/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.2.1                                                           *
* Date      :  31 October 2014                                                 *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2014                                         *
*                                                                              *
* 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              *
*                                                                              *
*******************************************************************************/

/* License:
The Clipper Library (including Delphi, C++ & C# source code, other accompanying
code, examples and documentation), hereafter called "the Software", has been 
released under the following license, terms and conditions:

Boost Software License - Version 1.0 - August 17th, 2003
http://www.boost.org/LICENSE_1_0.txt

Permission is hereby granted, free of charge, to any person or organization 
obtaining a copy of the Software covered by this license to use, reproduce, 
display, distribute, execute, and transmit the Software, and to prepare 
derivative works of the Software, and to permit third-parties to whom the 
Software is furnished to do so, all subject to the following:

The copyright notices in the Software and this entire statement, including the 
above license grant, this restriction and the following disclaimer, must be 
included in all copies of the Software, in whole or in part, and all derivative 
works of the Software, unless such copies or derivative works are solely in the 
form of machine-executable object code generated by a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT SHALL 
THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY 
DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING 
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 
THE SOFTWARE.
*/

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

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

namespace ClipperLib {

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

enum Direction { dRightToLeft, dLeftToRight };

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

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

struct TEdge {
  IntPoint Bot;
  IntPoint Curr;
  IntPoint Top;
  IntPoint Delta;
  double Dx;
  PolyType PolyTyp;
  EdgeSide Side;
  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;

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(): Childs(), 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
//------------------------------------------------------------------------------

void Swap(cInt& val1, cInt& val2)
{
  cInt tmp = val1;
  val1 = val2;
  val2 = tmp;
}
//------------------------------------------------------------------------------
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 OutRec &outRec)
{
  OutPt *op = outRec.Pts;
  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 != outRec.Pts);
  return a * 0.5;
}
//------------------------------------------------------------------------------

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;
}
//------------------------------------------------------------------------------

int PointInPolygon (const IntPoint &pt, const Path &path)
{
  //returns 0 if false, +1 if true, -1 if pt ON polygon boundary
  //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 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.Delta.Y, e2.Delta.X) == Int128Mul(e1.Delta.X, e2.Delta.Y);
  else 
#endif
    return e1.Delta.Y * e2.Delta.X == e1.Delta.X * e2.Delta.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.Delta.Y == 0;
}
//------------------------------------------------------------------------------

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)
{
  e.Delta.X = (e.Top.X - e.Bot.X);
  e.Delta.Y = (e.Top.Y - e.Bot.Y);

  if (e.Delta.Y == 0) e.Dx = HORIZONTAL;
  else e.Dx = (double)(e.Delta.X) / e.Delta.Y;
}
//---------------------------------------------------------------------------

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.Delta.X == 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.Delta.X == 0)
  {
    ip.X = Edge2.Bot.X;
    if (IsHorizontal(Edge1))
      ip.Y = Edge1.Bot.Y;
    else
    {
      b1 = Edge1.Bot.Y - (Edge1.Bot.X / Edge1.Dx);
      ip.Y = Round(ip.X / Edge1.Dx + b1);
    }
  } 
  else 
  {
    b1 = Edge1.Bot.X - Edge1.Bot.Y * Edge1.Dx;
    b2 = Edge2.Bot.X - Edge2.Bot.Y * Edge2.Dx;
    double q = (b2-b1) / (Edge1.Dx - Edge2.Dx);
    ip.Y = Round(q);
    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
      ip.X = Round(Edge1.Dx * q + b1);
    else 
      ip.X = Round(Edge2.Dx * q + b2);
  }

  if (ip.Y < Edge1.Top.Y || ip.Y < Edge2.Top.Y) 
  {
    if (Edge1.Top.Y > Edge2.Top.Y)
      ip.Y = Edge1.Top.Y;
    else
      ip.Y = Edge2.Top.Y;
    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
      ip.X = TopX(Edge1, ip.Y);
    else
      ip.X = TopX(Edge2, ip.Y);
  } 
  //finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
  if (ip.Y > Edge1.Curr.Y)
  {
    ip.Y = Edge1.Curr.Y;
    //use the more vertical edge to derive X ...
    if (std::fabs(Edge1.Dx) > std::fabs(Edge2.Dx))
      ip.X = TopX(Edge2, ip.Y); else
      ip.X = TopX(Edge1, ip.Y);
  }
}
//------------------------------------------------------------------------------

void ReversePolyPtLinks(OutPt *pp)
{
  if (!pp) return;
  OutPt *pp1, *pp2;
  pp1 = pp;
  do {
  pp2 = pp1->Next;
  pp1->Next = pp1->Prev;
  pp1->Prev = pp2;
  pp1 = pp2;
  } while( pp1 != pp );
}
//------------------------------------------------------------------------------

void DisposeOutPts(OutPt*& pp)
{
  if (pp == 0) return;
    pp->Prev->Next = 0;
  while( pp )
  {
    OutPt *tmpPp = pp;
    pp = pp->Next;
    delete tmpPp;
  }
}
//------------------------------------------------------------------------------

