+ add polyclipper to assimp repository.

git-svn-id: https://assimp.svn.sourceforge.net/svnroot/assimp/trunk@1116 67173fc5-114c-0410-ac8e-9d2fd5bffc1f

contrib/clipper/License.txt

@@ -0,0 +1,29 @@
+The Clipper code library, the "Software" (that includes Delphi, C++ & C# 
+source code, accompanying samples and documentation), 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 and accompanying documentation covered by
+this license (the "Software") 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.
+

contrib/clipper/clipper.cpp

@@ -0,0 +1,3302 @@
+/*******************************************************************************
+*                                                                              *
+* Author    :  Angus Johnson                                                   *
+* Version   :  4.6.3                                                           *
+* Date      :  11 November 2011                                                *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2011                                         *
+*                                                                              *
+* License:                                                                     *
+* Use, modification & distribution is subject to Boost Software License Ver 1. *
+* http://www.boost.org/LICENSE_1_0.txt                                         *
+*                                                                              *
+* Attributions:                                                                *
+* The code in this library is an extension of Bala Vatti's clipping algorithm: *
+* "A generic solution to polygon clipping"                                     *
+* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
+* http://portal.acm.org/citation.cfm?id=129906                                 *
+*                                                                              *
+* Computer graphics and geometric modeling: implementation and algorithms      *
+* By Max K. Agoston                                                            *
+* Springer; 1 edition (January 4, 2005)                                        *
+* http://books.google.com/books?q=vatti+clipping+agoston                       *
+*                                                                              *
+* See also:                                                                    *
+* "Polygon Offsetting by Computing Winding Numbers"                            *
+* Paper no. DETC2005-85513 pp. 565-575                                         *
+* ASME 2005 International Design Engineering Technical Conferences             *
+* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
+* September 24–28, 2005 , Long Beach, California, USA                          *
+* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
+*                                                                              *
+*******************************************************************************/
+
+/*******************************************************************************
+*                                                                              *
+* This is a translation of the Delphi Clipper library and the naming style     *
+* used has retained a Delphi flavour.                                          *
+*                                                                              *
+*******************************************************************************/
+
+#include "clipper.hpp"
+#include <cmath>
+#include <vector>
+#include <algorithm>
+#include <stdexcept>
+#include <cstring>
+#include <cstdlib>
+#include <ostream>
+
+namespace ClipperLib {
+
+static long64 const loRange = 1518500249;            //sqrt(2^63 -1)/2
+static long64 const hiRange = 6521908912666391106LL; //sqrt(2^127 -1)/2
+static double const pi = 3.141592653589793238;
+enum Direction { dRightToLeft, dLeftToRight };
+enum RangeTest { rtLo, rtHi, rtError };
+
+#define HORIZONTAL (-1.0E+40)
+#define TOLERANCE (1.0e-20)
+#define NEAR_ZERO(val) (((val) > -TOLERANCE) && ((val) < TOLERANCE))
