnion || e2->WindCnt2 == 0) )
            {
                AddOutPt( e1, Pt );

                if( e1Contributing )
                    e1->OutIdx = Unassigned;
            }
            else if( (e2->WindDelta == 0) && (abs( e1->WindCnt ) == 1)
                     && (m_ClipType != ctUnion || e1->WindCnt2 == 0) )
            {
                AddOutPt( e2, Pt );

                if( e2Contributing )
                    e2->OutIdx = Unassigned;
            }
        }

        return;
    }

#endif

    // update winding counts...
    // assumes that e1 will be to the Right of e2 ABOVE the intersection
    if( e1->PolyTyp == e2->PolyTyp )
    {
        if( IsEvenOddFillType( *e1 ) )
        {
            int oldE1WindCnt = e1->WindCnt;
            e1->WindCnt = e2->WindCnt;
            e2->WindCnt = oldE1WindCnt;
        }
        else
        {
            if( e1->WindCnt + e2->WindDelta == 0 )
                e1->WindCnt = -e1->WindCnt;
            else
                e1->WindCnt += e2->WindDelta;

            if( e2->WindCnt - e1->WindDelta == 0 )
                e2->WindCnt = -e2->WindCnt;
            else
                e2->WindCnt -= e1->WindDelta;
        }
    }
    else
    {
        if( !IsEvenOddFillType( *e2 ) )
            e1->WindCnt2 += e2->WindDelta;
        else
            e1->WindCnt2 = ( e1->WindCnt2 == 0 ) ? 1 : 0;

        if( !IsEvenOddFillType( *e1 ) )
            e2->WindCnt2 -= e1->WindDelta;
        else
            e2->WindCnt2 = ( e2->WindCnt2 == 0 ) ? 1 : 0;
    }

    PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;

    if( e1->PolyTyp == ptSubject )
    {
        e1FillType  = m_SubjFillType;
        e1FillType2 = m_ClipFillType;
    }
    else
    {
        e1FillType  = m_ClipFillType;
        e1FillType2 = m_SubjFillType;
    }

    if( e2->PolyTyp == ptSubject )
    {
        e2FillType  = m_SubjFillType;
        e2FillType2 = m_ClipFillType;
    }
    else
    {
        e2FillType  = m_ClipFillType;
        e2FillType2 = m_SubjFillType;
    }

    cInt e1Wc, e2Wc;

    switch( e1FillType )
    {
    case pftPositive:
        e1Wc = e1->WindCnt; break;

    case pftNegative:
        e1Wc = -e1->WindCnt; break;

    default:
        e1Wc = Abs( e1->WindCnt );
    }

    switch( e2FillType )
    {
    case pftPositive:
        e2Wc = e2->WindCnt; break;

    case pftNegative:
        e2Wc = -e2->WindCnt; break;

    default:
        e2Wc = Abs( e2->WindCnt );
    }

    if( e1Contributing && e2Contributing )
    {
        if( (e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1)
            || (e1->PolyTyp != e2->PolyTyp && m_ClipType != ctXor) )
        {
            AddLocalMaxPoly( e1, e2, Pt );
        }
        else
        {
            AddOutPt( e1, Pt );
            AddOutPt( e2, Pt );
            SwapSides( *e1, *e2 );
            SwapPolyIndexes( *e1, *e2 );
        }
    }
    else if( e1Contributing )
    {
        if( e2Wc == 0 || e2Wc == 1 )
        {
            AddOutPt( e1, Pt );
            SwapSides( *e1, *e2 );
            SwapPolyIndexes( *e1, *e2 );
        }
    }
    else if( e2Contributing )
    {
        if( e1Wc == 0 || e1Wc == 1 )
        {
            AddOutPt( e2, Pt );
            SwapSides( *e1, *e2 );
            SwapPolyIndexes( *e1, *e2 );
        }
    }
    else if( (e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1) )
    {
        // neither edge is currently contributing ...

        cInt e1Wc2, e2Wc2;

        switch( e1FillType2 )
        {
        case pftPositive:
            e1Wc2 = e1->WindCnt2; break;

        case pftNegative:
            e1Wc2 = -e1->WindCnt2; break;

        default:
            e1Wc2 = Abs( e1->WindCnt2 );
        }

        switch( e2FillType2 )
        {
        case pftPositive:
            e2Wc2 = e2->WindCnt2; break;

        case pftNegative:
            e2Wc2 = -e2->WindCnt2; break;

        default:
            e2Wc2 = Abs( e2->WindCnt2 );
        }

        if( e1->PolyTyp != e2->PolyTyp )
        {
            AddLocalMinPoly( e1, e2, Pt );
        }
        else if( e1Wc == 1 && e2Wc == 1 )
            switch( m_ClipType )
            {
            case ctIntersection:

                if( e1Wc2 > 0 && e2Wc2 > 0 )
                    AddLocalMinPoly( e1, e2, Pt );

                break;

            case ctUnion:

                if( e1Wc2 <= 0 && e2Wc2 <= 0 )
                    AddLocalMinPoly( e1, e2, Pt );

                break;

            case ctDifference:

                if( ( (e1->PolyTyp == ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0) )
                    || ( (e1->PolyTyp == ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0) ) )
                    AddLocalMinPoly( e1, e2, Pt );

                break;

            case ctXor:
                AddLocalMinPoly( e1, e2, Pt );
            }


        else
            SwapSides( *e1, *e2 );
    }
}


// ------------------------------------------------------------------------------

void Clipper::SetHoleState( TEdge* e, OutRec* outrec )
{
    TEdge* e2 = e->PrevInAEL;
    TEdge* eTmp = 0;

    while( e2 )
    {
        if( e2->OutIdx >= 0 && e2->WindDelta != 0 )
        {
            if( !eTmp )
                eTmp = e2;
            else if( eTmp->OutIdx == e2->OutIdx )
                eTmp = 0;
        }

        e2 = e2->PrevInAEL;
    }

    if( !eTmp )
    {
        outrec->FirstLeft = 0;
        outrec->IsHole = false;
    }
    else
    {
        outrec->FirstLeft = m_PolyOuts[eTmp->OutIdx];
        outrec->IsHole = !outrec->FirstLeft->IsHole;
    }
}


// ------------------------------------------------------------------------------

OutRec* GetLowermostRec( OutRec* outRec1, OutRec* outRec2 )
{
    // work out which polygon fragment has the correct hole state ...
    if( !outRec1->BottomPt )
        outRec1->BottomPt = GetBottomPt( outRec1->Pts );

    if( !outRec2->BottomPt )
        outRec2->BottomPt = GetBottomPt( outRec2->Pts );

    OutPt* OutPt1   = outRec1->BottomPt;
    OutPt* OutPt2   = outRec2->BottomPt;

    if( OutPt1->Pt.Y > OutPt2->Pt.Y )
        return outRec1;
    else if( OutPt1->Pt.Y < OutPt2->Pt.Y )
        return outRec2;
    else if( OutPt1->Pt.X < OutPt2->Pt.X )
        return outRec1;
    else if( OutPt1->Pt.X > OutPt2->Pt.X )
        return outRec2;
    else if( OutPt1->Next == OutPt1 )
        return outRec2;
    else if( OutPt2->Next == OutPt2 )
        return outRec1;
    else if( FirstIsBottomPt( OutPt1, OutPt2 ) )
        return outRec1;
    else
        return outRec2;
}


// ------------------------------------------------------------------------------

bool OutRec1RightOfOutRec2( OutRec* outRec1, OutRec* outRec2 )
{
    do
    {
        outRec1 = outRec1->FirstLeft;

        if( outRec1 == outRec2 )
            return true;
    } while( outRec1 );

    return false;
}


// ------------------------------------------------------------------------------

OutRec* Clipper::GetOutRec( int Idx )
{
    OutRec* outrec = m_PolyOuts[Idx];

    while( outrec != m_PolyOuts[outrec->Idx] )
        outrec = m_PolyOuts[outrec->Idx];

    return outrec;
}


// ------------------------------------------------------------------------------

void Clipper::AppendPolygon( TEdge* e1, TEdge* e2 )
{
    // get the start and ends of both output polygons ...
    OutRec* outRec1 = m_PolyOuts[e1->OutIdx];
    OutRec* outRec2 = m_PolyOuts[e2->OutIdx];

    OutRec* holeStateRec;

    if( OutRec1RightOfOutRec2( outRec1, outRec2 ) )
        holeStateRec = outRec2;
    else if( OutRec1RightOfOutRec2( outRec2, outRec1 ) )
        holeStateRec = outRec1;
    else
        holeStateRec = GetLowermostRec( outRec1, outRec2 );

    // get the start and ends of both output polygons and
    // join e2 poly onto e1 poly and delete pointers to e2 ...

    OutPt* p1_lft   = outRec1->Pts;
    OutPt* p1_rt    = p1_lft->Prev;
    OutPt* p2_lft   = outRec2->Pts;
    OutPt* p2_rt    = p2_lft->Prev;

    // join e2 poly onto e1 poly and delete pointers to e2 ...
    if(  e1->Side == esLeft )
    {
        if(  e2->Side == esLeft )
        {
            // z y x a b c
            ReversePolyPtLinks( p2_lft );
            p2_lft->Next = p1_lft;
            p1_lft->Prev = p2_lft;
            p1_rt->Next = p2_rt;
            p2_rt->Prev = p1_rt;
            outRec1->Pts = p2_rt;
        }
        else
        {
            // x y z a b c
            p2_rt->Next = p1_lft;
            p1_lft->Prev = p2_rt;
            p2_lft->Prev = p1_rt;
            p1_rt->Next = p2_lft;
            outRec1->Pts = p2_lft;
        }
    }
    else
    {
        if(  e2->Side == esRight )
        {
            // a b c z y x
            ReversePolyPtLinks( p2_lft );
            p1_rt->Next = p2_rt;
            p2_rt->Prev = p1_rt;
            p2_lft->Next = p1_lft;
            p1_lft->Prev = p2_lft;
        }
        else
        {
            // a b c x y z
            p1_rt->Next = p2_lft;
            p2_lft->Prev = p1_rt;
            p1_lft->Prev = p2_rt;
            p2_rt->Next = p1_lft;
        }
    }

    outRec1->BottomPt = 0;

    if( holeStateRec == outRec2 )
    {
        if( outRec2->FirstLeft != outRec1 )
            outRec1->FirstLeft = outRec2->FirstLeft;

        outRec1->IsHole = outRec2->IsHole;
    }

    outRec2->Pts = 0;
    outRec2->BottomPt = 0;
    outRec2->FirstLeft = outRec1;

    int OKIdx = e1->OutIdx;
    int ObsoleteIdx = e2->OutIdx;

    e1->OutIdx  = Unassigned; // nb: safe because we only get here via AddLocalMaxPoly
    e2->OutIdx  = Unassigned;

    TEdge* e = m_ActiveEdges;

    while( e )
    {
        if( e->OutIdx == ObsoleteIdx )
        {
            e->OutIdx = OKIdx;
            e->Side = e1->Side;
            break;
        }

        e = e->NextInAEL;
    }

    outRec2->Idx = outRec1->Idx;
}


// ------------------------------------------------------------------------------