inline void InitEdge(TEdge* e, TEdge* eNext, TEdge* ePrev, const IntPoint& Pt)
{
  // std::memset(e, 0, sizeof(TEdge));
  *e = 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.]
  Swap(e.Top.X, e.Bot.X);
#ifdef use_xyz  
  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));
  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) Swap(seg1a, seg1b);
  if (seg2a > seg2b) 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 "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 (EStart->OutIdx != Skip)
    {
      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) 
      {
        if (!NextIsForward) Result = Horz->Prev;
      }
      else 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) 
      {
        if (!NextIsForward) Result = Horz->Next;
      }
      else if (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;
    if (E->Prev->Bot.X < E->Prev->Top.X) ReverseHorizontal(*E->Prev);
    MinimaList::value_type locMin;
    locMin.Y = E->Bot.Y;
    locMin.LeftBound = 0;
    locMin.RightBound = E;
    locMin.RightBound->Side = esRight;
    locMin.RightBound->WindDelta = 0;
    while (E->Next->OutIdx != Skip)
    {
      E->NextInLML = E->Next;
      if (E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
      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
    }
    locMin.LeftBound->Side = esLeft;
    locMin.RightBound->Side = esRight;

    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)
  {
    //for each edge array in turn, find the first used edge and 
    //check for and remove any hiddenPts in each edge in the array.
    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());

  //reset all edges ...
  for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
  {
    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;
    }
  }
}
//------------------------------------------------------------------------------

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

void ClipperBase::PopLocalMinima()
{
  if (m_CurrentLM == m_MinimaList.end()) return;
  ++m_CurrentLM;
}
//------------------------------------------------------------------------------

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())
  {
    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;
}

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

Clipper::Clipper(int initOptions) : ClipperBase() //constructor
{
  m_ActiveEdges = 0;
  m_SortedEdges = 0;
  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
}
//------------------------------------------------------------------------------

Clipper::~Clipper() //destructor
{
  Clear();
}
//------------------------------------------------------------------------------

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

void Clipper::Reset()
{
  ClipperBase::Reset();
  m_Scanbeam = ScanbeamList();
  m_ActiveEdges = 0;
  m_SortedEdges = 0;
  for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
    InsertScanbeam(lm->Y);
}
//------------------------------------------------------------------------------

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 need 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();
    if (m_CurrentLM == m_MinimaList.end()) return true;
    cInt botY = PopScanbeam();
    do {
      InsertLocalMinimaIntoAEL(botY);
      ClearGhostJoins();
      ProcessHorizontals(false);
      if (m_Scanbeam.empty()) break;
      cInt topY = PopScanbeam();
      succeeded = ProcessIntersections(topY);
      if (!succeeded) break;
      ProcessEdgesAtTopOfScanbeam(topY);
      botY = topY;
    } while (!m_Scanbeam.empty() || m_CurrentLM != m_MinimaList.end());
  }
  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 && !outRec->IsOpen)
        FixupOutPolygon(*outRec);
    }

    if (m_StrictSimple) DoSimplePolygons();
  }

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

void Clipper::InsertScanbeam(const cInt Y)
{
  //if (!m_Scanbeam.empty() && Y == m_Scanbeam.top()) return;// avoid duplicates.
  m_Scanbeam.push(Y);
}
//------------------------------------------------------------------------------

cInt Clipper::PopScanbeam()
{
  const cInt Y = m_Scanbeam.top();
  m_Scanbeam.pop();
  while (!m_Scanbeam.empty() && Y == m_Scanbeam.top()) { m_Scanbeam.pop(); } // Pop duplicates.
  return Y;
}
//------------------------------------------------------------------------------

void Clipper::DisposeAllOutRecs(){
  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
    DisposeOutRec(i);
  m_PolyOuts.clear();
}
//------------------------------------------------------------------------------

void Clipper::DisposeOutRec(PolyOutList::size_type index)
{
  OutRec *outRec = m_PolyOuts[index];
  if (outRec->Pts) DisposeOutPts(outRec->Pts);
  delete outRec;
  m_PolyOuts[index] = 0;
}
//------------------------------------------------------------------------------

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)
  {
    edge.WindCnt = (edge.WindDelta == 0 ? 1 : 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 &&
      (TopX(*prevE, Pt.Y) == TopX(*e, Pt.Y)) &&
      SlopesEqual(*e, *prevE, m_UseFullRange) &&
      (e->WindDelta != 0) && (prevE->WindDelta != 0))
  {
    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;
  }
}
//------------------------------------------------------------------------------

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)
{
  while (m_CurrentLM != m_MinimaList.end() && (m_CurrentLM->Y == botY))
  {
    TEdge* lb = m_CurrentLM->LeftBound;
    TEdge* rb = m_CurrentLM->RightBound;
    PopLocalMinima();
    OutPt *Op1 = 0;
    if (!lb)
    {
      //nb: don't insert LB into either AEL or SEL
      InsertEdgeIntoAEL(rb, 0);
      SetWindingCount(*rb);
      if (IsContributing(*rb))
        Op1 = AddOutPt(rb, rb->Bot); 
    } 
    else if (!rb)
    {
      InsertEdgeIntoAEL(lb, 0);
      SetWindingCount(*lb);
      if (IsContributing(*lb))
        Op1 = AddOutPt(lb, lb->Bot);
      InsertScanbeam(lb->Top.Y);
    }
    else
    {
      InsertEdgeIntoAEL(lb, 0);
      InsertEdgeIntoAEL(rb, lb);
      SetWindingCount( *lb );
      rb->WindCnt = lb->WindCnt;
      rb->WindCnt2 = lb->WindCnt2;
      if (IsContributing(*lb))
        Op1 = AddLocalMinPoly(lb, rb, lb->Bot);      
      InsertScanbeam(lb->Top.Y);
    }

     if (rb)
     {
       if(IsHorizontal(*rb)) AddEdgeToSEL(rb);
       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, *lb, 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, *rb, 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::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;
}
//------------------------------------------------------------------------------