+#define NEAR_EQUAL(a, b) NEAR_ZERO((a) - (b))
+
+inline long64 Abs(long64 val)
+{
+  if (val < 0) return -val; else return val;
+}
+//------------------------------------------------------------------------------
+
+//------------------------------------------------------------------------------
+// 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:
+
+    Int128(long64 _lo = 0)
+    {
+      hi = 0;
+      if (_lo < 0) {
+        lo = -_lo;
+        Negate(*this);
+      } else
+          lo = _lo;
+    }
+
+    Int128(const Int128 &val): hi(val.hi), lo(val.lo){}
+
+    long64 operator = (const long64 &val)
+    {
+      hi = 0;
+      lo = Abs(val);
+      if (val < 0) Negate(*this);
+      return val;
+    }
+
+    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 true;
+      else if (hi < val.hi) return false;
+      else return ulong64(lo) > ulong64(val.lo);
+    }
+
+    bool operator < (const Int128 &val) const
+    {
+      if (hi < val.hi) return true;
+      else if (hi > val.hi) return false;
+      else return ulong64(lo) < ulong64(val.lo);
+    }
+
+    Int128& operator += (const Int128 &rhs)
+    {
+      hi += rhs.hi;
+      lo += rhs.lo;
+      if (ulong64(lo) < ulong64(rhs.lo)) hi++;
+      return *this;
+    }
+
+    Int128 operator + (const Int128 &rhs) const
+    {
+      Int128 result(*this);
+      result+= rhs;
+      return result;
+    }
+
+    Int128& operator -= (const Int128 &rhs)
+    {
+      Int128 tmp(rhs);
+      Negate(tmp);
+      *this += tmp;
+      return *this;
+    }
+
+    Int128 operator - (const Int128 &rhs) const
+    {
+      Int128 result(*this);
+      result-= rhs;
+      return result;
+    }
+
+    Int128 operator * (const Int128 &rhs) const {
+      if ( !(hi == 0 || hi == -1) || !(rhs.hi == 0 || rhs.hi == -1))
+        throw "Int128 operator*: overflow error";
+      bool negate = (hi < 0) != (rhs.hi < 0);
+
+      Int128 tmp(*this);
+      if (tmp.hi < 0) Negate(tmp);
+      ulong64 int1Hi = ulong64(tmp.lo) >> 32;
+      ulong64 int1Lo = ulong64(tmp.lo & 0xFFFFFFFF);
+
+      tmp = rhs;
+      if (tmp.hi < 0) Negate(tmp);
+      ulong64 int2Hi = ulong64(tmp.lo) >> 32;
+      ulong64 int2Lo = ulong64(tmp.lo & 0xFFFFFFFF);
+
+      //nb: see comments in clipper.pas
+      ulong64 a = int1Hi * int2Hi;
+      ulong64 b = int1Lo * int2Lo;
+      ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;
+
+      tmp.hi = long64(a + (c >> 32));
+      tmp.lo = long64(c << 32);
+      tmp.lo += long64(b);
+      if (ulong64(tmp.lo) < b) tmp.hi++;
+      if (negate) Negate(tmp);
+      return tmp;
+    }
+
+    Int128 operator/ (const Int128 &rhs) const
+    {
+      if (rhs.lo == 0 && rhs.hi == 0)
+        throw "Int128 operator/: divide by zero";
+      bool negate = (rhs.hi < 0) != (hi < 0);
+      Int128 result(*this), denom(rhs);
+      if (result.hi < 0) Negate(result);
+      if (denom.hi < 0)  Negate(denom);
+      if (denom > result) return Int128(0); //result is only a fraction of 1
+      Negate(denom);
+
+      Int128 p(0);
+      for (int i = 0; i < 128; ++i)
+      {
+        p.hi = p.hi << 1;
+        if (p.lo < 0) p.hi++;
+        p.lo = long64(p.lo) << 1;
+        if (result.hi < 0) p.lo++;
+        result.hi = result.hi << 1;
+        if (result.lo < 0) result.hi++;
+        result.lo = long64(result.lo) << 1;
+        Int128 p2(p);
+        p += denom;
+        if (p.hi < 0) p = p2;
+        else result.lo++;
+      }
+      if (negate) Negate(result);
+      return result;
+    }
+
+    double AsDouble() const
+    {
+      const double shift64 = 18446744073709551616.0; //2^64
+      const double bit64 = 9223372036854775808.0;
+      if (hi < 0)
+      {
+        Int128 tmp(*this);
+        Negate(tmp);
+        if (tmp.lo < 0)
+          return (double)tmp.lo - bit64 - tmp.hi * shift64;
+        else
+          return -(double)tmp.lo - tmp.hi * shift64;
+      }
+      else if (lo < 0)
+        return -(double)lo + bit64 + hi * shift64;
+      else
+        return (double)lo + (double)hi * shift64;
+    }
+
+    //for bug testing ...
