PaddleX/deploy/ultra-infer/ultra_infer/vision/ocr/ppocr/utils/clipper.cc

/*******************************************************************************
 *                                                                              *
 * 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 <algorithm>
#include <cmath>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <ostream>
#include <stdexcept>
#include <vector>

#include "clipper.h"

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 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, int(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 preceeds 'edge' in AEL
  while (e && ((e->PolyTyp != edge.PolyTyp) || (e->WindDelta == 0)))
    e = e->PrevInAEL;
  if (!e) {
    if (edge.WindDelta == 0) {
      PolyFillType pft =
          (edge.PolyTyp == ptSubject ? m_SubjFillType : m_ClipFillType);
      edge.WindCnt = (pft == pftNegative ? -1 : 1);
    } else
      edge.WindCnt = edge.WindDelta;
    edge.WindCnt2 = 0;
    e = m_ActiveEdges; // ie get ready to calc WindCnt2
  } else if (edge.WindDelta == 0 && m_ClipType != ctUnion) {
    edge.WindCnt = 1;
    edge.WindCnt2 = e->WindCnt2;
    e = e->NextInAEL; // ie get ready to calc WindCnt2
  } else if (IsEvenOddFillType(edge)) {
    // EvenOdd filling ...
    if (edge.WindDelta == 0) {
      // are we inside a subj polygon ...
      bool Inside = true;
      TEdge *e2 = e->PrevInAEL;
      while (e2) {
        if (e2->PolyTyp == e->PolyTyp && e2->WindDelta != 0)
          Inside = !Inside;
        e2 = e2->PrevInAEL;
      }
      edge.WindCnt = (Inside ? 0 : 1);
    } else {
      edge.WindCnt = edge.WindDelta;
    }
    edge.WindCnt2 = e->WindCnt2;
    e = e->NextInAEL; // ie get ready to calc WindCnt2
  } else {
    // nonZero, Positive or Negative filling ...
    if (e->WindCnt * e->WindDelta < 0) {
      // prev edge is 'decreasing' WindCount (WC) toward zero
      // so we're outside the previous polygon ...
      if (Abs(e->WindCnt) > 1) {
        // outside prev poly but still inside another.
        // when reversing direction of prev poly use the same WC
        if (e->WindDelta * edge.WindDelta < 0)
          edge.WindCnt = e->WindCnt;
        // otherwise continue to 'decrease' WC ...
        else
          edge.WindCnt = e->WindCnt + edge.WindDelta;
      } else
        // now outside all polys of same polytype so set own WC ...
        edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
    } else {
      // prev edge is 'increasing' WindCount (WC) away from zero
      // so we're inside the previous polygon ...
      if (edge.WindDelta == 0)
        edge.WindCnt = (e->WindCnt < 0 ? e->WindCnt - 1 : e->WindCnt + 1);
      // if wind direction is reversing prev then use same WC
      else if (e->WindDelta * edge.WindDelta < 0)
        edge.WindCnt = e->WindCnt;
      // otherwise add to WC ...
      else
        edge.WindCnt = e->WindCnt + edge.WindDelta;
    }
    edge.WindCnt2 = e->WindCnt2;
    e = e->NextInAEL; // ie get ready to calc WindCnt2
  }

  // update WindCnt2 ...
  if (IsEvenOddAltFillType(edge)) {
    // EvenOdd filling ...
    while (e != &edge) {
      if (e->WindDelta != 0)
        edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);
      e = e->NextInAEL;
    }
  } else {
    // nonZero, Positive or Negative filling ...
    while (e != &edge) {
      edge.WindCnt2 += e->WindDelta;
      e = e->NextInAEL;
    }
  }
}
//------------------------------------------------------------------------------

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

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

bool Clipper::IsContributing(const TEdge &edge) const {
  PolyFillType pft, pft2;
  if (edge.PolyTyp == ptSubject) {
    pft = m_SubjFillType;
    pft2 = m_ClipFillType;
  } else {
    pft = m_ClipFillType;
    pft2 = m_SubjFillType;
  }

  switch (pft) {
  case pftEvenOdd:
    // return false if a subj line has been flagged as inside a subj polygon
    if (edge.WindDelta == 0 && edge.WindCnt != 1)
      return false;
    break;
  case pftNonZero:
    if (Abs(edge.WindCnt) != 1)
      return false;
    break;
  case pftPositive:
    if (edge.WindCnt != 1)
      return false;
    break;
  default: // pftNegative
    if (edge.WindCnt != -1)
      return false;
  }