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)
{
  bool IsHole = false;
  TEdge *e2 = e->PrevInAEL;
  while (e2)
  {
    if (e2->OutIdx >= 0 && e2->WindDelta != 0)
    {
      IsHole = !IsHole;
      if (! outrec->FirstLeft)
        outrec->FirstLeft = m_PolyOuts[e2->OutIdx];
    }
    e2 = e2->PrevInAEL;
  }
  if (IsHole) outrec->IsHole = true;
}
//------------------------------------------------------------------------------

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 Param1RightOfParam2(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 (Param1RightOfParam2(outRec1, outRec2)) 
    holeStateRec = outRec2;
  else if (Param1RightOfParam2(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;

  EdgeSide Side;
  //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;
    }
    Side = esLeft;
  } 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;
    }
    Side = esRight;
  }

  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 = Side;
      break;
    }
    e = e->NextInAEL;
  }

  outRec2->Idx = outRec1->Idx;
}
//------------------------------------------------------------------------------

OutRec* Clipper::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;
}
//------------------------------------------------------------------------------

OutPt* Clipper::AddOutPt(TEdge *e, const IntPoint &pt)
{
  bool ToFront = (e->Side == esLeft);
  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;

    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;
  }
}
//------------------------------------------------------------------------------

void Clipper::ProcessHorizontals(bool IsTopOfScanbeam)
{
  TEdge* horzEdge = m_SortedEdges;
  while(horzEdge)
  {
    DeleteFromSEL(horzEdge);
    ProcessHorizontal(horzEdge, IsTopOfScanbeam);
    horzEdge = m_SortedEdges;
  }
}
//------------------------------------------------------------------------------

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

  if (result && (result->OutIdx == Skip ||
    //result is false if both NextInAEL & PrevInAEL are nil & not horizontal ...
    (result->NextInAEL == result->PrevInAEL && !IsHorizontal(*result))))
      return 0;
  return result;
}
//------------------------------------------------------------------------------

void Clipper::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 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, bool isTopOfScanbeam)
{
  Direction dir;
  cInt horzLeft, horzRight;

  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);

  for (;;)
  {
    bool IsLastHorz = (horzEdge == eLastHorz);
    TEdge* e = GetNextInAEL(horzEdge, dir);
    while(e)
    {
      //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;

      TEdge* eNext = GetNextInAEL(e, dir); //saves eNext for later

      if ((dir == dLeftToRight && e->Curr.X <= horzRight) ||
        (dir == dRightToLeft && e->Curr.X >= horzLeft))
      {
        //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)
          {
            OutPt* op1 = AddOutPt(horzEdge, horzEdge->Top);
            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 = AddOutPt(eNextHorz, eNextHorz->Bot);
                AddJoin(op2, op1, eNextHorz->Top);
              }
              eNextHorz = eNextHorz->NextInSEL;
            }
            AddGhostJoin(op1, horzEdge->Bot);
            AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge->Top);
          }
          DeleteFromAEL(horzEdge);
          DeleteFromAEL(eMaxPair);
          return;
        }
        else 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);
        }
        SwapPositionsInAEL( horzEdge, e );
      }
      else if( (dir == dLeftToRight && e->Curr.X >= horzRight) ||
       (dir == dRightToLeft && e->Curr.X <= horzLeft) ) break;
      e = eNext;
    } //end while

    if (horzEdge->NextInLML && IsHorizontal(*horzEdge->NextInLML))
    {
      UpdateEdgeIntoAEL(horzEdge);
      if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Bot);
      GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);
    } else
      break;
  } //end for (;;)

  if(horzEdge->NextInLML)
  {
    if(horzEdge->OutIdx >= 0)
    {
      OutPt* op1 = AddOutPt( horzEdge, horzEdge->Top);
      if (isTopOfScanbeam) AddGhostJoin(op1, horzEdge->Bot);
      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);
  }
}
//------------------------------------------------------------------------------

void Clipper::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 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);
        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 = GetMaximaPair(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 = GetMaximaPair(e);
      IsMaximaEdge = (!eMaxPair || !IsHorizontal(*eMaxPair));
    }

    if(IsMaximaEdge)
    {
      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;
      }

      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 ...
  ProcessHorizontals(true);

  //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, *ePrev, 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, *eNext, m_UseFullRange) &&
        (e->WindDelta != 0) && (eNext->WindDelta != 0))
      {
        OutPt* op2 = AddOutPt(eNext, e->Bot);
        AddJoin(op, op2, e->Top);
      }
    }
    e = e->NextInAEL;
  }
}
//------------------------------------------------------------------------------

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;