OutPt* Clipper::AddOutPt( TEdge* e, const IntPoint& pt )
{
    if(  e->OutIdx < 0 )
    {
        OutRec* outRec = CreateOutRec();
        outRec->IsOpen = (e->WindDelta == 0);
        OutPt* newOp = new OutPt;
        outRec->Pts = newOp;
        newOp->Idx  = outRec->Idx;
        newOp->Pt = pt;
        newOp->Next = newOp;
        newOp->Prev = newOp;

        if( !outRec->IsOpen )
            SetHoleState( e, outRec );

        e->OutIdx = outRec->Idx;
        return newOp;
    }
    else
    {
        OutRec* outRec = m_PolyOuts[e->OutIdx];
        // OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
        OutPt* op = outRec->Pts;

        bool ToFront = (e->Side == esLeft);

        if( ToFront && (pt == op->Pt) )
            return op;
        else if( !ToFront && (pt == op->Prev->Pt) )
            return op->Prev;

        OutPt* newOp = new OutPt;
        newOp->Idx  = outRec->Idx;
        newOp->Pt   = pt;
        newOp->Next = op;
        newOp->Prev = op->Prev;
        newOp->Prev->Next = newOp;
        op->Prev = newOp;

        if( ToFront )
            outRec->Pts = newOp;

        return newOp;
    }
}


// ------------------------------------------------------------------------------

OutPt* Clipper::GetLastOutPt( TEdge* e )
{
    OutRec* outRec = m_PolyOuts[e->OutIdx];

    if( e->Side == esLeft )
        return outRec->Pts;
    else
        return outRec->Pts->Prev;
}


// ------------------------------------------------------------------------------

void Clipper::ProcessHorizontals()
{
    TEdge* horzEdge;

    while( PopEdgeFromSEL( horzEdge ) )
        ProcessHorizontal( horzEdge );
}


// ------------------------------------------------------------------------------

inline bool IsMinima( TEdge* e )
{
    return e  && (e->Prev->NextInLML != e) && (e->Next->NextInLML != e);
}


// ------------------------------------------------------------------------------

inline bool IsMaxima( TEdge* e, const cInt Y )
{
    return e && e->Top.Y == Y && !e->NextInLML;
}


// ------------------------------------------------------------------------------

inline bool IsIntermediate( TEdge* e, const cInt Y )
{
    return e->Top.Y == Y && e->NextInLML;
}


// ------------------------------------------------------------------------------

TEdge* GetMaximaPair( TEdge* e )
{
    if( (e->Next->Top == e->Top) && !e->Next->NextInLML )
        return e->Next;
    else if( (e->Prev->Top == e->Top) && !e->Prev->NextInLML )
        return e->Prev;
    else
        return 0;
}


// ------------------------------------------------------------------------------

TEdge* GetMaximaPairEx( TEdge* e )
{
    // as GetMaximaPair() but returns 0 if MaxPair isn't in AEL (unless it's horizontal)
    TEdge* result = GetMaximaPair( e );

    if( result && ( result->OutIdx == Skip
                    || ( result->NextInAEL == result->PrevInAEL && !IsHorizontal( *result ) ) ) )
        return 0;

    return result;
}


// ------------------------------------------------------------------------------

void Clipper::SwapPositionsInSEL( TEdge* Edge1, TEdge* Edge2 )
{
    if( !( Edge1->NextInSEL ) &&  !( Edge1->PrevInSEL ) )
        return;

    if( !( Edge2->NextInSEL ) &&  !( Edge2->PrevInSEL ) )
        return;

    if(  Edge1->NextInSEL == Edge2 )
    {
        TEdge* Next = Edge2->NextInSEL;

        if( Next )
            Next->PrevInSEL = Edge1;

        TEdge* Prev = Edge1->PrevInSEL;

        if( Prev )
            Prev->NextInSEL = Edge2;

        Edge2->PrevInSEL = Prev;
        Edge2->NextInSEL = Edge1;
        Edge1->PrevInSEL = Edge2;
        Edge1->NextInSEL = Next;
    }
    else if(  Edge2->NextInSEL == Edge1 )
    {
        TEdge* Next = Edge1->NextInSEL;

        if( Next )
            Next->PrevInSEL = Edge2;

        TEdge* Prev = Edge2->PrevInSEL;

        if( Prev )
            Prev->NextInSEL = Edge1;

        Edge1->PrevInSEL = Prev;
        Edge1->NextInSEL = Edge2;
        Edge2->PrevInSEL = Edge1;
        Edge2->NextInSEL = Next;
    }
    else
    {
        TEdge* Next = Edge1->NextInSEL;
        TEdge* Prev = Edge1->PrevInSEL;
        Edge1->NextInSEL = Edge2->NextInSEL;

        if( Edge1->NextInSEL )
            Edge1->NextInSEL->PrevInSEL = Edge1;

        Edge1->PrevInSEL = Edge2->PrevInSEL;

        if( Edge1->PrevInSEL )
            Edge1->PrevInSEL->NextInSEL = Edge1;

        Edge2->NextInSEL = Next;

        if( Edge2->NextInSEL )
            Edge2->NextInSEL->PrevInSEL = Edge2;

        Edge2->PrevInSEL = Prev;

        if( Edge2->PrevInSEL )
            Edge2->PrevInSEL->NextInSEL = Edge2;
    }

    if( !Edge1->PrevInSEL )
        m_SortedEdges = Edge1;
    else if( !Edge2->PrevInSEL )
        m_SortedEdges = Edge2;
}


// ------------------------------------------------------------------------------

TEdge* GetNextInAEL( TEdge* e, Direction dir )
{
    return dir == dLeftToRight ? e->NextInAEL : e->PrevInAEL;
}


// ------------------------------------------------------------------------------

void GetHorzDirection( TEdge& HorzEdge, Direction& Dir, cInt& Left, cInt& Right )
{
    if( HorzEdge.Bot.X < HorzEdge.Top.X )
    {
        Left = HorzEdge.Bot.X;
        Right = HorzEdge.Top.X;
        Dir = dLeftToRight;
    }
    else
    {
        Left = HorzEdge.Top.X;
        Right = HorzEdge.Bot.X;
        Dir = dRightToLeft;
    }
}


// ------------------------------------------------------------------------

/*******************************************************************************
* Notes: Horizontal edges (HEs) at scanline intersections (ie at the Top or    *
* Bottom of a scanbeam) are processed as if layered. The order in which HEs    *
* are processed doesn't matter. HEs intersect with other HE Bot.Xs only [#]    *
* (or they could intersect with Top.Xs only, ie EITHER Bot.Xs OR Top.Xs),      *
* and with other non-horizontal edges [*]. Once these intersections are        *
* processed, intermediate HEs then 'promote' the Edge above (NextInLML) into   *
* the AEL. These 'promoted' edges may in turn intersect [%] with other HEs.    *
*******************************************************************************/

void Clipper::ProcessHorizontal( TEdge* horzEdge )
{
    Direction   dir;
    cInt    horzLeft, horzRight;
    bool    IsOpen = (horzEdge->WindDelta == 0);

    GetHorzDirection( *horzEdge, dir, horzLeft, horzRight );

    TEdge* eLastHorz = horzEdge, * eMaxPair = 0;

    while( eLastHorz->NextInLML && IsHorizontal( *eLastHorz->NextInLML ) )
        eLastHorz = eLastHorz->NextInLML;

    if( !eLastHorz->NextInLML )
        eMaxPair = GetMaximaPair( eLastHorz );

    MaximaList::const_iterator maxIt;
    MaximaList::const_reverse_iterator maxRit;

    if( m_Maxima.size() > 0 )
    {
        // get the first maxima in range (X) ...
        if( dir == dLeftToRight )
        {
            maxIt = m_Maxima.begin();

            while( maxIt != m_Maxima.end() && *maxIt <= horzEdge->Bot.X )
                maxIt++;

            if( maxIt != m_Maxima.end() && *maxIt >= eLastHorz->Top.X )
                maxIt = m_Maxima.end();
        }
        else
        {
            maxRit = m_Maxima.rbegin();

            while( maxRit != m_Maxima.rend() && *maxRit > horzEdge->Bot.X )
                maxRit++;

            if( maxRit != m_Maxima.rend() && *maxRit <= eLastHorz->Top.X )
                maxRit = m_Maxima.rend();
        }
    }

    OutPt* op1 = 0;

    for( ; ; ) // loop through consec. horizontal edges
    {
        bool IsLastHorz = (horzEdge == eLastHorz);
        TEdge* e = GetNextInAEL( horzEdge, dir );

        while( e )
        {
            // this code block inserts extra coords into horizontal edges (in output
            // polygons) whereever maxima touch these horizontal edges. This helps
            // 'simplifying' polygons (ie if the Simplify property is set).
            if( m_Maxima.size() > 0 )
            {
                if( dir == dLeftToRight )
                {
                    while( maxIt != m_Maxima.end() && *maxIt < e->Curr.X )
                    {
                        if( horzEdge->OutIdx >= 0 && !IsOpen )
                            AddOutPt( horzEdge, IntPoint( *maxIt, horzEdge->Bot.Y ) );

                        maxIt++;
                    }
                }
                else
                {
                    while( maxRit != m_Maxima.rend() && *maxRit > e->Curr.X )
                    {
                        if( horzEdge->OutIdx >= 0 && !IsOpen )
                            AddOutPt( horzEdge, IntPoint( *maxRit, horzEdge->Bot.Y ) );

                        maxRit++;
                    }
                }
            }

            ;

            if( (dir == dLeftToRight && e->Curr.X > horzRight)
                || (dir == dRightToLeft && e->Curr.X < horzLeft) )
                break;

            // Also break if we've got to the end of an intermediate horizontal edge ...
            // nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
            if( e->Curr.X == horzEdge->Top.X && horzEdge->NextInLML
                && e->Dx < horzEdge->NextInLML->Dx )
                break;

            if( horzEdge->OutIdx >= 0 && !IsOpen ) // note: may be done multiple times
            {
#ifdef use_xyz

                if( dir == dLeftToRight )
                    SetZ( e->Curr, *horzEdge, *e );
                else
                    SetZ( e->Curr, *e, *horzEdge );

#endif
                op1 = AddOutPt( horzEdge, e->Curr );
                TEdge* eNextHorz = m_SortedEdges;

                while( eNextHorz )
                {
                    if( eNextHorz->OutIdx >= 0
                        && HorzSegmentsOverlap( horzEdge->Bot.X,
                                horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X ) )
                    {
                        OutPt* op2 = GetLastOutPt( eNextHorz );
                        AddJoin( op2, op1, eNextHorz->Top );
                    }

                    eNextHorz = eNextHorz->NextInSEL;
                }

                AddGhostJoin( op1, horzEdge->Bot );
            }

            // OK, so far we're still in range of the horizontal Edge  but make sure
            // we're at the last of consec. horizontals when matching with eMaxPair
            if( e == eMaxPair && IsLastHorz )
            {
                if( horzEdge->OutIdx >= 0 )
                    AddLocalMaxPoly( horzEdge, eMaxPair, horzEdge->Top );

                DeleteFromAEL( horzEdge );
                DeleteFromAEL( eMaxPair );
                return;
            }

            if( dir == dLeftToRight )
            {
                IntPoint Pt = IntPoint( e->Curr.X, horzEdge->Curr.Y );
                IntersectEdges( horzEdge, e, Pt );
            }
            else
            {
                IntPoint Pt = IntPoint( e->Curr.X, horzEdge->Curr.Y );
                IntersectEdges( e, horzEdge, Pt );
            }

            TEdge* eNext = GetNextInAEL( e, dir );
            SwapPositionsInAEL( horzEdge, e );
            e = eNext;
        }   // end while(e)

        // Break out of loop if HorzEdge.NextInLML is not also horizontal ...
        if( !horzEdge->NextInLML || !IsHorizontal( *horzEdge->NextInLML ) )
            break;