+    std::string AsString() const
+    {
+      std::string result;
+      unsigned char r = 0;
+      Int128 tmp(0), val(*this);
+      if (hi < 0) Negate(val);
+      result.resize(50);
+      std::string::size_type i = result.size() -1;
+      while (val.hi != 0 || val.lo != 0)
+      {
+        Div10(val, tmp, r);
+        result[i--] = char('0' + r);
+        val = tmp;
+      }
+      if (hi < 0) result[i--] = '-';
+      result.erase(0,i+1);
+      if (result.size() == 0) result = "0";
+      return result;
+    }
+
+private:
+    long64 hi;
+    long64 lo;
+
+    static void Negate(Int128 &val)
+    {
+      if (val.lo == 0)
+      {
+        if( val.hi == 0) return;
+        val.lo = ~val.lo;
+        val.hi = ~val.hi +1;
+      }
+      else
+      {
+        val.lo = ~val.lo +1;
+        val.hi = ~val.hi;
+      }
+    }
+
+    //debugging only ...
+    void Div10(const Int128 val, Int128& result, unsigned char & remainder) const
+    {
+      remainder = 0;
+      result = 0;
+      for (int i = 63; i >= 0; --i)
+      {
+        if ((val.hi & ((long64)1 << i)) != 0)
+          remainder = char((remainder * 2) + 1); else
+          remainder *= char(2);
+        if (remainder >= 10)
+        {
+          result.hi += ((long64)1 << i);
+          remainder -= char(10);
+        }
+      }
+      for (int i = 63; i >= 0; --i)
+      {
+        if ((val.lo & ((long64)1 << i)) != 0)
+          remainder = char((remainder * 2) + 1); else
+          remainder *= char(2);
+        if (remainder >= 10)
+        {
+          result.lo += ((long64)1 << i);
+          remainder -= char(10);
+        }
+      }
+    }
+};
+
+//------------------------------------------------------------------------------
+//------------------------------------------------------------------------------
+
+RangeTest TestRange(const Polygon &pts)
+{
+  RangeTest result = rtLo;
+  for (Polygon::size_type i = 0; i <  pts.size(); ++i)
+  {
+    if (Abs(pts[i].X) > hiRange || Abs(pts[i].Y) > hiRange)
+        return rtError;
+      else if (Abs(pts[i].X) > loRange || Abs(pts[i].Y) > loRange)
+        result = rtHi;
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+bool Orientation(const Polygon &poly)
+{
+  int highI = (int)poly.size() -1;
+  if (highI < 2) return false;
+  bool UseFullInt64Range = false;
+
+  int j = 0, jplus, jminus;
+  for (int i = 0; i <= highI; ++i)
+  {
+    if (Abs(poly[i].X) > hiRange || Abs(poly[i].Y) > hiRange)
+    throw "Coordinate exceeds range bounds.";
+    if (Abs(poly[i].X) > loRange || Abs(poly[i].Y) > loRange)
+    UseFullInt64Range = true;
+    if (poly[i].Y < poly[j].Y) continue;
+    if ((poly[i].Y > poly[j].Y || poly[i].X < poly[j].X)) j = i;
+  };
+  if (j == highI) jplus = 0;
+  else jplus = j +1;
+  if (j == 0) jminus = highI;
+  else jminus = j -1;
+
+  IntPoint vec1, vec2;
+  //get cross product of vectors of the edges adjacent to highest point ...