  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) &&
      (!m_PreserveCollinear || 
      !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 a 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];
    if (!outRec->Pts || !outRec->FirstLeft) continue;
    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
    if (firstLeft == OldOutRec)
    {
      if (Poly2ContainsPoly1(outRec->Pts, NewOutRec->Pts))
        outRec->FirstLeft = NewOutRec;
    }
  }
}
//----------------------------------------------------------------------

void Clipper::FixupFirstLefts2(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];
    if (outRec->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;

    //get the polygon fragment with the correct hole state (FirstLeft)
    //before calling JoinPoints() ...
    OutRec *holeStateRec;
    if (outRec1 == outRec2) holeStateRec = outRec1;
    else if (Param1RightOfParam2(outRec1, outRec2)) holeStateRec = outRec2;
    else if (Param1RightOfParam2(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);

      //We now need to check every OutRec.FirstLeft pointer. If it points
      //to OutRec1 it may need to point to OutRec2 instead ...
      if (m_UsingPolyTree)
        for (PolyOutList::size_type j = 0; j < m_PolyOuts.size() - 1; j++)
        {
          OutRec* oRec = m_PolyOuts[j];
          if (!oRec->Pts || ParseFirstLeft(oRec->FirstLeft) != outRec1 ||
            oRec->IsHole == outRec1->IsHole) continue;
          if (Poly2ContainsPoly1(oRec->Pts, join->OutPt2))
            oRec->FirstLeft = outRec2;
        }

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

        //fixup FirstLeft pointers that may need reassigning to 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))
      {
        //outRec1 is contained by outRec2 ...
        outRec2->IsHole = outRec1->IsHole;
        outRec1->IsHole = !outRec2->IsHole;
        outRec2->FirstLeft = outRec1->FirstLeft;
        outRec1->FirstLeft = outRec2;

        //fixup FirstLeft pointers that may need reassigning to OutRec1
        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;

      //fixup FirstLeft pointers that may need reassigning to OutRec1
      if (m_UsingPolyTree) FixupFirstLefts2(outRec2, outRec1);
    }
  }
}

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

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

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

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

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

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

void ClipperOffset::Clear()
{
  for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
    delete m_polyNodes.Childs[i];
  m_polyNodes.Childs.clear();
  m_lowest.X = -1;
}
//------------------------------------------------------------------------------

void ClipperOffset::AddPath(const Path& path, JoinType joinType, EndType endType)
{
  int highI = (int)path.size() - 1;
  if (highI < 0) return;
  PolyNode* newNode = new PolyNode();
  newNode->m_jointype = joinType;
  newNode->m_endtype = endType;

  //strip duplicate points from path and also get index to the lowest point ...
  if (endType == etClosedLine || endType == etClosedPolygon)
    while (highI > 0 && path[0] == path[highI]) highI--;
  newNode->Contour.reserve(highI + 1);
  newNode->Contour.push_back(path[0]);
  int j = 0, k = 0;
  for (int i = 1; i <= highI; i++)
    if (newNode->Contour[j] != path[i])
    {
      j++;
      newNode->Contour.push_back(path[i]);
      if (path[i].Y > newNode->Contour[k].Y ||
        (path[i].Y == newNode->Contour[k].Y &&
        path[i].X < newNode->Contour[k].X)) k = j;
    }
  if (endType == etClosedPolygon && j < 2)
  {
    delete newNode;
    return;
  }
  m_polyNodes.AddChild(*newNode);

  //if this path's lowest pt is lower than all the others then update m_lowest
  if (endType != etClosedPolygon) return;
  if (m_lowest.X < 0)
    m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
  else
  {
    IntPoint ip = m_polyNodes.Childs[(int)m_lowest.X]->Contour[(int)m_lowest.Y];
    if (newNode->Contour[k].Y > ip.Y ||
      (newNode->Contour[k].Y == ip.Y &&
      newNode->Contour[k].X < ip.X))
      m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
  }
}
//------------------------------------------------------------------------------

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

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

void ClipperOffset::Execute(Paths& solution, double delta)
{
  solution.clear();
  FixOrientations();
  DoOffset(delta);
  
  //now clean up 'corners' ...
  Clipper clpr;
  clpr.AddPaths(m_destPolys, ptSubject, true);
  if (delta > 0)
  {
    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
  }
  else
  {
    IntRect r = clpr.GetBounds();
    Path outer(4);
    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
    outer[2] = IntPoint(r.right + 10, r.top - 10);
    outer[3] = IntPoint(r.left - 10, r.top - 10);

    clpr.AddPath(outer, ptSubject, true);
    clpr.ReverseSolution(true);
    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
    if (solution.size() > 0) solution.erase(solution.begin());
  }
}
//------------------------------------------------------------------------------