        UpdateEdgeIntoAEL( horzEdge );

        if( horzEdge->OutIdx >= 0 )
            AddOutPt( horzEdge, horzEdge->Bot );

        GetHorzDirection( *horzEdge, dir, horzLeft, horzRight );
    }   // end for (;;)

    if( horzEdge->OutIdx >= 0 && !op1 )
    {
        op1 = GetLastOutPt( horzEdge );
        TEdge* eNextHorz = m_SortedEdges;

        while( eNextHorz )
        {
            if( eNextHorz->OutIdx >= 0
                && HorzSegmentsOverlap( horzEdge->Bot.X,
                        horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X ) )
            {
                OutPt* op2 = GetLastOutPt( eNextHorz );
                AddJoin( op2, op1, eNextHorz->Top );
            }

            eNextHorz = eNextHorz->NextInSEL;
        }

        AddGhostJoin( op1, horzEdge->Top );
    }

    if( horzEdge->NextInLML )
    {
        if( horzEdge->OutIdx >= 0 )
        {
            op1 = AddOutPt( horzEdge, horzEdge->Top );
            UpdateEdgeIntoAEL( horzEdge );

            if( horzEdge->WindDelta == 0 )
                return;

            // nb: HorzEdge is no longer horizontal here
            TEdge* ePrev = horzEdge->PrevInAEL;
            TEdge* eNext = horzEdge->NextInAEL;

            if( ePrev && ePrev->Curr.X == horzEdge->Bot.X
                && ePrev->Curr.Y == horzEdge->Bot.Y && ePrev->WindDelta != 0
                && ( ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y
                     && SlopesEqual( *horzEdge, *ePrev, m_UseFullRange ) ) )
            {
                OutPt* op2 = AddOutPt( ePrev, horzEdge->Bot );
                AddJoin( op1, op2, horzEdge->Top );
            }
            else if( eNext && eNext->Curr.X == horzEdge->Bot.X
                     && eNext->Curr.Y == horzEdge->Bot.Y && eNext->WindDelta != 0
                     && eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y
                     && SlopesEqual( *horzEdge, *eNext, m_UseFullRange ) )
            {
                OutPt* op2 = AddOutPt( eNext, horzEdge->Bot );
                AddJoin( op1, op2, horzEdge->Top );
            }
        }
        else
            UpdateEdgeIntoAEL( horzEdge );
    }
    else
    {
        if( horzEdge->OutIdx >= 0 )
            AddOutPt( horzEdge, horzEdge->Top );

        DeleteFromAEL( horzEdge );
    }
}


// ------------------------------------------------------------------------------

bool Clipper::ProcessIntersections( const cInt topY )
{
    if( !m_ActiveEdges )
        return true;

    try
    {
        BuildIntersectList( topY );
        size_t IlSize = m_IntersectList.size();

        if( IlSize == 0 )
            return true;

        if( IlSize == 1 || FixupIntersectionOrder() )
            ProcessIntersectList();
        else
            return false;
    }
    catch( ... )
    {
        m_SortedEdges = 0;
        DisposeIntersectNodes();
        throw clipperException( "ProcessIntersections error" );
    }
    m_SortedEdges = 0;
    return true;
}


// ------------------------------------------------------------------------------

void Clipper::DisposeIntersectNodes()
{
    for( size_t i = 0; i < m_IntersectList.size(); ++i )
        delete m_IntersectList[i];

    m_IntersectList.clear();
}


// ------------------------------------------------------------------------------

void Clipper::BuildIntersectList( const cInt topY )
{
    if( !m_ActiveEdges )
        return;

    // prepare for sorting ...
    TEdge* e = m_ActiveEdges;
    m_SortedEdges = e;

    while( e )
    {
        e->PrevInSEL = e->PrevInAEL;
        e->NextInSEL = e->NextInAEL;
        e->Curr.X = TopX( *e, topY );
        e = e->NextInAEL;
    }

    // bubblesort ...
    bool isModified;

    do
    {
        isModified = false;
        e = m_SortedEdges;

        while( e->NextInSEL )
        {
            TEdge* eNext = e->NextInSEL;
            IntPoint Pt;

            if( e->Curr.X > eNext->Curr.X )
            {
                IntersectPoint( *e, *eNext, Pt );

                if( Pt.Y < topY )
                    Pt = IntPoint( TopX( *e, topY ), topY );

                IntersectNode* newNode = new IntersectNode;
                newNode->Edge1  = e;
                newNode->Edge2  = eNext;
                newNode->Pt = Pt;
                m_IntersectList.push_back( newNode );

                SwapPositionsInSEL( e, eNext );
                isModified = true;
            }
            else
                e = eNext;
        }

        if( e->PrevInSEL )
            e->PrevInSEL->NextInSEL = 0;
        else
            break;
    } while( isModified );

    m_SortedEdges = 0; // important
}


// ------------------------------------------------------------------------------


void Clipper::ProcessIntersectList()
{
    for( size_t i = 0; i < m_IntersectList.size(); ++i )
    {
        IntersectNode* iNode = m_IntersectList[i];
        {
            IntersectEdges( iNode->Edge1, iNode->Edge2, iNode->Pt );
            SwapPositionsInAEL( iNode->Edge1, iNode->Edge2 );
        }
        delete iNode;
    }

    m_IntersectList.clear();
}


// ------------------------------------------------------------------------------

bool IntersectListSort( IntersectNode* node1, IntersectNode* node2 )
{
    return node2->Pt.Y < node1->Pt.Y;
}


// ------------------------------------------------------------------------------

inline bool EdgesAdjacent( const IntersectNode& inode )
{
    return (inode.Edge1->NextInSEL == inode.Edge2)
           || (inode.Edge1->PrevInSEL == inode.Edge2);
}


// ------------------------------------------------------------------------------

bool Clipper::FixupIntersectionOrder()
{
    // pre-condition: intersections are sorted Bottom-most first.
    // Now it's crucial that intersections are made only between adjacent edges,
    // so to ensure this the order of intersections may need adjusting ...
    CopyAELToSEL();
    std::sort( m_IntersectList.begin(), m_IntersectList.end(), IntersectListSort );
    size_t cnt = m_IntersectList.size();

    for( size_t i = 0; i < cnt; ++i )
    {
        if( !EdgesAdjacent( *m_IntersectList[i] ) )
        {
            size_t j = i + 1;

            while( j < cnt && !EdgesAdjacent( *m_IntersectList[j] ) )
                j++;

            if( j == cnt )
                return false;

            std::swap( m_IntersectList[i], m_IntersectList[j] );
        }

        SwapPositionsInSEL( m_IntersectList[i]->Edge1, m_IntersectList[i]->Edge2 );
    }

    return true;
}


// ------------------------------------------------------------------------------

void Clipper::DoMaxima( TEdge* e )
{
    TEdge* eMaxPair = GetMaximaPairEx( e );

    if( !eMaxPair )
    {
        if( e->OutIdx >= 0 )
            AddOutPt( e, e->Top );

        DeleteFromAEL( e );
        return;
    }

    TEdge* eNext = e->NextInAEL;

    while( eNext && eNext != eMaxPair )
    {
        IntersectEdges( e, eNext, e->Top );
        SwapPositionsInAEL( e, eNext );
        eNext = e->NextInAEL;
    }

    if( e->OutIdx == Unassigned && eMaxPair->OutIdx == Unassigned )
    {
        DeleteFromAEL( e );
        DeleteFromAEL( eMaxPair );
    }
    else if( e->OutIdx >= 0 && eMaxPair->OutIdx >= 0 )
    {
        if( e->OutIdx >= 0 )
            AddLocalMaxPoly( e, eMaxPair, e->Top );

        DeleteFromAEL( e );
        DeleteFromAEL( eMaxPair );
    }

#ifdef use_lines
    else if( e->WindDelta == 0 )
    {
        if( e->OutIdx >= 0 )
        {
            AddOutPt( e, e->Top );
            e->OutIdx = Unassigned;
        }

        DeleteFromAEL( e );

        if( eMaxPair->OutIdx >= 0 )
        {
            AddOutPt( eMaxPair, e->Top );
            eMaxPair->OutIdx = Unassigned;
        }

        DeleteFromAEL( eMaxPair );
    }
#endif
    else
        throw clipperException( "DoMaxima error" );
}


// ------------------------------------------------------------------------------

void Clipper::ProcessEdgesAtTopOfScanbeam( const cInt topY )
{
    TEdge* e = m_ActiveEdges;

    while( e )
    {
        // 1. process maxima, treating them as if they're 'bent' horizontal edges,
        // but exclude maxima with horizontal edges. nb: e can't be a horizontal.
        bool IsMaximaEdge = IsMaxima( e, topY );

        if( IsMaximaEdge )
        {
            TEdge* eMaxPair = GetMaximaPairEx( e );
            IsMaximaEdge = ( !eMaxPair || !IsHorizontal( *eMaxPair ) );
        }

        if( IsMaximaEdge )
        {
            if( m_StrictSimple )
                m_Maxima.push_back( e->Top.X );

            TEdge* ePrev = e->PrevInAEL;
            DoMaxima( e );

            if( !ePrev )
                e = m_ActiveEdges;
            else
                e = ePrev->NextInAEL;
        }
        else
        {
            // 2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
            if( IsIntermediate( e, topY ) && IsHorizontal( *e->NextInLML ) )
            {
                UpdateEdgeIntoAEL( e );

                if( e->OutIdx >= 0 )
                    AddOutPt( e, e->Bot );

                AddEdgeToSEL( e );
            }
            else
            {
                e->Curr.X = TopX( *e, topY );
                e->Curr.Y = topY;
#ifdef use_xyz
                e->Curr.Z = topY == e->Top.Y ? e->Top.Z : (topY == e->Bot.Y ? e->Bot.Z : 0);
#endif
            }

            // When StrictlySimple and 'e' is being touched by another edge, then
            // make sure both edges have a vertex here ...
            if( m_StrictSimple )
            {
                TEdge* ePrev = e->PrevInAEL;

                if( (e->OutIdx >= 0) && (e->WindDelta != 0) && ePrev && (ePrev->OutIdx >= 0)
                    && (ePrev->Curr.X == e->Curr.X) && (ePrev->WindDelta != 0) )
                {
                    IntPoint pt = e->Curr;
#ifdef use_xyz
                    SetZ( pt, *ePrev, *e );
#endif
                    OutPt* op   = AddOutPt( ePrev, pt );
                    OutPt* op2  = AddOutPt( e, pt );
                    AddJoin( op, op2, pt ); // StrictlySimple (type-3) join
                }
            }

            e = e->NextInAEL;
        }
    }

    // 3. Process horizontals at the Top of the scanbeam ...
    m_Maxima.sort();
    ProcessHorizontals();
    m_Maxima.clear();

    // 4. Promote intermediate vertices ...
    e = m_ActiveEdges;

    while( e )
    {
        if( IsIntermediate( e, topY ) )
        {
            OutPt* op = 0;

            if( e->OutIdx >= 0 )
                op = AddOutPt( e, e->Top );

            UpdateEdgeIntoAEL( e );