+  vec1.X = poly[j].X - poly[jminus].X;
+  vec1.Y = poly[j].Y - poly[jminus].Y;
+  vec2.X = poly[jplus].X - poly[j].X;
+  vec2.Y = poly[jplus].Y - poly[j].Y;
+
+  if (UseFullInt64Range)
+  {
+    Int128 cross = Int128(vec1.X) * Int128(vec2.Y) -
+      Int128(vec2.X) * Int128(vec1.Y);
+    return cross > 0;
+  }
+  else
+  {
+    return (vec1.X * vec2.Y - vec2.X * vec1.Y) > 0;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Orientation(OutRec *outRec, bool UseFullInt64Range)
+{
+  OutPt *opBottom = outRec->pts, *op = outRec->pts->next;
+  while (op != outRec->pts)
+  {
+    if (op->pt.Y >= opBottom->pt.Y)
+    {
+      if (op->pt.Y > opBottom->pt.Y || op->pt.X < opBottom->pt.X)
+      opBottom = op;
+    }
+    op = op->next;
+  }
+
+  IntPoint vec1, vec2;
+  vec1.X = op->pt.X - op->prev->pt.X;
+  vec1.Y = op->pt.Y - op->prev->pt.Y;
+  vec2.X = op->next->pt.X - op->pt.X;
+  vec2.Y = op->next->pt.Y - op->pt.Y;
+
+  if (UseFullInt64Range)
+  {
+    Int128 cross = Int128(vec1.X) * Int128(vec2.Y) - Int128(vec2.X) * Int128(vec1.Y);
+    return cross > 0;
+  }
+  else
+  {
+    return (vec1.X * vec2.Y - vec2.X * vec1.Y) > 0;
+  }
+}
+//------------------------------------------------------------------------------
+
+inline bool PointsEqual( const IntPoint &pt1, const IntPoint &pt2)
+{
+  return ( pt1.X == pt2.X && pt1.Y == pt2.Y );
+}
+//------------------------------------------------------------------------------
+
+double Area(const Polygon &poly)
+{
+  int highI = (int)poly.size() -1;
+  if (highI < 2) return 0;
+  bool UseFullInt64Range;
+  RangeTest rt = TestRange(poly);
+  switch (rt) {
+    case rtLo:
+      UseFullInt64Range = false;
+      break;
+    case rtHi:
+      UseFullInt64Range = true;
+      break;
+    default:
+      throw "Coordinate exceeds range bounds.";
+  }
+
+  if (UseFullInt64Range) {
+    Int128 a(0);
+    a = (Int128(poly[highI].X) * Int128(poly[0].Y)) -
+      Int128(poly[0].X) * Int128(poly[highI].Y);
+    for (int i = 0; i < highI; ++i)
+      a += Int128(poly[i].X) * Int128(poly[i+1].Y) -
+        Int128(poly[i+1].X) * Int128(poly[i].Y);
+    return a.AsDouble() / 2;
+  }
+  else
+  {
+    double a;
+    a = (double)poly[highI].X * poly[0].Y - (double)poly[0].X * poly[highI].Y;
+    for (int i = 0; i < highI; ++i)
+      a += (double)poly[i].X * poly[i+1].Y - (double)poly[i+1].X * poly[i].Y;
+    return a/2;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool PointIsVertex(const IntPoint &pt, OutPt *pp)
+{
+  OutPt *pp2 = pp;
+  do
+  {
+    if (PointsEqual(pp2->pt, pt)) return true;
+    pp2 = pp2->next;
+  }
+  while (pp2 != pp);
+  return false;
+}
+//------------------------------------------------------------------------------
+
+bool PointInPolygon(const IntPoint &pt, OutPt *pp, bool UseFullInt64Range)
+{
+  OutPt *pp2 = pp;
+  bool result = false;
+  if (UseFullInt64Range) {
+    do
+    {
+      if ((((pp2->pt.Y <= pt.Y) && (pt.Y < pp2->prev->pt.Y)) ||
+          ((pp2->prev->pt.Y <= pt.Y) && (pt.Y < pp2->pt.Y))) &&