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

  //now clean up 'corners' ...
  Clipper clpr;
  clpr.AddPaths(m_destPolys, ptSubject, true);
  if (delta > 0)
  {
    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
  }
  else
  {
    IntRect r = clpr.GetBounds();
    Path outer(4);
    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
    outer[2] = IntPoint(r.right + 10, r.top - 10);
    outer[3] = IntPoint(r.left - 10, r.top - 10);

    clpr.AddPath(outer, ptSubject, true);
    clpr.ReverseSolution(true);
    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
    //remove the outer PolyNode rectangle ...
    if (solution.ChildCount() == 1 && solution.Childs[0]->ChildCount() > 0)
    {
      PolyNode* outerNode = solution.Childs[0];
      solution.Childs.reserve(outerNode->ChildCount());
      solution.Childs[0] = outerNode->Childs[0];
      solution.Childs[0]->Parent = outerNode->Parent;
      for (int i = 1; i < outerNode->ChildCount(); ++i)
        solution.AddChild(*outerNode->Childs[i]);
    }
    else
      solution.Clear();
  }
}
//------------------------------------------------------------------------------

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

  //if Zero offset, just copy any CLOSED polygons to m_p and return ...
  if (NEAR_ZERO(delta)) 
  {
    m_destPolys.reserve(m_polyNodes.ChildCount());
    for (int i = 0; i < m_polyNodes.ChildCount(); i++)
    {
      PolyNode& node = *m_polyNodes.Childs[i];
      if (node.m_endtype == etClosedPolygon)
        m_destPolys.push_back(node.Contour);
    }
    return;
  }

  //see offset_triginometry3.svg in the documentation folder ...
  if (MiterLimit > 2) m_miterLim = 2/(MiterLimit * MiterLimit);
  else m_miterLim = 0.5;

  double y;
  if (ArcTolerance <= 0.0) y = def_arc_tolerance;
  else if (ArcTolerance > std::fabs(delta) * def_arc_tolerance) 
    y = std::fabs(delta) * def_arc_tolerance;
  else y = ArcTolerance;
  //see offset_triginometry2.svg in the documentation folder ...
  double steps = pi / std::acos(1 - y / std::fabs(delta));
  if (steps > std::fabs(delta) * pi) 
    steps = std::fabs(delta) * pi;  //ie excessive precision check
  m_sin = std::sin(two_pi / steps);
  m_cos = std::cos(two_pi / steps);
  m_StepsPerRad = steps / two_pi;
  if (delta < 0.0) m_sin = -m_sin;

  m_destPolys.reserve(m_polyNodes.ChildCount() * 2);
  for (int i = 0; i < m_polyNodes.ChildCount(); i++)
  {
    PolyNode& node = *m_polyNodes.Childs[i];
    m_srcPoly = node.Contour;

    int len = (int)m_srcPoly.size();
    if (len == 0 || (delta <= 0 && (len < 3 || node.m_endtype != etClosedPolygon)))
        continue;

    m_destPoly.clear();
    if (len == 1)
    {
      if (node.m_jointype == jtRound)
      {
        double X = 1.0, Y = 0.0;
        for (cInt j = 1; j <= steps; j++)
        {
          m_destPoly.push_back(IntPoint(
            Round(m_srcPoly[0].X + X * delta),
            Round(m_srcPoly[0].Y + Y * delta)));
          double X2 = X;
          X = X * m_cos - m_sin * Y;
          Y = X2 * m_sin + Y * m_cos;
        }
      }
      else
      {
        double X = -1.0, Y = -1.0;
        for (int j = 0; j < 4; ++j)
        {
          m_destPoly.push_back(IntPoint(
            Round(m_srcPoly[0].X + X * delta),
            Round(m_srcPoly[0].Y + Y * delta)));
          if (X < 0) X = 1;
          else if (Y < 0) Y = 1;
          else X = -1;
        }
      }
      m_destPolys.push_back(m_destPoly);
      continue;
    }
    //build m_normals ...
    m_normals.clear();
    m_normals.reserve(len);
    for (int j = 0; j < len - 1; ++j)
      m_normals.push_back(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
    if (node.m_endtype == etClosedLine || node.m_endtype == etClosedPolygon)
      m_normals.push_back(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
    else
      m_normals.push_back(DoublePoint(m_normals[len - 2]));

    if (node.m_endtype == etClosedPolygon)
    {
      int k = len - 1;
      for (int j = 0; j < len; ++j)
        OffsetPoint(j, k, node.m_jointype);
      m_destPolys.push_back(m_destPoly);
    }
    else if (node.m_endtype == etClosedLine)
    {
      int k = len - 1;
      for (int j = 0; j < len; ++j)
        OffsetPoint(j, k, node.m_jointype);
      m_destPolys.push_back(m_destPoly);
      m_destPoly.clear();
      //re-build m_normals ...
      DoublePoint n = m_normals[len -1];
      for (int j = len - 1; j > 0; j--)
        m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
      m_normals[0] = DoublePoint(-n.X, -n.Y);
      k = 0;
      for (int j = len - 1; j >= 0; j--)
        OffsetPoint(j, k, node.m_jointype);
      m_destPolys.push_back(m_destPoly);
    }
    else
    {
      int k = 0;
      for (int j = 1; j < len - 1; ++j)
        OffsetPoint(j, k, node.m_jointype);