            // if output polygons share an edge, they'll need joining later ...
            TEdge* ePrev = e->PrevInAEL;
            TEdge* eNext = e->NextInAEL;

            if( ePrev && ePrev->Curr.X == e->Bot.X
                && ePrev->Curr.Y == e->Bot.Y && op
                && ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y
                && SlopesEqual( e->Curr, e->Top, ePrev->Curr, ePrev->Top, m_UseFullRange )
                && (e->WindDelta != 0) && (ePrev->WindDelta != 0) )
            {
                OutPt* op2 = AddOutPt( ePrev, e->Bot );
                AddJoin( op, op2, e->Top );
            }
            else if( eNext && eNext->Curr.X == e->Bot.X
                     && eNext->Curr.Y == e->Bot.Y && op
                     && eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y
                     && SlopesEqual( e->Curr, e->Top, eNext->Curr, eNext->Top, m_UseFullRange )
                     && (e->WindDelta != 0) && (eNext->WindDelta != 0) )
            {
                OutPt* op2 = AddOutPt( eNext, e->Bot );
                AddJoin( op, op2, e->Top );
            }
        }

        e = e->NextInAEL;
    }
}


// ------------------------------------------------------------------------------

void Clipper::FixupOutPolyline( OutRec& outrec )
{
    OutPt* pp = outrec.Pts;
    OutPt* lastPP = pp->Prev;

    while( pp != lastPP )
    {
        pp = pp->Next;

        if( pp->Pt == pp->Prev->Pt )
        {
            if( pp == lastPP )
                lastPP = pp->Prev;

            OutPt* tmpPP = pp->Prev;
            tmpPP->Next = pp->Next;
            pp->Next->Prev = tmpPP;
            delete pp;
            pp = tmpPP;
        }
    }

    if( pp == pp->Prev )
    {
        DisposeOutPts( pp );
        outrec.Pts = 0;
        return;
    }
}


// ------------------------------------------------------------------------------

void Clipper::FixupOutPolygon( OutRec& outrec )
{
    // FixupOutPolygon() - removes duplicate points and simplifies consecutive
    // parallel edges by removing the middle vertex.
    OutPt* lastOK = 0;

    outrec.BottomPt = 0;
    OutPt* pp = outrec.Pts;
    bool preserveCol = m_PreserveCollinear || m_StrictSimple;

    for( ; ; )
    {
        if( pp->Prev == pp || pp->Prev == pp->Next )
        {
            DisposeOutPts( pp );
            outrec.Pts = 0;
            return;
        }

        // test for duplicate points and collinear edges ...
        if( (pp->Pt == pp->Next->Pt) || (pp->Pt == pp->Prev->Pt)
            || ( SlopesEqual( pp->Prev->Pt, pp->Pt, pp->Next->Pt, m_UseFullRange )
                 && ( !preserveCol
                      || !Pt2IsBetweenPt1AndPt3( pp->Prev->Pt, pp->Pt, pp->Next->Pt ) ) ) )
        {
            lastOK = 0;
            OutPt* tmp = pp;
            pp->Prev->Next  = pp->Next;
            pp->Next->Prev  = pp->Prev;
            pp = pp->Prev;
            delete tmp;
        }
        else if( pp == lastOK )
            break;
        else
        {
            if( !lastOK )
                lastOK = pp;

            pp = pp->Next;
        }
    }

    outrec.Pts = pp;
}


// ------------------------------------------------------------------------------

int PointCount( OutPt* Pts )
{
    if( !Pts )
        return 0;

    int result = 0;
    OutPt* p = Pts;

    do
    {
        result++;
        p = p->Next;
    } while( p != Pts );

    return result;
}


// ------------------------------------------------------------------------------

void Clipper::BuildResult( Paths& polys )
{
    polys.reserve( m_PolyOuts.size() );

    for( PolyOutList::size_type ii = 0; ii < m_PolyOuts.size(); ++ii )
    {
        if( !m_PolyOuts[ii]->Pts )
            continue;

        Path pg;
        OutPt* p = m_PolyOuts[ii]->Pts->Prev;
        int cnt = PointCount( p );

        if( cnt < 2 )
            continue;

        pg.reserve( cnt );

        for( int jj = 0; jj < cnt; ++jj )
        {
            pg.push_back( p->Pt );
            p = p->Prev;
        }

        polys.push_back( pg );
    }
}


// ------------------------------------------------------------------------------

void Clipper::BuildResult2( PolyTree& polytree )
{
    polytree.Clear();
    polytree.AllNodes.reserve( m_PolyOuts.size() );

    // add each output polygon/contour to polytree ...
    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++ )
    {
        OutRec* outRec = m_PolyOuts[i];
        int cnt = PointCount( outRec->Pts );

        if( (outRec->IsOpen && cnt < 2) || (!outRec->IsOpen && cnt < 3) )
            continue;

        FixHoleLinkage( *outRec );
        PolyNode* pn = new PolyNode();
        // nb: polytree takes ownership of all the PolyNodes
        polytree.AllNodes.push_back( pn );
        outRec->PolyNd = pn;
        pn->Parent  = 0;
        pn->Index   = 0;
        pn->Contour.reserve( cnt );
        OutPt* op = outRec->Pts->Prev;

        for( int j = 0; j < cnt; j++ )
        {
            pn->Contour.push_back( op->Pt );
            op = op->Prev;
        }
    }

    // fixup PolyNode links etc ...
    polytree.Childs.reserve( m_PolyOuts.size() );

    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++ )
    {
        OutRec* outRec = m_PolyOuts[i];

        if( !outRec->PolyNd )
            continue;

        if( outRec->IsOpen )
        {
            outRec->PolyNd->m_IsOpen = true;
            polytree.AddChild( *outRec->PolyNd );
        }
        else if( outRec->FirstLeft && outRec->FirstLeft->PolyNd )
            outRec->FirstLeft->PolyNd->AddChild( *outRec->PolyNd );
        else
            polytree.AddChild( *outRec->PolyNd );
    }
}


// ------------------------------------------------------------------------------

void SwapIntersectNodes( IntersectNode& int1, IntersectNode& int2 )
{
    // just swap the contents (because fIntersectNodes is a single-linked-list)
    IntersectNode inode = int1; // gets a copy of Int1

    int1.Edge1  = int2.Edge1;
    int1.Edge2  = int2.Edge2;
    int1.Pt = int2.Pt;
    int2.Edge1  = inode.Edge1;
    int2.Edge2  = inode.Edge2;
    int2.Pt = inode.Pt;
}


// ------------------------------------------------------------------------------

inline bool E2InsertsBeforeE1( TEdge& e1, TEdge& e2 )
{
    if( e2.Curr.X == e1.Curr.X )
    {
        if( e2.Top.Y > e1.Top.Y )
            return e2.Top.X < TopX( e1, e2.Top.Y );
        else
            return e1.Top.X > TopX( e2, e1.Top.Y );
    }
    else
        return e2.Curr.X < e1.Curr.X;
}


// ------------------------------------------------------------------------------

bool GetOverlap( const cInt a1, const cInt a2, const cInt b1, const cInt b2,
        cInt& Left, cInt& Right )
{
    if( a1 < a2 )
    {
        if( b1 < b2 )
        {
            Left = std::max( a1, b1 ); Right = std::min( a2, b2 );
        }
        else
        {
            Left = std::max( a1, b2 ); Right = std::min( a2, b1 );
        }
    }
    else
    {
        if( b1 < b2 )
        {
            Left = std::max( a2, b1 ); Right = std::min( a1, b2 );
        }
        else
        {
            Left = std::max( a2, b2 ); Right = std::min( a1, b1 );
        }
    }

    return Left < Right;
}


// ------------------------------------------------------------------------------

inline void UpdateOutPtIdxs( OutRec& outrec )
{
    OutPt* op = outrec.Pts;

    do
    {
        op->Idx = outrec.Idx;
        op = op->Prev;
    } while( op != outrec.Pts );
}


// ------------------------------------------------------------------------------

void Clipper::InsertEdgeIntoAEL( TEdge* edge, TEdge* startEdge )
{
    if( !m_ActiveEdges )
    {
        edge->PrevInAEL = 0;
        edge->NextInAEL = 0;
        m_ActiveEdges = edge;
    }
    else if( !startEdge && E2InsertsBeforeE1( *m_ActiveEdges, *edge ) )
    {
        edge->PrevInAEL = 0;
        edge->NextInAEL = m_ActiveEdges;
        m_ActiveEdges->PrevInAEL = edge;
        m_ActiveEdges = edge;
    }
    else
    {
        if( !startEdge )
            startEdge = m_ActiveEdges;

        while( startEdge->NextInAEL
               && !E2InsertsBeforeE1( *startEdge->NextInAEL, *edge ) )
            startEdge = startEdge->NextInAEL;

        edge->NextInAEL = startEdge->NextInAEL;

        if( startEdge->NextInAEL )
            startEdge->NextInAEL->PrevInAEL = edge;

        edge->PrevInAEL = startEdge;
        startEdge->NextInAEL = edge;
    }
}


// ----------------------------------------------------------------------

OutPt* DupOutPt( OutPt* outPt, bool InsertAfter )
{
    OutPt* result = new OutPt;

    result->Pt  = outPt->Pt;
    result->Idx = outPt->Idx;

    if( InsertAfter )
    {
        result->Next = outPt->Next;
        result->Prev = outPt;
        outPt->Next->Prev = result;
        outPt->Next = result;
    }
    else
    {
        result->Prev = outPt->Prev;
        result->Next = outPt;
        outPt->Prev->Next = result;
        outPt->Prev = result;
    }

    return result;
}


// ------------------------------------------------------------------------------

bool JoinHorz( OutPt* op1, OutPt* op1b, OutPt* op2, OutPt* op2b,
        const IntPoint Pt, bool DiscardLeft )
{
    Direction Dir1 = (op1->Pt.X > op1b->Pt.X ? dRightToLeft : dLeftToRight);
    Direction Dir2 = (op2->Pt.X > op2b->Pt.X ? dRightToLeft : dLeftToRight);

    if( Dir1 == Dir2 )
        return false;

    // When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
    // want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
    // So, to facilitate this while inserting Op1b and Op2b ...
    // when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
    // otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
    if( Dir1 == dLeftToRight )
    {
        while( op1->Next->Pt.X <= Pt.X
               && op1->Next->Pt.X >= op1->Pt.X && op1->Next->Pt.Y == Pt.Y )
            op1 = op1->Next;

        if( DiscardLeft && (op1->Pt.X != Pt.X) )
            op1 = op1->Next;

        op1b = DupOutPt( op1, !DiscardLeft );

        if( op1b->Pt != Pt )
        {
            op1 = op1b;
            op1->Pt = Pt;
            op1b = DupOutPt( op1, !DiscardLeft );
        }
    }
    else
    {
        while( op1->Next->Pt.X >= Pt.X
               && op1->Next->Pt.X <= op1->Pt.X && op1->Next->Pt.Y == Pt.Y )
            op1 = op1->Next;

        if( !DiscardLeft && (op1->Pt.X != Pt.X) )
            op1 = op1->Next;

        op1b = DupOutPt( op1, DiscardLeft );

        if( op1b->Pt != Pt )
        {
            op1 = op1b;
            op1->Pt = Pt;
            op1b = DupOutPt( op1, DiscardLeft );
        }
    }

    if( Dir2 == dLeftToRight )
    {
        while( op2->Next->Pt.X <= Pt.X
               && op2->Next->Pt.X >= op2->Pt.X && op2->Next->Pt.Y == Pt.Y )
            op2 = op2->Next;

        if( DiscardLeft && (op2->Pt.X != Pt.X) )
            op2 = op2->Next;

        op2b = DupOutPt( op2, !DiscardLeft );

        if( op2b->Pt != Pt )
        {
            op2 = op2b;
            op2->Pt = Pt;
            op2b = DupOutPt( op2, !DiscardLeft );
        }