+          Int128(pt.X - pp2->pt.X) < (Int128(pp2->prev->pt.X - pp2->pt.X) *
+          Int128(pt.Y - pp2->pt.Y)) / Int128(pp2->prev->pt.Y - pp2->pt.Y))
+            result = !result;
+      pp2 = pp2->next;
+    }
+    while (pp2 != pp);
+  }
+  else
+  {
+    do
+    {
+      if ((((pp2->pt.Y <= pt.Y) && (pt.Y < pp2->prev->pt.Y)) ||
+        ((pp2->prev->pt.Y <= pt.Y) && (pt.Y < pp2->pt.Y))) &&
+        (pt.X < (pp2->prev->pt.X - pp2->pt.X) * (pt.Y - pp2->pt.Y) /
+        (pp2->prev->pt.Y - pp2->pt.Y) + pp2->pt.X )) result = !result;
+      pp2 = pp2->next;
+    }
+    while (pp2 != pp);
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+bool SlopesEqual(TEdge &e1, TEdge &e2, bool UseFullInt64Range)
+{
+  if (e1.ybot == e1.ytop) return (e2.ybot == e2.ytop);
+  else if (e1.xbot == e1.xtop) return (e2.xbot == e2.xtop);
+  else if (UseFullInt64Range)
+    return Int128(e1.ytop - e1.ybot) * Int128(e2.xtop - e2.xbot) ==
+      Int128(e1.xtop - e1.xbot) * Int128(e2.ytop - e2.ybot);
+  else return (e1.ytop - e1.ybot)*(e2.xtop - e2.xbot) ==
+      (e1.xtop - e1.xbot)*(e2.ytop - e2.ybot);
+}
+//------------------------------------------------------------------------------
+
+bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
+  const IntPoint pt3, bool UseFullInt64Range)
+{
+  if (pt1.Y == pt2.Y) return (pt2.Y == pt3.Y);
+  else if (pt1.X == pt2.X) return (pt2.X == pt3.X);
+  else if (UseFullInt64Range)
+    return Int128(pt1.Y-pt2.Y) * Int128(pt2.X-pt3.X) ==
+      Int128(pt1.X-pt2.X) * Int128(pt2.Y-pt3.Y);
+  else 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)
+{
+  if (pt1.Y == pt2.Y) return (pt3.Y == pt4.Y);
+  else if (pt1.X == pt2.X) return (pt3.X == pt4.X);
+  else if (UseFullInt64Range)
+    return Int128(pt1.Y-pt2.Y) * Int128(pt3.X-pt4.X) ==
+      Int128(pt1.X-pt2.X) * Int128(pt3.Y-pt4.Y);
+  else return (pt1.Y-pt2.Y)*(pt3.X-pt4.X) == (pt1.X-pt2.X)*(pt3.Y-pt4.Y);
+}
+//------------------------------------------------------------------------------
+
+double GetDx(const IntPoint pt1, const IntPoint pt2)
+{
+  if (pt1.Y == pt2.Y) return HORIZONTAL;
+  else return
+    (double)(pt2.X - pt1.X) / (double)(pt2.Y - pt1.Y);
+}
+//---------------------------------------------------------------------------
+
+void SetDx(TEdge &e)
+{
+  if (e.ybot == e.ytop) e.dx = HORIZONTAL;
+  else e.dx =
+    (double)(e.xtop - e.xbot) / (double)(e.ytop - e.ybot);
+}
+//---------------------------------------------------------------------------
+
+void SwapSides(TEdge &edge1, TEdge &edge2)
+{
+  EdgeSide side =  edge1.side;
+  edge1.side = edge2.side;
+  edge2.side = side;
+}
+//------------------------------------------------------------------------------
+
+void SwapPolyIndexes(TEdge &edge1, TEdge &edge2)
+{
+  int outIdx =  edge1.outIdx;
+  edge1.outIdx = edge2.outIdx;
+  edge2.outIdx = outIdx;
+}
+//------------------------------------------------------------------------------
+
+inline long64 Round(double val)
+{
+  if ((val < 0)) return static_cast<long64>(val - 0.5);
+  else return static_cast<long64>(val + 0.5);
+}