      IntPoint pt1;
      if (node.m_endtype == etOpenButt)
      {
        int j = len - 1;
        pt1 = IntPoint((cInt)Round(m_srcPoly[j].X + m_normals[j].X *
          delta), (cInt)Round(m_srcPoly[j].Y + m_normals[j].Y * delta));
        m_destPoly.push_back(pt1);
        pt1 = IntPoint((cInt)Round(m_srcPoly[j].X - m_normals[j].X *
          delta), (cInt)Round(m_srcPoly[j].Y - m_normals[j].Y * delta));
        m_destPoly.push_back(pt1);
      }
      else
      {
        int j = len - 1;
        k = len - 2;
        m_sinA = 0;
        m_normals[j] = DoublePoint(-m_normals[j].X, -m_normals[j].Y);
        if (node.m_endtype == etOpenSquare)
          DoSquare(j, k);
        else
          DoRound(j, k);
      }

      //re-build m_normals ...
      for (int j = len - 1; j > 0; j--)
        m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
      m_normals[0] = DoublePoint(-m_normals[1].X, -m_normals[1].Y);

      k = len - 1;
      for (int j = k - 1; j > 0; --j) OffsetPoint(j, k, node.m_jointype);

      if (node.m_endtype == etOpenButt)
      {
        pt1 = IntPoint((cInt)Round(m_srcPoly[0].X - m_normals[0].X * delta),
          (cInt)Round(m_srcPoly[0].Y - m_normals[0].Y * delta));
        m_destPoly.push_back(pt1);
        pt1 = IntPoint((cInt)Round(m_srcPoly[0].X + m_normals[0].X * delta),
          (cInt)Round(m_srcPoly[0].Y + m_normals[0].Y * delta));
        m_destPoly.push_back(pt1);
      }
      else
      {
        k = 1;
        m_sinA = 0;
        if (node.m_endtype == etOpenSquare)
          DoSquare(0, 1);
        else
          DoRound(0, 1);
      }
      m_destPolys.push_back(m_destPoly);
    }
  }
}
//------------------------------------------------------------------------------

void ClipperOffset::OffsetPoint(int j, int& k, JoinType jointype)
{
  //cross product ...
  m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);
  if (std::fabs(m_sinA * m_delta) < 1.0) 
  {
    //dot product ...
    double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y ); 
    if (cosA > 0) // angle => 0 degrees
    {
      m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
        Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
      return; 
    }
    //else angle => 180 degrees   
  }
  else if (m_sinA > 1.0) m_sinA = 1.0;
  else if (m_sinA < -1.0) m_sinA = -1.0;

  if (m_sinA * m_delta < 0)
  {
    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
      Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
    m_destPoly.push_back(m_srcPoly[j]);
    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
      Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
  }
  else
    switch (jointype)
    {
      case jtMiter:
        {
          double r = 1 + (m_normals[j].X * m_normals[k].X +
            m_normals[j].Y * m_normals[k].Y);
          if (r >= m_miterLim) DoMiter(j, k, r); else DoSquare(j, k);
          break;
        }
      case jtSquare: DoSquare(j, k); break;
      case jtRound: DoRound(j, k); break;
    }
  k = j;
}
//------------------------------------------------------------------------------

void ClipperOffset::DoSquare(int j, int k)
{
  double dx = std::tan(std::atan2(m_sinA,
      m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
  m_destPoly.push_back(IntPoint(
      Round(m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx)),
      Round(m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx))));
  m_destPoly.push_back(IntPoint(
      Round(m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx)),
      Round(m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx))));
}
//------------------------------------------------------------------------------

void ClipperOffset::DoMiter(int j, int k, double r)
{
  double q = m_delta / r;
  m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + (m_normals[k].X + m_normals[j].X) * q),
      Round(m_srcPoly[j].Y + (m_normals[k].Y + m_normals[j].Y) * q)));
}
//------------------------------------------------------------------------------

void ClipperOffset::DoRound(int j, int k)
{
  double a = std::atan2(m_sinA,
  m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
  int steps = std::max((int)Round(m_StepsPerRad * std::fabs(a)), 1);

  double X = m_normals[k].X, Y = m_normals[k].Y, X2;
  for (int i = 0; i < steps; ++i)
  {
    m_destPoly.push_back(IntPoint(
        Round(m_srcPoly[j].X + X * m_delta),
        Round(m_srcPoly[j].Y + Y * m_delta)));
    X2 = X;
    X = X * m_cos - m_sin * Y;
    Y = X2 * m_sin + Y * m_cos;
  }
  m_destPoly.push_back(IntPoint(
  Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
  Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
}

//------------------------------------------------------------------------------
// Miscellaneous public functions
//------------------------------------------------------------------------------

void Clipper::DoSimplePolygons()
{
  PolyOutList::size_type i = 0;
  while (i < m_PolyOuts.size()) 
  {
    OutRec* outrec = m_PolyOuts[i++];
    OutPt* op = outrec->Pts;
    if (!op || outrec->IsOpen) continue;
    do //for each Pt in Polygon until duplicate found do ...
    {
      OutPt* op2 = op->Next;
      while (op2 != outrec->Pts) 
      {
        if ((op->Pt == op2->Pt) && op2->Next != op && op2->Prev != op) 
        {
          //split the polygon into two ...
          OutPt* op3 = op->Prev;
          OutPt* op4 = op2->Prev;
          op->Prev = op4;
          op4->Next = op;
          op2->Prev = op3;
          op3->Next = op2;