        ;
    }
    else
    {
        while( op2->Next->Pt.X >= Pt.X
               && op2->Next->Pt.X <= op2->Pt.X && op2->Next->Pt.Y == Pt.Y )
            op2 = op2->Next;

        if( !DiscardLeft && (op2->Pt.X != Pt.X) )
            op2 = op2->Next;

        op2b = DupOutPt( op2, DiscardLeft );

        if( op2b->Pt != Pt )
        {
            op2 = op2b;
            op2->Pt = Pt;
            op2b = DupOutPt( op2, DiscardLeft );
        }

        ;
    }

    ;

    if( (Dir1 == dLeftToRight) == DiscardLeft )
    {
        op1->Prev = op2;
        op2->Next = op1;
        op1b->Next  = op2b;
        op2b->Prev  = op1b;
    }
    else
    {
        op1->Next = op2;
        op2->Prev = op1;
        op1b->Prev  = op2b;
        op2b->Next  = op1b;
    }

    return true;
}


// ------------------------------------------------------------------------------

bool Clipper::JoinPoints( Join* j, OutRec* outRec1, OutRec* outRec2 )
{
    OutPt* op1  = j->OutPt1, * op1b;
    OutPt* op2  = j->OutPt2, * op2b;

    // There are 3 kinds of joins for output polygons ...
    // 1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
    // along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
    // 2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
    // location at the Bottom of the overlapping segment (& Join.OffPt is above).
    // 3. StrictSimple joins where edges touch but are not collinear and where
    // Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
    bool isHorizontal = (j->OutPt1->Pt.Y == j->OffPt.Y);

    if( isHorizontal  && (j->OffPt == j->OutPt1->Pt)
        && (j->OffPt == j->OutPt2->Pt) )
    {
        // Strictly Simple join ...
        if( outRec1 != outRec2 )
            return false;

        op1b = j->OutPt1->Next;

        while( op1b != op1 && (op1b->Pt == j->OffPt) )
            op1b = op1b->Next;

        bool reverse1 = (op1b->Pt.Y > j->OffPt.Y);
        op2b = j->OutPt2->Next;

        while( op2b != op2 && (op2b->Pt == j->OffPt) )
            op2b = op2b->Next;

        bool reverse2 = (op2b->Pt.Y > j->OffPt.Y);

        if( reverse1 == reverse2 )
            return false;

        if( reverse1 )
        {
            op1b = DupOutPt( op1, false );
            op2b = DupOutPt( op2, true );
            op1->Prev = op2;
            op2->Next = op1;
            op1b->Next  = op2b;
            op2b->Prev  = op1b;
            j->OutPt1   = op1;
            j->OutPt2   = op1b;
            return true;
        }
        else
        {
            op1b = DupOutPt( op1, true );
            op2b = DupOutPt( op2, false );
            op1->Next = op2;
            op2->Prev = op1;
            op1b->Prev  = op2b;
            op2b->Next  = op1b;
            j->OutPt1   = op1;
            j->OutPt2   = op1b;
            return true;
        }
    }
    else if( isHorizontal )
    {
        // treat horizontal joins differently to non-horizontal joins since with
        // them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
        // may be anywhere along the horizontal edge.
        op1b = op1;

        while( op1->Prev->Pt.Y == op1->Pt.Y && op1->Prev != op1b && op1->Prev != op2 )
            op1 = op1->Prev;

        while( op1b->Next->Pt.Y == op1b->Pt.Y && op1b->Next != op1 && op1b->Next != op2 )
            op1b = op1b->Next;

        if( op1b->Next == op1 || op1b->Next == op2 )
            return false;                                     // a flat 'polygon'

        op2b = op2;

        while( op2->Prev->Pt.Y == op2->Pt.Y && op2->Prev != op2b && op2->Prev != op1b )
            op2 = op2->Prev;

        while( op2b->Next->Pt.Y == op2b->Pt.Y && op2b->Next != op2 && op2b->Next != op1 )
            op2b = op2b->Next;

        if( op2b->Next == op2 || op2b->Next == op1 )
            return false;                                     // a flat 'polygon'

        cInt Left, Right;

        // Op1 --> Op1b & Op2 --> Op2b are the extremites of the horizontal edges
        if( !GetOverlap( op1->Pt.X, op1b->Pt.X, op2->Pt.X, op2b->Pt.X, Left, Right ) )
            return false;

        // DiscardLeftSide: when overlapping edges are joined, a spike will created
        // which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
        // on the discard Side as either may still be needed for other joins ...
        IntPoint Pt;
        bool DiscardLeftSide;

        if( op1->Pt.X >= Left && op1->Pt.X <= Right )
        {
            Pt = op1->Pt; DiscardLeftSide = (op1->Pt.X > op1b->Pt.X);
        }
        else if( op2->Pt.X >= Left&& op2->Pt.X <= Right )
        {
            Pt = op2->Pt; DiscardLeftSide = (op2->Pt.X > op2b->Pt.X);
        }
        else if( op1b->Pt.X >= Left && op1b->Pt.X <= Right )
        {
            Pt = op1b->Pt; DiscardLeftSide = op1b->Pt.X > op1->Pt.X;
        }
        else
        {
            Pt = op2b->Pt; DiscardLeftSide = (op2b->Pt.X > op2->Pt.X);
        }

        j->OutPt1 = op1; j->OutPt2 = op2;
        return JoinHorz( op1, op1b, op2, op2b, Pt, DiscardLeftSide );
    }
    else
    {
        // nb: For non-horizontal joins ...
        // 1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
        // 2. Jr.OutPt1.Pt > Jr.OffPt.Y

        // make sure the polygons are correctly oriented ...
        op1b = op1->Next;

        while( (op1b->Pt == op1->Pt) && (op1b != op1) )
            op1b = op1b->Next;

        bool Reverse1 = ( (op1b->Pt.Y > op1->Pt.Y)
                          || !SlopesEqual( op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange ) );

        if( Reverse1 )
        {
            op1b = op1->Prev;

            while( (op1b->Pt == op1->Pt) && (op1b != op1) )
                op1b = op1b->Prev;

            if( (op1b->Pt.Y > op1->Pt.Y)
                || !SlopesEqual( op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange ) )
                return false;
        }

        ;
        op2b = op2->Next;

        while( (op2b->Pt == op2->Pt) && (op2b != op2) )
            op2b = op2b->Next;

        bool Reverse2 = ( (op2b->Pt.Y > op2->Pt.Y)
                          || !SlopesEqual( op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange ) );

        if( Reverse2 )
        {
            op2b = op2->Prev;

            while( (op2b->Pt == op2->Pt) && (op2b != op2) )
                op2b = op2b->Prev;

            if( (op2b->Pt.Y > op2->Pt.Y)
                || !SlopesEqual( op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange ) )
                return false;
        }

        if( (op1b == op1) || (op2b == op2) || (op1b == op2b)
            || ( (outRec1 == outRec2) && (Reverse1 == Reverse2) ) )
            return false;

        if( Reverse1 )
        {
            op1b = DupOutPt( op1, false );
            op2b = DupOutPt( op2, true );
            op1->Prev = op2;
            op2->Next = op1;
            op1b->Next  = op2b;
            op2b->Prev  = op1b;
            j->OutPt1   = op1;
            j->OutPt2   = op1b;
            return true;
        }
        else
        {
            op1b = DupOutPt( op1, true );
            op2b = DupOutPt( op2, false );
            op1->Next = op2;
            op2->Prev = op1;
            op1b->Prev  = op2b;
            op2b->Next  = op1b;
            j->OutPt1   = op1;
            j->OutPt2   = op1b;
            return true;
        }
    }
}


// ----------------------------------------------------------------------

static OutRec* ParseFirstLeft( OutRec* FirstLeft )
{
    while( FirstLeft && !FirstLeft->Pts )
        FirstLeft = FirstLeft->FirstLeft;

    return FirstLeft;
}


// ------------------------------------------------------------------------------

void Clipper::FixupFirstLefts1( OutRec* OldOutRec, OutRec* NewOutRec )
{
    // tests if NewOutRec contains the polygon before reassigning FirstLeft
    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
    {
        OutRec* outRec = m_PolyOuts[i];
        OutRec* firstLeft = ParseFirstLeft( outRec->FirstLeft );

        if( outRec->Pts  && firstLeft == OldOutRec )
        {
            if( Poly2ContainsPoly1( outRec->Pts, NewOutRec->Pts ) )
                outRec->FirstLeft = NewOutRec;
        }
    }
}


// ----------------------------------------------------------------------

void Clipper::FixupFirstLefts2( OutRec* InnerOutRec, OutRec* OuterOutRec )
{
    // A polygon has split into two such that one is now the inner of the other.
    // It's possible that these polygons now wrap around other polygons, so check
    // every polygon that's also contained by OuterOutRec's FirstLeft container
    // (including 0) to see if they've become inner to the new inner polygon ...
    OutRec* orfl = OuterOutRec->FirstLeft;

    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
    {
        OutRec* outRec = m_PolyOuts[i];

        if( !outRec->Pts || outRec == OuterOutRec || outRec == InnerOutRec )
            continue;

        OutRec* firstLeft = ParseFirstLeft( outRec->FirstLeft );

        if( firstLeft != orfl && firstLeft != InnerOutRec && firstLeft != OuterOutRec )
            continue;

        if( Poly2ContainsPoly1( outRec->Pts, InnerOutRec->Pts ) )
            outRec->FirstLeft = InnerOutRec;
        else if( Poly2ContainsPoly1( outRec->Pts, OuterOutRec->Pts ) )
            outRec->FirstLeft = OuterOutRec;
        else if( outRec->FirstLeft == InnerOutRec || outRec->FirstLeft == OuterOutRec )
            outRec->FirstLeft = orfl;
    }
}


// ----------------------------------------------------------------------
void Clipper::FixupFirstLefts3( OutRec* OldOutRec, OutRec* NewOutRec )
{
    // reassigns FirstLeft WITHOUT testing if NewOutRec contains the polygon
    for( PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i )
    {
        OutRec* outRec = m_PolyOuts[i];
        OutRec* firstLeft = ParseFirstLeft( outRec->FirstLeft );

        if( outRec->Pts && firstLeft == OldOutRec )
            outRec->FirstLeft = NewOutRec;
    }
}


// ----------------------------------------------------------------------

void Clipper::JoinCommonEdges()
{
    for( JoinList::size_type i = 0; i < m_Joins.size(); i++ )
    {
        Join* join = m_Joins[i];

        OutRec* outRec1 = GetOutRec( join->OutPt1->Idx );
        OutRec* outRec2 = GetOutRec( join->OutPt2->Idx );

        if( !outRec1->Pts || !outRec2->Pts )
            continue;

        if( outRec1->IsOpen || outRec2->IsOpen )
            continue;

        // get the polygon fragment with the correct hole state (FirstLeft)
        // before calling JoinPoints() ...
        OutRec* holeStateRec;

        if( outRec1 == outRec2 )
            holeStateRec = outRec1;
        else if( OutRec1RightOfOutRec2( outRec1, outRec2 ) )
            holeStateRec = outRec2;
        else if( OutRec1RightOfOutRec2( outRec2, outRec1 ) )
            holeStateRec = outRec1;
        else
            holeStateRec = GetLowermostRec( outRec1, outRec2 );

        if( !JoinPoints( join, outRec1, outRec2 ) )
            continue;

        if( outRec1 == outRec2 )
        {
            // instead of joining two polygons, we've just created a new one by
            // splitting one polygon into two.
            outRec1->Pts = join->OutPt1;
            outRec1->BottomPt = 0;
            outRec2 = CreateOutRec();
            outRec2->Pts = join->OutPt2;