+//------------------------------------------------------------------------------
+
+long64 TopX(TEdge &edge, const long64 currentY)
+{
+  if( currentY == edge.ytop ) return edge.xtop;
+  return edge.xbot + Round(edge.dx *(currentY - edge.ybot));
+}
+//------------------------------------------------------------------------------
+
+long64 TopX(const IntPoint pt1, const IntPoint pt2, const long64 currentY)
+{
+  //preconditions: pt1.Y <> pt2.Y and pt1.Y > pt2.Y
+  if (currentY >= pt1.Y) return pt1.X;
+  else if (currentY == pt2.Y) return pt2.X;
+  else if (pt1.X == pt2.X) return pt1.X;
+  else
+  {
+    double q = (double)(pt1.X-pt2.X)/(double)(pt1.Y-pt2.Y);
+    return Round(pt1.X + (currentY - pt1.Y) *q);
+  }
+}
+//------------------------------------------------------------------------------
+
+bool IntersectPoint(TEdge &edge1, TEdge &edge2,
+  IntPoint &ip, bool UseFullInt64Range)
+{
+  double b1, b2;
+  if (SlopesEqual(edge1, edge2, UseFullInt64Range)) return false;
+  else if (NEAR_ZERO(edge1.dx))
+  {
+    ip.X = edge1.xbot;
+    if (NEAR_EQUAL(edge2.dx, HORIZONTAL))
+    {
+      ip.Y = edge2.ybot;
+    } else
+    {
+      b2 = edge2.ybot - (edge2.xbot/edge2.dx);
+      ip.Y = Round(ip.X/edge2.dx + b2);
+    }
+  }
+  else if (NEAR_ZERO(edge2.dx))
+  {
+    ip.X = edge2.xbot;
+    if (NEAR_EQUAL(edge1.dx, HORIZONTAL))
+    {
+      ip.Y = edge1.ybot;
+    } else
+    {
+      b1 = edge1.ybot - (edge1.xbot/edge1.dx);
+      ip.Y = Round(ip.X/edge1.dx + b1);
+    }
+  } else
+  {
+    b1 = edge1.xbot - edge1.ybot * edge1.dx;
+    b2 = edge2.xbot - edge2.ybot * edge2.dx;
+    b2 = (b2-b1)/(edge1.dx - edge2.dx);
+    ip.Y = Round(b2);
+    ip.X = Round(edge1.dx * b2 + b1);
+  }
+
+  return
+    //can be *so close* to the top of one edge that the rounded Y equals one ytop ...
+    (ip.Y == edge1.ytop && ip.Y >= edge2.ytop && edge1.tmpX > edge2.tmpX) ||
+    (ip.Y == edge2.ytop && ip.Y >= edge1.ytop && edge1.tmpX > edge2.tmpX) ||
+    (ip.Y > edge1.ytop && ip.Y > edge2.ytop);
+}
+//------------------------------------------------------------------------------
+
+void ReversePolyPtLinks(OutPt &pp)
+{
+  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 ;
+  }
+}
+//------------------------------------------------------------------------------
+
+void InitEdge(TEdge *e, TEdge *eNext,
+  TEdge *ePrev, const IntPoint &pt, PolyType polyType)
+{
+  std::memset( e, 0, sizeof( TEdge ));
+
+  e->next = eNext;
+  e->prev = ePrev;
+  e->xcurr = pt.X;
+  e->ycurr = pt.Y;
+  if (e->ycurr >= e->next->ycurr)
+  {
+    e->xbot = e->xcurr;
+    e->ybot = e->ycurr;
+    e->xtop = e->next->xcurr;
+    e->ytop = e->next->ycurr;
+    e->windDelta = 1;
+  } else
+  {
+    e->xtop = e->xcurr;
+    e->ytop = e->ycurr;
+    e->xbot = e->next->xcurr;
+    e->ybot = e->next->ycurr;
+    e->windDelta = -1;
+  }
+  SetDx(*e);
+  e->polyType = polyType;
+  e->outIdx = -1;
+}
+//------------------------------------------------------------------------------
+
+inline void SwapX(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.]