          outrec->Pts = op;
          OutRec* outrec2 = CreateOutRec();
          outrec2->Pts = op2;
          UpdateOutPtIdxs(*outrec2);
          if (Poly2ContainsPoly1(outrec2->Pts, outrec->Pts))
          {
            //OutRec2 is contained by OutRec1 ...
            outrec2->IsHole = !outrec->IsHole;
            outrec2->FirstLeft = outrec;
            if (m_UsingPolyTree) FixupFirstLefts2(outrec2, outrec);
          }
          else
            if (Poly2ContainsPoly1(outrec->Pts, outrec2->Pts))
          {
            //OutRec1 is contained by OutRec2 ...
            outrec2->IsHole = outrec->IsHole;
            outrec->IsHole = !outrec2->IsHole;
            outrec2->FirstLeft = outrec->FirstLeft;
            outrec->FirstLeft = outrec2;
            if (m_UsingPolyTree) FixupFirstLefts2(outrec, outrec2);
            }
            else
          {
            //the 2 polygons are separate ...
            outrec2->IsHole = outrec->IsHole;
            outrec2->FirstLeft = outrec->FirstLeft;
            if (m_UsingPolyTree) FixupFirstLefts1(outrec, outrec2);
            }
          op2 = op; //ie get ready for the Next iteration
        }
        op2 = op2->Next;
      }
      op = op->Next;
    }
    while (op != outrec->Pts);
  }
}
//------------------------------------------------------------------------------

void ReversePath(Path& p)
{
  std::reverse(p.begin(), p.end());
}
//------------------------------------------------------------------------------

void ReversePaths(Paths& p)
{
  for (Paths::size_type i = 0; i < p.size(); ++i)
    ReversePath(p[i]);
}
//------------------------------------------------------------------------------

void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType)
{
  Clipper c;
  c.StrictlySimple(true);
  c.AddPath(in_poly, ptSubject, true);
  c.Execute(ctUnion, out_polys, fillType, fillType);
}
//------------------------------------------------------------------------------

void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType)
{
  Clipper c;
  c.StrictlySimple(true);
  c.AddPaths(in_polys, ptSubject, true);
  c.Execute(ctUnion, out_polys, fillType, fillType);
}
//------------------------------------------------------------------------------

void SimplifyPolygons(Paths &polys, PolyFillType fillType)
{
  SimplifyPolygons(polys, polys, fillType);
}
//------------------------------------------------------------------------------

inline double DistanceSqrd(const IntPoint& pt1, const IntPoint& pt2)
{
  double Dx = ((double)pt1.X - pt2.X);
  double dy = ((double)pt1.Y - pt2.Y);
  return (Dx*Dx + dy*dy);
}
//------------------------------------------------------------------------------

double DistanceFromLineSqrd(
  const IntPoint& pt, const IntPoint& ln1, const IntPoint& ln2)
{
  //The equation of a line in general form (Ax + By + C = 0)
  //given 2 points (x¹,y¹) & (x²,y²) is ...
  //(y¹ - y²)x + (x² - x¹)y + (y² - y¹)x¹ - (x² - x¹)y¹ = 0
  //A = (y¹ - y²); B = (x² - x¹); C = (y² - y¹)x¹ - (x² - x¹)y¹
  //perpendicular distance of point (x³,y³) = (Ax³ + By³ + C)/Sqrt(A² + B²)
  //see http://en.wikipedia.org/wiki/Perpendicular_distance
  double A = double(ln1.Y - ln2.Y);
  double B = double(ln2.X - ln1.X);
  double C = A * ln1.X  + B * ln1.Y;
  C = A * pt.X + B * pt.Y - C;
  return (C * C) / (A * A + B * B);
}
//---------------------------------------------------------------------------

bool SlopesNearCollinear(const IntPoint& pt1, 
    const IntPoint& pt2, const IntPoint& pt3, double distSqrd)
{
  //this function is more accurate when the point that's geometrically
  //between the other 2 points is the one that's tested for distance.
  //ie makes it more likely to pick up 'spikes' ...
	if (Abs(pt1.X - pt2.X) > Abs(pt1.Y - pt2.Y))
	{
    if ((pt1.X > pt2.X) == (pt1.X < pt3.X))
      return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
    else if ((pt2.X > pt1.X) == (pt2.X < pt3.X))
      return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
		else
	    return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
	}
	else
	{
    if ((pt1.Y > pt2.Y) == (pt1.Y < pt3.Y))
      return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
    else if ((pt2.Y > pt1.Y) == (pt2.Y < pt3.Y))
      return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
		else
      return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
	}
}
//------------------------------------------------------------------------------

bool PointsAreClose(IntPoint pt1, IntPoint pt2, double distSqrd)
{
    double Dx = (double)pt1.X - pt2.X;
    double dy = (double)pt1.Y - pt2.Y;
    return ((Dx * Dx) + (dy * dy) <= distSqrd);
}
//------------------------------------------------------------------------------

OutPt* ExcludeOp(OutPt* op)
{
  OutPt* result = op->Prev;
  result->Next = op->Next;
  op->Next->Prev = result;
  result->Idx = 0;
  return result;
}
//------------------------------------------------------------------------------

void CleanPolygon(const Path& in_poly, Path& out_poly, double distance)
{
  //distance = proximity in units/pixels below which vertices
  //will be stripped. Default ~= sqrt(2).
  
