src/Mod/CAM/libarea/clipper.cpp

// SPDX-License-Identifier: BSL-1.0

/*******************************************************************************
 *                                                                              *
 * 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)
{}
//------------------------------------------------------------------------------

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 Int128&) = default;

    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)
{
    std::memset(e, 0, sizeof(TEdge));
    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;
}
//------------------------------------------------------------------------------

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;
#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 precedes '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) wherever 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 i = 0; i < m_PolyOuts.size(); ++i) {
        if (!m_PolyOuts[i]->Pts) {
            continue;
        }
        Path pg;
        OutPt* p = m_PolyOuts[i]->Pts->Prev;
        int cnt = PointCount(p);
        if (cnt < 2) {
            continue;
        }
        pg.reserve(cnt);
        for (int i = 0; i < cnt; ++i) {
            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;
}
//------------------------------------------------------------------------------

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.push_back(
                        IntPoint(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.push_back(
                        IntPoint(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.push_back(DoublePoint(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.push_back(IntPoint(
                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.push_back(IntPoint(
            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.push_back(IntPoint(
            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 {
                    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.push_back(IntPoint(
        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);
    int steps = std::max((int)Round(m_StepsPerRad * std::fabs(a)), 1);

    double X = m_normals[k].X, Y = m_normals[k].Y, X2;
    for (int i = 0; i < steps; ++i) {
        m_destPoly.push_back(
            IntPoint(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;
    }
    m_destPoly.push_back(IntPoint(
        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.push_back(IntPoint(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.push_back(IntPoint(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;
}
//------------------------------------------------------------------------------

}  // namespace ClipperLib