  switch (m_ClipType) {
  case ctIntersection:
    switch (pft2) {
    case pftEvenOdd:
    case pftNonZero:
      return (edge.WindCnt2 != 0);
    case pftPositive:
      return (edge.WindCnt2 > 0);
    default:
      return (edge.WindCnt2 < 0);
    }
    break;
  case ctUnion:
    switch (pft2) {
    case pftEvenOdd:
    case pftNonZero:
      return (edge.WindCnt2 == 0);
    case pftPositive:
      return (edge.WindCnt2 <= 0);
    default:
      return (edge.WindCnt2 >= 0);
    }
    break;
  case ctDifference:
    if (edge.PolyTyp == ptSubject)
      switch (pft2) {
      case pftEvenOdd:
      case pftNonZero:
        return (edge.WindCnt2 == 0);
      case pftPositive:
        return (edge.WindCnt2 <= 0);
      default:
        return (edge.WindCnt2 >= 0);
      }
    else
      switch (pft2) {
      case pftEvenOdd:
      case pftNonZero:
        return (edge.WindCnt2 != 0);
      case pftPositive:
        return (edge.WindCnt2 > 0);
      default:
        return (edge.WindCnt2 < 0);
      }
    break;
  case ctXor:
    if (edge.WindDelta == 0) // XOr always contributing unless open
      switch (pft2) {
      case pftEvenOdd:
      case pftNonZero:
        return (edge.WindCnt2 == 0);
      case pftPositive:
        return (edge.WindCnt2 <= 0);
      default:
        return (edge.WindCnt2 >= 0);
      }
    else
      return true;
    break;
  default:
    return true;
  }
}
//------------------------------------------------------------------------------

OutPt *Clipper::AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt) {
  OutPt *result;
  TEdge *e, *prevE;
  if (IsHorizontal(*e2) || (e1->Dx > e2->Dx)) {
    result = AddOutPt(e1, Pt);
    e2->OutIdx = e1->OutIdx;
    e1->Side = esLeft;
    e2->Side = esRight;
    e = e1;
    if (e->PrevInAEL == e2)
      prevE = e2->PrevInAEL;
    else
      prevE = e->PrevInAEL;
  } else {
    result = AddOutPt(e2, Pt);
    e1->OutIdx = e2->OutIdx;
    e1->Side = esRight;
    e2->Side = esLeft;
    e = e2;
    if (e->PrevInAEL == e1)
      prevE = e1->PrevInAEL;
    else
      prevE = e->PrevInAEL;
  }

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

void Clipper::AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt) {
  AddOutPt(e1, Pt);
  if (e2->WindDelta == 0)
    AddOutPt(e2, Pt);
  if (e1->OutIdx == e2->OutIdx) {
    e1->OutIdx = Unassigned;
    e2->OutIdx = Unassigned;
  } else if (e1->OutIdx < e2->OutIdx)
    AppendPolygon(e1, e2);
  else
    AppendPolygon(e2, e1);
}
//------------------------------------------------------------------------------

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

bool Clipper::PopEdgeFromSEL(TEdge *&edge) {
  if (!m_SortedEdges)
    return false;
  edge = m_SortedEdges;
  DeleteFromSEL(m_SortedEdges);
  return true;
}
//------------------------------------------------------------------------------

void Clipper::CopyAELToSEL() {
  TEdge *e = m_ActiveEdges;
  m_SortedEdges = e;
  while (e) {
    e->PrevInSEL = e->PrevInAEL;
    e->NextInSEL = e->NextInAEL;
    e = e->NextInAEL;
  }
}
//------------------------------------------------------------------------------

void Clipper::AddJoin(OutPt *op1, OutPt *op2, const IntPoint OffPt) {
  Join *j = new Join;
  j->OutPt1 = op1;
  j->OutPt2 = op2;
  j->OffPt = OffPt;
  m_Joins.push_back(j);
}
//------------------------------------------------------------------------------

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

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

void Clipper::AddGhostJoin(OutPt *op, const IntPoint OffPt) {
  Join *j = new Join;
  j->OutPt1 = op;
  j->OutPt2 = 0;
  j->OffPt = OffPt;
  m_GhostJoins.push_back(j);
}
//------------------------------------------------------------------------------

void Clipper::InsertLocalMinimaIntoAEL(const cInt botY) {
  const LocalMinimum *lm;
  while (PopLocalMinima(botY, lm)) {
    TEdge *lb = lm->LeftBound;
    TEdge *rb = lm->RightBound;

    OutPt *Op1 = 0;
    if (!lb || !rb) {
      // 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 (x�,y�) & (x�,y�) is ...
  //(y� - y�)x + (x� - x�)y + (y� - y�)x� - (x� - x�)y� = 0
  // A = (y� - y�); B = (x� - x�); C = (y� - y�)x� - (x� - x�)y�
  // perpendicular distance of point (x�,y�) = (Ax� + By� + C)/Sqrt(A� + B�)
  // 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