            // update all OutRec2.Pts Idx's ...
            UpdateOutPtIdxs( *outRec2 );

            if( Poly2ContainsPoly1( outRec2->Pts, outRec1->Pts ) )
            {
                // outRec1 contains outRec2 ...
                outRec2->IsHole = !outRec1->IsHole;
                outRec2->FirstLeft = outRec1;

                if( m_UsingPolyTree )
                    FixupFirstLefts2( outRec2, outRec1 );

                if( (outRec2->IsHole ^ m_ReverseOutput) == (Area( *outRec2 ) > 0) )
                    ReversePolyPtLinks( outRec2->Pts );
            }
            else if( Poly2ContainsPoly1( outRec1->Pts, outRec2->Pts ) )
            {
                // outRec2 contains outRec1 ...
                outRec2->IsHole = outRec1->IsHole;
                outRec1->IsHole = !outRec2->IsHole;
                outRec2->FirstLeft  = outRec1->FirstLeft;
                outRec1->FirstLeft  = outRec2;

                if( m_UsingPolyTree )
                    FixupFirstLefts2( outRec1, outRec2 );

                if( (outRec1->IsHole ^ m_ReverseOutput) == (Area( *outRec1 ) > 0) )
                    ReversePolyPtLinks( outRec1->Pts );
            }
            else
            {
                // the 2 polygons are completely separate ...
                outRec2->IsHole = outRec1->IsHole;
                outRec2->FirstLeft = outRec1->FirstLeft;

                // fixup FirstLeft pointers that may need reassigning to OutRec2
                if( m_UsingPolyTree )
                    FixupFirstLefts1( outRec1, outRec2 );
            }
        }
        else
        {
            // joined 2 polygons together ...

            outRec2->Pts = 0;
            outRec2->BottomPt = 0;
            outRec2->Idx = outRec1->Idx;

            outRec1->IsHole = holeStateRec->IsHole;

            if( holeStateRec == outRec2 )
                outRec1->FirstLeft = outRec2->FirstLeft;

            outRec2->FirstLeft = outRec1;

            if( m_UsingPolyTree )
                FixupFirstLefts3( outRec2, outRec1 );
        }
    }
}


// ------------------------------------------------------------------------------
// ClipperOffset support functions ...
// ------------------------------------------------------------------------------

DoublePoint GetUnitNormal( const IntPoint& pt1, const IntPoint& pt2 )
{
    if( pt2.X == pt1.X && pt2.Y == pt1.Y )
        return DoublePoint( 0, 0 );

    double Dx   = (double) (pt2.X - pt1.X);
    double dy   = (double) (pt2.Y - pt1.Y);
    double f    = 1 * 1.0 / std::sqrt( Dx * Dx + dy * dy );
    Dx  *= f;
    dy  *= f;
    return DoublePoint( dy, -Dx );
}


// ------------------------------------------------------------------------------
// ClipperOffset class
// ------------------------------------------------------------------------------

ClipperOffset::ClipperOffset( double miterLimit, double arcTolerance )
{
    this->MiterLimit = miterLimit;
    this->ArcTolerance = arcTolerance;
    m_lowest.X = -1;

    //Avoid uninitialized vars:
    MiterFallback = jtSquare;
    m_delta = 1.0;
    m_sinA = 0.0;
    m_sin = 0.0;
    m_cos = 0.0;
    m_miterLim = 1.0;
    m_StepsPerRad = 1.0;
}


// ------------------------------------------------------------------------------

ClipperOffset::~ClipperOffset()
{
    Clear();
}


// ------------------------------------------------------------------------------

void ClipperOffset::Clear()
{
    for( int i = 0; i < m_polyNodes.ChildCount(); ++i )
        delete m_polyNodes.Childs[i];

    m_polyNodes.Childs.clear();
    m_lowest.X = -1;
}


// ------------------------------------------------------------------------------

void ClipperOffset::AddPath( const Path& path, JoinType joinType, EndType endType )
{
    int highI = (int) path.size() - 1;

    if( highI < 0 )
        return;

    PolyNode* newNode = new PolyNode();
    newNode->m_jointype = joinType;
    newNode->m_endtype  = endType;

    // strip duplicate points from path and also get index to the lowest point ...
    if( endType == etClosedLine || endType == etClosedPolygon )
        while( highI > 0 && path[0] == path[highI] )
            highI--;


    newNode->Contour.reserve( highI + 1 );
    newNode->Contour.push_back( path[0] );
    int j = 0, k = 0;

    for( int i = 1; i <= highI; i++ )
        if( newNode->Contour[j] != path[i] )
        {
            j++;
            newNode->Contour.push_back( path[i] );

            if( path[i].Y > newNode->Contour[k].Y
                || (path[i].Y == newNode->Contour[k].Y
                    && path[i].X < newNode->Contour[k].X) )
                k = j;
        }


    if( endType == etClosedPolygon && j < 2 )
    {
        delete newNode;
        return;
    }

    m_polyNodes.AddChild( *newNode );

    // if this path's lowest pt is lower than all the others then update m_lowest
    if( endType != etClosedPolygon )
        return;

    if( m_lowest.X < 0 )
        m_lowest = IntPoint( m_polyNodes.ChildCount() - 1, k );
    else
    {
        IntPoint ip = m_polyNodes.Childs[(int) m_lowest.X]->Contour[(int) m_lowest.Y];

        if( newNode->Contour[k].Y > ip.Y
            || (newNode->Contour[k].Y == ip.Y
                && newNode->Contour[k].X < ip.X) )
            m_lowest = IntPoint( m_polyNodes.ChildCount() - 1, k );
    }
}


// ------------------------------------------------------------------------------

void ClipperOffset::AddPaths( const Paths& paths, JoinType joinType, EndType endType )
{
    for( Paths::size_type i = 0; i < paths.size(); ++i )
        AddPath( paths[i], joinType, endType );
}


// ------------------------------------------------------------------------------

void ClipperOffset::FixOrientations()
{
    // fixup orientations of all closed paths if the orientation of the
    // closed path with the lowermost vertex is wrong ...
    if( m_lowest.X >= 0
        && !Orientation( m_polyNodes.Childs[(int) m_lowest.X]->Contour ) )
    {
        for( int i = 0; i < m_polyNodes.ChildCount(); ++i )
        {
            PolyNode& node = *m_polyNodes.Childs[i];

            if( node.m_endtype == etClosedPolygon
                || ( node.m_endtype == etClosedLine && Orientation( node.Contour ) ) )
                ReversePath( node.Contour );
        }
    }
    else
    {
        for( int i = 0; i < m_polyNodes.ChildCount(); ++i )
        {
            PolyNode& node = *m_polyNodes.Childs[i];

            if( node.m_endtype == etClosedLine && !Orientation( node.Contour ) )
                ReversePath( node.Contour );
        }
    }
}


// ------------------------------------------------------------------------------

void ClipperOffset::Execute( Paths& solution, double delta )
{
    solution.clear();
    FixOrientations();
    DoOffset( delta );

    // now clean up 'corners' ...
    Clipper clpr;
    clpr.AddPaths( m_destPolys, ptSubject, true );

    if( delta > 0 )
    {
        clpr.Execute( ctUnion, solution, pftPositive, pftPositive );
    }
    else
    {
        IntRect r = clpr.GetBounds();
        Path outer( 4 );
        outer[0] = IntPoint( r.left - 10, r.bottom + 10 );
        outer[1] = IntPoint( r.right + 10, r.bottom + 10 );
        outer[2] = IntPoint( r.right + 10, r.top - 10 );
        outer[3] = IntPoint( r.left - 10, r.top - 10 );

        clpr.AddPath( outer, ptSubject, true );
        clpr.ReverseSolution( true );
        clpr.Execute( ctUnion, solution, pftNegative, pftNegative );

        if( solution.size() > 0 )
            solution.erase( solution.begin() );
    }
}


// ------------------------------------------------------------------------------

void ClipperOffset::Execute( PolyTree& solution, double delta )
{
    solution.Clear();
    FixOrientations();
    DoOffset( delta );

    // now clean up 'corners' ...
    Clipper clpr;
    clpr.AddPaths( m_destPolys, ptSubject, true );

    if( delta > 0 )
    {
        clpr.Execute( ctUnion, solution, pftPositive, pftPositive );
    }
    else
    {
        IntRect r = clpr.GetBounds();
        Path outer( 4 );
        outer[0] = IntPoint( r.left - 10, r.bottom + 10 );
        outer[1] = IntPoint( r.right + 10, r.bottom + 10 );
        outer[2] = IntPoint( r.right + 10, r.top - 10 );
        outer[3] = IntPoint( r.left - 10, r.top - 10 );

        clpr.AddPath( outer, ptSubject, true );
        clpr.ReverseSolution( true );
        clpr.Execute( ctUnion, solution, pftNegative, pftNegative );

        // remove the outer PolyNode rectangle ...
        if( solution.ChildCount() == 1 && solution.Childs[0]->ChildCount() > 0 )
        {
            PolyNode* outerNode = solution.Childs[0];
            solution.Childs.reserve( outerNode->ChildCount() );
            solution.Childs[0] = outerNode->Childs[0];
            solution.Childs[0]->Parent = outerNode->Parent;

            for( int i = 1; i < outerNode->ChildCount(); ++i )
                solution.AddChild( *outerNode->Childs[i] );
        }
        else
            solution.Clear();
    }
}


// ------------------------------------------------------------------------------

void ClipperOffset::DoOffset( double delta )
{
    m_destPolys.clear();
    m_delta = delta;

    // if Zero offset, just copy any CLOSED polygons to m_p and return ...
    if( NEAR_ZERO( delta ) )
    {
        m_destPolys.reserve( m_polyNodes.ChildCount() );

        for( int i = 0; i < m_polyNodes.ChildCount(); i++ )
        {
            PolyNode& node = *m_polyNodes.Childs[i];

            if( node.m_endtype == etClosedPolygon )
                m_destPolys.push_back( node.Contour );
        }

        return;
    }

    // see offset_triginometry3.svg in the documentation folder ...
    if( MiterLimit > 2 )
        m_miterLim = 2 / (MiterLimit * MiterLimit);
    else
        m_miterLim = 0.5;

    double y;

    if( ArcTolerance <= 0.0 )
        y = def_arc_tolerance;
    else if( ArcTolerance > std::fabs( delta ) * def_arc_tolerance )
        y = std::fabs( delta ) * def_arc_tolerance;
    else
        y = ArcTolerance;