  size_t size = in_poly.size();
  
  if (size == 0) 
  {
    out_poly.clear();
    return;
  }

  OutPt* outPts = new OutPt[size];
  for (size_t i = 0; i < size; ++i)
  {
    outPts[i].Pt = in_poly[i];
    outPts[i].Next = &outPts[(i + 1) % size];
    outPts[i].Next->Prev = &outPts[i];
    outPts[i].Idx = 0;
  }

  double distSqrd = distance * distance;
  OutPt* op = &outPts[0];
  while (op->Idx == 0 && op->Next != op->Prev) 
  {
    if (PointsAreClose(op->Pt, op->Prev->Pt, distSqrd))
    {
      op = ExcludeOp(op);
      size--;
    } 
    else if (PointsAreClose(op->Prev->Pt, op->Next->Pt, distSqrd))
    {
      ExcludeOp(op->Next);
      op = ExcludeOp(op);
      size -= 2;
    }
    else if (SlopesNearCollinear(op->Prev->Pt, op->Pt, op->Next->Pt, distSqrd))
    {
      op = ExcludeOp(op);
      size--;
    }
    else
    {
      op->Idx = 1;
      op = op->Next;
    }
  }

  if (size < 3) size = 0;
  out_poly.resize(size);
  for (size_t i = 0; i < size; ++i)
  {
    out_poly[i] = op->Pt;
    op = op->Next;
  }
  delete [] outPts;
}
//------------------------------------------------------------------------------

void CleanPolygon(Path& poly, double distance)
{
  CleanPolygon(poly, poly, distance);
}
//------------------------------------------------------------------------------

void CleanPolygons(const Paths& in_polys, Paths& out_polys, double distance)
{
  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, IntPoint delta) 
{
  //precondition: input != output
  output.resize(input.size());
  for (size_t i = 0; i < input.size(); ++i)
    output[i] = IntPoint(input[i].X + delta.X, input[i].Y + delta.Y);
}
//------------------------------------------------------------------------------

void MinkowskiSum(const Path& pattern, const Paths& paths, Paths& solution, bool pathIsClosed)
{
  Clipper c;
  for (size_t i = 0; i < paths.size(); ++i)
  {
    Paths tmp;
    Minkowski(pattern, paths[i], tmp, true, pathIsClosed);
    c.AddPaths(tmp, ptSubject, true);
    if (pathIsClosed)
    {
      Path tmp2;
      TranslatePath(paths[i], tmp2, pattern[0]);
      c.AddPath(tmp2, ptClip, true);
    }
  }
    c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
}
//------------------------------------------------------------------------------

void MinkowskiDiff(const Path& poly1, const Path& poly2, Paths& solution)
{
  Minkowski(poly1, poly2, solution, false, true);
  Clipper c;
  c.AddPaths(solution, ptSubject, true);
  c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
}
//------------------------------------------------------------------------------

enum NodeType {ntAny, ntOpen, ntClosed};

void AddPolyNodeToPaths(const PolyNode& polynode, NodeType nodetype, Paths& paths)
{
  bool match = true;
  if (nodetype == ntClosed) match = !polynode.IsOpen();
  else if (nodetype == ntOpen) return;

  if (!polynode.Contour.empty() && match)
    paths.push_back(polynode.Contour);
  for (int i = 0; i < polynode.ChildCount(); ++i)
    AddPolyNodeToPaths(*polynode.Childs[i], nodetype, paths);
}
//------------------------------------------------------------------------------

void PolyTreeToPaths(const PolyTree& polytree, Paths& paths)
{
  paths.resize(0); 
  paths.reserve(polytree.Total());
  AddPolyNodeToPaths(polytree, ntAny, paths);
}
//------------------------------------------------------------------------------

void ClosedPathsFromPolyTree(const PolyTree& polytree, Paths& paths)
{
  paths.resize(0); 
  paths.reserve(polytree.Total());
  AddPolyNodeToPaths(polytree, ntClosed, paths);
}
//------------------------------------------------------------------------------

void OpenPathsFromPolyTree(PolyTree& polytree, Paths& paths)
{
  paths.resize(0); 
  paths.reserve(polytree.Total());
  //Open paths are top level only, so ...
  for (int i = 0; i < polytree.ChildCount(); ++i)
    if (polytree.Childs[i]->IsOpen())
      paths.push_back(polytree.Childs[i]->Contour);
}
//------------------------------------------------------------------------------

std::ostream& operator <<(std::ostream &s, const IntPoint &p)
{
  s << "(" << p.X << "," << p.Y << ")";
  return s;
}
//------------------------------------------------------------------------------

std::ostream& operator <<(std::ostream &s, const Path &p)
{
  if (p.empty()) return s;
  Path::size_type last = p.size() -1;
  for (Path::size_type i = 0; i < last; i++)
    s << "(" << p[i].X << "," << p[i].Y << "), ";
  s << "(" << p[last].X << "," << p[last].Y << ")\n";
  return s;
}
//------------------------------------------------------------------------------

std::ostream& operator <<(std::ostream &s, const Paths &p)
{
  for (Paths::size_type i = 0; i < p.size(); i++)
    s << p[i];
  s << "\n";
  return s;
}
//------------------------------------------------------------------------------

} //ClipperLib namespace