    // see offset_triginometry2.svg in the documentation folder ...
    double steps = pi / std::acos( 1 - y / std::fabs( delta ) );

    if( steps > std::fabs( delta ) * pi )
        steps = std::fabs( delta ) * pi; // ie excessive precision check

    m_sin = std::sin( two_pi / steps );
    m_cos = std::cos( two_pi / steps );
    m_StepsPerRad = steps / two_pi;

    if( delta < 0.0 )
        m_sin = -m_sin;

    m_destPolys.reserve( m_polyNodes.ChildCount() * 2 );

    for( int i = 0; i < m_polyNodes.ChildCount(); i++ )
    {
        PolyNode& node = *m_polyNodes.Childs[i];
        m_srcPoly = node.Contour;

        int len = (int) m_srcPoly.size();

        if( len == 0 || ( delta <= 0 && (len < 3 || node.m_endtype != etClosedPolygon) ) )
            continue;

        m_destPoly.clear();

        if( len == 1 )
        {
            if( node.m_jointype == jtRound )
            {
                double X = 1.0, Y = 0.0;

                for( cInt j = 1; j <= steps; j++ )
                {
                    m_destPoly.emplace_back( Round( m_srcPoly[0].X + X * delta ),
                                             Round( m_srcPoly[0].Y + Y * delta ) );
                    double X2 = X;
                    X = X * m_cos - m_sin * Y;
                    Y = X2 * m_sin + Y * m_cos;
                }
            }
            else
            {
                double X = -1.0, Y = -1.0;

                for( int j = 0; j < 4; ++j )
                {
                    m_destPoly.emplace_back( Round( m_srcPoly[0].X + X * delta ),
                                             Round( m_srcPoly[0].Y + Y * delta ) );

                    if( X < 0 )
                        X = 1;
                    else if( Y < 0 )
                        Y = 1;
                    else
                        X = -1;
                }
            }

            m_destPolys.push_back( m_destPoly );
            continue;
        }

        // build m_normals ...
        m_normals.clear();
        m_normals.reserve( len );

        for( int j = 0; j < len - 1; ++j )
            m_normals.push_back( GetUnitNormal( m_srcPoly[j], m_srcPoly[j + 1] ) );

        if( node.m_endtype == etClosedLine || node.m_endtype == etClosedPolygon )
            m_normals.push_back( GetUnitNormal( m_srcPoly[len - 1], m_srcPoly[0] ) );
        else
            m_normals.emplace_back( m_normals[len - 2] );

        if( node.m_endtype == etClosedPolygon )
        {
            int k = len - 1;

            for( int j = 0; j < len; ++j )
                OffsetPoint( j, k, node.m_jointype );

            m_destPolys.push_back( m_destPoly );
        }
        else if( node.m_endtype == etClosedLine )
        {
            int k = len - 1;

            for( int j = 0; j < len; ++j )
                OffsetPoint( j, k, node.m_jointype );

            m_destPolys.push_back( m_destPoly );
            m_destPoly.clear();
            // re-build m_normals ...
            DoublePoint n = m_normals[len - 1];

            for( int j = len - 1; j > 0; j-- )
                m_normals[j] = DoublePoint( -m_normals[j - 1].X, -m_normals[j - 1].Y );

            m_normals[0] = DoublePoint( -n.X, -n.Y );
            k = 0;

            for( int j = len - 1; j >= 0; j-- )
                OffsetPoint( j, k, node.m_jointype );

            m_destPolys.push_back( m_destPoly );
        }
        else
        {
            int k = 0;

            for( int j = 1; j < len - 1; ++j )
                OffsetPoint( j, k, node.m_jointype );

            IntPoint pt1;

            if( node.m_endtype == etOpenButt )
            {
                int j = len - 1;
                pt1 = IntPoint( (cInt) Round( m_srcPoly[j].X + m_normals[j].X *
                                delta ), (cInt) Round( m_srcPoly[j].Y + m_normals[j].Y * delta ) );
                m_destPoly.push_back( pt1 );
                pt1 = IntPoint( (cInt) Round( m_srcPoly[j].X - m_normals[j].X *
                                delta ), (cInt) Round( m_srcPoly[j].Y - m_normals[j].Y * delta ) );
                m_destPoly.push_back( pt1 );
            }
            else
            {
                int j = len - 1;
                k = len - 2;
                m_sinA = 0;
                m_normals[j] = DoublePoint( -m_normals[j].X, -m_normals[j].Y );

                if( node.m_endtype == etOpenSquare )
                    DoSquare( j, k );
                else
                    DoRound( j, k );
            }

            // re-build m_normals ...
            for( int j = len - 1; j > 0; j-- )
                m_normals[j] = DoublePoint( -m_normals[j - 1].X, -m_normals[j - 1].Y );

            m_normals[0] = DoublePoint( -m_normals[1].X, -m_normals[1].Y );

            k = len - 1;

            for( int j = k - 1; j > 0; --j )
                OffsetPoint( j, k, node.m_jointype );

            if( node.m_endtype == etOpenButt )
            {
                pt1 = IntPoint( (cInt) Round( m_srcPoly[0].X - m_normals[0].X * delta ),
                        (cInt) Round( m_srcPoly[0].Y - m_normals[0].Y * delta ) );
                m_destPoly.push_back( pt1 );
                pt1 = IntPoint( (cInt) Round( m_srcPoly[0].X + m_normals[0].X * delta ),
                        (cInt) Round( m_srcPoly[0].Y + m_normals[0].Y * delta ) );
                m_destPoly.push_back( pt1 );
            }
            else
            {
                k = 1;
                m_sinA = 0;

                if( node.m_endtype == etOpenSquare )
                    DoSquare( 0, 1 );
                else
                    DoRound( 0, 1 );
            }

            m_destPolys.push_back( m_destPoly );
        }
    }
}


// ------------------------------------------------------------------------------

void ClipperOffset::OffsetPoint( int j, int& k, JoinType jointype )
{
    // cross product ...
    m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);

    if( std::fabs( m_sinA * m_delta ) < 1.0 )
    {
        // dot product ...
        double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y );

        if( cosA > 0 ) // angle => 0 degrees
        {
            m_destPoly.emplace_back( Round( m_srcPoly[j].X + m_normals[k].X * m_delta ),
                                     Round( m_srcPoly[j].Y + m_normals[k].Y * m_delta ) );
            return;
        }

        // else angle => 180 degrees
    }
    else if( m_sinA > 1.0 )
        m_sinA = 1.0;
    else if( m_sinA < -1.0 )
        m_sinA = -1.0;

    if( m_sinA * m_delta < 0 )
    {
        m_destPoly.emplace_back( Round( m_srcPoly[j].X + m_normals[k].X * m_delta ),
                                 Round( m_srcPoly[j].Y + m_normals[k].Y * m_delta ) );
        m_destPoly.push_back( m_srcPoly[j] );
        m_destPoly.emplace_back( Round( m_srcPoly[j].X + m_normals[j].X * m_delta ),
                                 Round( m_srcPoly[j].Y + m_normals[j].Y * m_delta ) );
    }
    else
        switch( jointype )
        {
        case jtMiter:
        {
            double r = 1 + (m_normals[j].X * m_normals[k].X +
                            m_normals[j].Y * m_normals[k].Y);

            if( r >= m_miterLim )
                DoMiter( j, k, r );
            else if( MiterFallback == jtRound )
                DoRound( j, k );
            else
                DoSquare( j, k );

            break;
        }

        case jtSquare:
            DoSquare( j, k ); break;

        case jtRound:
            DoRound( j, k ); break;
        }


    k = j;
}


// ------------------------------------------------------------------------------

void ClipperOffset::DoSquare( int j, int k )
{
    double dx = std::tan( std::atan2( m_sinA,
                    m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y ) / 4 );

    m_destPoly.push_back( IntPoint(
                    Round( m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx) ),
                    Round( m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx) ) ) );
    m_destPoly.push_back( IntPoint(
                    Round( m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx) ),
                    Round( m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx) ) ) );
}


// ------------------------------------------------------------------------------

void ClipperOffset::DoMiter( int j, int k, double r )
{
    double q = m_delta / r;

    m_destPoly.emplace_back( Round( m_srcPoly[j].X + ( m_normals[k].X + m_normals[j].X ) * q ),
                             Round( m_srcPoly[j].Y + ( m_normals[k].Y + m_normals[j].Y ) * q ) );
}


// ------------------------------------------------------------------------------

void ClipperOffset::DoRound( int j, int k )
{
    double a = std::atan2( m_sinA,
            m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y );
    double steps = m_StepsPerRad * std::fabs( a );
    int    takenSteps = std::max((int) std::floor( steps ), 1 );

    double X = m_normals[k].X, Y = m_normals[k].Y, X2;

    for( int i = 0; i < takenSteps; ++i )
    {
        m_destPoly.emplace_back( Round( m_srcPoly[j].X + X * m_delta ),
                                 Round( m_srcPoly[j].Y + Y * m_delta ) );
        X2  = X;
        X   = X * m_cos - m_sin * Y;
        Y   = X2 * m_sin + Y * m_cos;
    }

    // A 10% error on chord length won't make much error difference, and it keeps us
    // from generating geometrically noisy solutions.
    if( steps > takenSteps + 0.1 )
    {
        m_destPoly.emplace_back( Round( m_srcPoly[j].X + X * m_delta ),
                                 Round( m_srcPoly[j].Y + Y * m_delta ) );
    }

    m_destPoly.emplace_back( Round( m_srcPoly[j].X + m_normals[j].X * m_delta ),
                             Round( m_srcPoly[j].Y + m_normals[j].Y * m_delta ) );
}


// ------------------------------------------------------------------------------
// Miscellaneous public functions
// ------------------------------------------------------------------------------

void Clipper::DoSimplePolygons()
{
    PolyOutList::size_type i = 0;

    while( i < m_PolyOuts.size() )
    {
        OutRec* outrec = m_PolyOuts[i++];
        OutPt*  op = outrec->Pts;

        if( !op || outrec->IsOpen )
            continue;

        do  // for each Pt in Polygon until duplicate found do ...
        {
            OutPt* op2 = op->Next;

            while( op2 != outrec->Pts )
            {
                if( (op->Pt == op2->Pt) && op2->Next != op && op2->Prev != op )
                {
                    // split the polygon into two ...
                    OutPt* op3  = op->Prev;
                    OutPt* op4  = op2->Prev;
                    op->Prev = op4;
                    op4->Next = op;
                    op2->Prev = op3;
                    op3->Next = op2;

                    outrec->Pts = op;
                    OutRec* outrec2 = CreateOutRec();
                    outrec2->Pts = op2;
                    UpdateOutPtIdxs( *outrec2 );

                    if( Poly2ContainsPoly1( outrec2->Pts, outrec->Pts ) )
                    {
                        // OutRec2 is contained by OutRec1 ...
                        outrec2->IsHole = !outrec->IsHole;
                        outrec2->FirstLeft = outrec;

                        if( m_UsingPolyTree )
                            FixupFirstLefts2( outrec2, outrec );
                    }
                    else
                        if( Poly2ContainsPoly1( outrec->Pts, outrec2->Pts ) )
                        {
                            // OutRec1 is contained by OutRec2 ...
                            outrec2->IsHole = outrec->IsHole;
                            outrec->IsHole  = !outrec2->IsHole;
                            outrec2->FirstLeft  = outrec->FirstLeft;
                            outrec->FirstLeft   = outrec2;

                            if( m_UsingPolyTree )
                                FixupFirstLefts2( outrec, outrec2 );
                        }
                        else
                        {
                            // the 2 polygons are separate ...
                            outrec2->IsHole = outrec->IsHole;
                            outrec2->FirstLeft = outrec->FirstLeft;

                            if( m_UsingPolyTree )
                                FixupFirstLefts1( outrec, outrec2 );
                        }


                    op2 = op; // ie get ready for the Next iteration
                }

                op2 = op2->Next;
            }

            op = op->Next;
        } while( op != outrec->Pts );
    }
}


// ------------------------------------------------------------------------------

void ReversePath( Path& p )
{
    std::reverse( p.begin(), p.end() );
}


// ------------------------------------------------------------------------------

void ReversePaths( Paths& p )
{
    for( Paths::size_type i = 0; i < p.size(); ++i )
        ReversePath( p[i] );
}


// ------------------------------------------------------------------------------

void SimplifyPolygon( const Path& in_poly, Paths& out_polys, PolyFillType fillType )
{
    Clipper c;

    c.StrictlySimple( true );
    c.AddPath( in_poly, ptSubject, true );
    c.Execute( ctUnion, out_polys, fillType, fillType );
}


// ------------------------------------------------------------------------------

void SimplifyPolygons( const Paths& in_polys, Paths& out_polys, PolyFillType fillType )
{
    Clipper c;

    c.StrictlySimple( true );
    c.AddPaths( in_polys, ptSubject, true );
    c.Execute( ctUnion, out_polys, fillType, fillType );
}


// ------------------------------------------------------------------------------

void SimplifyPolygons( Paths& polys, PolyFillType fillType )
{
    SimplifyPolygons( polys, polys, fillType );
}


// ------------------------------------------------------------------------------

inline double DistanceSqrd( const IntPoint& pt1, const IntPoint& pt2 )
{
    double Dx   = ( (double) pt1.X - pt2.X );
    double dy   = ( (double) pt1.Y - pt2.Y );

    return Dx * Dx + dy * dy;
}


// ------------------------------------------------------------------------------

double DistanceFromLineSqrd( const IntPoint& pt, const IntPoint& ln1, const IntPoint& ln2 )
{
    // The equation of a line in general form (Ax + By + C = 0)
    // given 2 points (x¹,y¹) & (x²,y²) is ...
    // (y¹ - y²)x + (x² - x¹)y + (y² - y¹)x¹ - (x² - x¹)y¹ = 0
    // A = (y¹ - y²); B = (x² - x¹); C = (y² - y¹)x¹ - (x² - x¹)y¹
    // perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
    // see http://en.wikipedia.org/wiki/Perpendicular_distance
    double A = double(ln1.Y - ln2.Y);
    double B = double(ln2.X - ln1.X);
    double C = A * ln1.X + B * ln1.Y;

    C = A * pt.X + B * pt.Y - C;
    return (C * C) / (A * A + B * B);
}


// ---------------------------------------------------------------------------

bool SlopesNearCollinear( const IntPoint& pt1,
        const IntPoint& pt2, const IntPoint& pt3, double distSqrd )
{
    // this function is more accurate when the point that's geometrically
    // between the other 2 points is the one that's tested for distance.
    // ie makes it more likely to pick up 'spikes' ...
    if( Abs( pt1.X - pt2.X ) > Abs( pt1.Y - pt2.Y ) )
    {
        if( (pt1.X > pt2.X) == (pt1.X < pt3.X) )
            return DistanceFromLineSqrd( pt1, pt2, pt3 ) < distSqrd;
        else if( (pt2.X > pt1.X) == (pt2.X < pt3.X) )
            return DistanceFromLineSqrd( pt2, pt1, pt3 ) < distSqrd;
        else
            return DistanceFromLineSqrd( pt3, pt1, pt2 ) < distSqrd;
    }
    else
    {
        if( (pt1.Y > pt2.Y) == (pt1.Y < pt3.Y) )
            return DistanceFromLineSqrd( pt1, pt2, pt3 ) < distSqrd;
        else if( (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y) )
            return DistanceFromLineSqrd( pt2, pt1, pt3 ) < distSqrd;
        else
            return DistanceFromLineSqrd( pt3, pt1, pt2 ) < distSqrd;
    }
}


// ------------------------------------------------------------------------------

bool PointsAreClose( IntPoint pt1, IntPoint pt2, double distSqrd )
{
    double Dx   = (double) pt1.X - pt2.X;
    double dy   = (double) pt1.Y - pt2.Y;

    return (Dx * Dx) + (dy * dy) <= distSqrd;
}


// ------------------------------------------------------------------------------

OutPt* ExcludeOp( OutPt* op )
{
    OutPt* result = op->Prev;

    result->Next = op->Next;
    op->Next->Prev = result;
    result->Idx = 0;
    return result;
}


// ------------------------------------------------------------------------------

void CleanPolygon( const Path& in_poly, Path& out_poly, double distance )
{
    // distance = proximity in units/pixels below which vertices
    // will be stripped. Default ~= sqrt(2).

    size_t size = in_poly.size();

    if( size == 0 )
    {
        out_poly.clear();
        return;
    }

    OutPt* outPts = new OutPt[size];

    for( size_t i = 0; i < size; ++i )
    {
        outPts[i].Pt = in_poly[i];
        outPts[i].Next = &outPts[(i + 1) % size];
        outPts[i].Next->Prev = &outPts[i];
        outPts[i].Idx = 0;
    }

    double distSqrd = distance * distance;
    OutPt* op = &outPts[0];

    while( op->Idx == 0 && op->Next != op->Prev )
    {
        if( PointsAreClose( op->Pt, op->Prev->Pt, distSqrd ) )
        {
            op = ExcludeOp( op );
            size--;
        }
        else if( PointsAreClose( op->Prev->Pt, op->Next->Pt, distSqrd ) )
        {
            ExcludeOp( op->Next );
            op = ExcludeOp( op );
            size -= 2;
        }
        else if( SlopesNearCollinear( op->Prev->Pt, op->Pt, op->Next->Pt, distSqrd ) )
        {
            op = ExcludeOp( op );
            size--;
        }
        else
        {
            op->Idx = 1;
            op = op->Next;
        }
    }

    if( size < 3 )
        size = 0;

    out_poly.resize( size );

    for( size_t i = 0; i < size; ++i )
    {
        out_poly[i] = op->Pt;
        op = op->Next;
    }

    delete [] outPts;
}


// ------------------------------------------------------------------------------

void CleanPolygon( Path& poly, double distance )
{
    CleanPolygon( poly, poly, distance );
}


// ------------------------------------------------------------------------------

void CleanPolygons( const Paths& in_polys, Paths& out_polys, double distance )
{
    out_polys.resize( in_polys.size() );

    for( Paths::size_type i = 0; i < in_polys.size(); ++i )
        CleanPolygon( in_polys[i], out_polys[i], distance );
}


// ------------------------------------------------------------------------------

void CleanPolygons( Paths& polys, double distance )
{
    CleanPolygons( polys, polys, distance );
}


// ------------------------------------------------------------------------------

void Minkowski( const Path& poly, const Path& path,
        Paths& solution, bool isSum, bool isClosed )
{
    int delta = (isClosed ? 1 : 0);
    size_t polyCnt  = poly.size();
    size_t pathCnt  = path.size();
    Paths pp;

    pp.reserve( pathCnt );

    if( isSum )
        for( size_t i = 0; i < pathCnt; ++i )
        {
            Path p;
            p.reserve( polyCnt );

            for( size_t j = 0; j < poly.size(); ++j )
                p.emplace_back( path[i].X + poly[j].X, path[i].Y + poly[j].Y );

            pp.push_back( p );
        }


    else
        for( size_t i = 0; i < pathCnt; ++i )
        {
            Path p;
            p.reserve( polyCnt );

            for( size_t j = 0; j < poly.size(); ++j )
                p.emplace_back( path[i].X - poly[j].X, path[i].Y - poly[j].Y );

            pp.push_back( p );
        }



    solution.clear();
    solution.reserve( (pathCnt + delta) * (polyCnt + 1) );

    for( size_t i = 0; i < pathCnt - 1 + delta; ++i )
        for( size_t j = 0; j < polyCnt; ++j )
        {
            Path quad;
            quad.reserve( 4 );
            quad.push_back( pp[i % pathCnt][j % polyCnt] );
            quad.push_back( pp[(i + 1) % pathCnt][j % polyCnt] );
            quad.push_back( pp[(i + 1) % pathCnt][(j + 1) % polyCnt] );
            quad.push_back( pp[i % pathCnt][(j + 1) % polyCnt] );

            if( !Orientation( quad ) )
                ReversePath( quad );

            solution.push_back( quad );
        }


}


// ------------------------------------------------------------------------------

void MinkowskiSum( const Path& pattern, const Path& path, Paths& solution, bool pathIsClosed )
{
    Minkowski( pattern, path, solution, true, pathIsClosed );
    Clipper c;
    c.AddPaths( solution, ptSubject, true );
    c.Execute( ctUnion, solution, pftNonZero, pftNonZero );
}


// ------------------------------------------------------------------------------

void TranslatePath( const Path& input, Path& output, const IntPoint delta )
{
    // precondition: input != output
    output.resize( input.size() );

    for( size_t i = 0; i < input.size(); ++i )
        output[i] = IntPoint( input[i].X + delta.X, input[i].Y + delta.Y );
}


// ------------------------------------------------------------------------------

void MinkowskiSum( const Path& pattern, const Paths& paths, Paths& solution, bool pathIsClosed )
{
    Clipper c;

    for( size_t i = 0; i < paths.size(); ++i )
    {
        Paths tmp;
        Minkowski( pattern, paths[i], tmp, true, pathIsClosed );
        c.AddPaths( tmp, ptSubject, true );

        if( pathIsClosed )
        {
            Path tmp2;
            TranslatePath( paths[i], tmp2, pattern[0] );
            c.AddPath( tmp2, ptClip, true );
        }
    }

    c.Execute( ctUnion, solution, pftNonZero, pftNonZero );
}


// ------------------------------------------------------------------------------

void MinkowskiDiff( const Path& poly1, const Path& poly2, Paths& solution )
{
    Minkowski( poly1, poly2, solution, false, true );
    Clipper c;
    c.AddPaths( solution, ptSubject, true );
    c.Execute( ctUnion, solution, pftNonZero, pftNonZero );
}


// ------------------------------------------------------------------------------

enum NodeType
{
    ntAny, ntOpen, ntClosed
};

void AddPolyNodeToPaths( const PolyNode& polynode, NodeType nodetype, Paths& paths )
{
    bool match = true;

    if( nodetype == ntClosed )
        match = !polynode.IsOpen();
    else if( nodetype == ntOpen )
        return;

    if( !polynode.Contour.empty() && match )
        paths.push_back( polynode.Contour );

    for( int i = 0; i < polynode.ChildCount(); ++i )
        AddPolyNodeToPaths( *polynode.Childs[i], nodetype, paths );
}


// ------------------------------------------------------------------------------

void PolyTreeToPaths( const PolyTree& polytree, Paths& paths )
{
    paths.resize( 0 );
    paths.reserve( polytree.Total() );
    AddPolyNodeToPaths( polytree, ntAny, paths );
}


// ------------------------------------------------------------------------------

void ClosedPathsFromPolyTree( const PolyTree& polytree, Paths& paths )
{
    paths.resize( 0 );
    paths.reserve( polytree.Total() );
    AddPolyNodeToPaths( polytree, ntClosed, paths );
}


// ------------------------------------------------------------------------------

void OpenPathsFromPolyTree( PolyTree& polytree, Paths& paths )
{
    paths.resize( 0 );
    paths.reserve( polytree.Total() );

    // Open paths are top level only, so ...
    for( int i = 0; i < polytree.ChildCount(); ++i )
        if( polytree.Childs[i]->IsOpen() )
            paths.push_back( polytree.Childs[i]->Contour );


}


// ------------------------------------------------------------------------------

std::ostream& operator <<( std::ostream& s, const IntPoint& p )
{
    s << "(" << p.X << "," << p.Y << ")";
    return s;
}


// ------------------------------------------------------------------------------

std::ostream& operator <<( std::ostream& s, const Path& p )
{
    if( p.empty() )
        return s;

    Path::size_type last = p.size() - 1;

    for( Path::size_type i = 0; i < last; i++ )
        s << "(" << p[i].X << "," << p[i].Y << "), ";

    s << "(" << p[last].X << "," << p[last].Y << ")\n";
    return s;
}


// ------------------------------------------------------------------------------

std::ostream& operator <<( std::ostream& s, const Paths& p )
{
    for( Paths::size_type i = 0; i < p.size(); i++ )
        s << p[i];

    s << "\n";
    return s;
}


// ------------------------------------------------------------------------------
}    // ClipperLib namespace