+  e.xcurr = e.xtop;
+  e.xtop = e.xbot;
+  e.xbot = e.xcurr;
+}
+//------------------------------------------------------------------------------
+
+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 colinear.
+  if ( pt1a.Y == pt1b.Y || Abs((pt1a.X - pt1b.X)/(pt1a.Y - pt1b.Y)) > 1 )
+  {
+    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;
+  }
+}
+//------------------------------------------------------------------------------
+
+OutPt* PolygonBottom(OutPt* pp)
+{
+  OutPt* p = pp->next;
+  OutPt* result = pp;
+  while (p != pp)
+  {
+    if (p->pt.Y > result->pt.Y) result = p;
+    else if (p->pt.Y == result->pt.Y && p->pt.X < result->pt.X) result = p;
+    p = p->next;
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+bool FindSegment(OutPt* &pp, IntPoint &pt1, IntPoint &pt2)
+{
+  //outPt1 & outPt2 => the overlap segment (if the function returns true)
+  if (!pp) return false;
+  OutPt* pp2 = pp;
+  IntPoint pt1a = pt1, pt2a = pt2;
+  do
+  {
+    if (SlopesEqual(pt1a, pt2a, pp->pt, pp->prev->pt, true) &&
+      SlopesEqual(pt1a, pt2a, pp->pt, true) &&
+      GetOverlapSegment(pt1a, pt2a, pp->pt, pp->prev->pt, pt1, pt2))
+        return true;
+    pp = pp->next;
+  }
+  while (pp != pp2);
+  return false;
+}
+//------------------------------------------------------------------------------
+
+bool Pt3IsBetweenPt1AndPt2(const IntPoint pt1,
+  const IntPoint pt2, const IntPoint pt3)
+{
+  if (PointsEqual(pt1, pt3) || PointsEqual(pt2, pt3)) return true;
+  else if (pt1.X != pt2.X) return (pt1.X < pt3.X) == (pt3.X < pt2.X);
+  else return (pt1.Y < pt3.Y) == (pt3.Y < pt2.Y);
+}
+//------------------------------------------------------------------------------
+
+OutPt* InsertPolyPtBetween(OutPt* p1, OutPt* p2, const IntPoint pt)
+{
+  if (p1 == p2) throw "JoinError";
+  OutPt* result = new OutPt;
+  result->pt = pt;
+  if (p2 == p1->next)
+  {
+    p1->next = result;
+    p2->prev = result;
+    result->next = p2;
+    result->prev = p1;
+  } else
+  {
+    p2->next = result;
+    p1->prev = result;
+    result->next = p1;
+    result->prev = p2;
+  }
+  return result;
+}
+
+//------------------------------------------------------------------------------
+// ClipperBase class methods ...
+//------------------------------------------------------------------------------
+
+ClipperBase::ClipperBase() //constructor
+{
+  m_MinimaList = 0;
+  m_CurrentLM = 0;
+  m_UseFullRange = true;
+}
+//------------------------------------------------------------------------------
+
+ClipperBase::~ClipperBase() //destructor
+{
+  Clear();
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::AddPolygon( const Polygon &pg, PolyType polyType)
+{
+  int len = (int)pg.size();
+  if (len < 3) return false;
+  Polygon p(len);
+  p[0] = pg[0];
+  int j = 0;
+
+  long64 maxVal;
+  if (m_UseFullRange) maxVal = hiRange; else maxVal = loRange;
+
+  for (int i = 0; i < len; ++i)
+  {
+    if (Abs(pg[i].X) > maxVal || Abs(pg[i].Y) > maxVal)
+    {
+      if (m_UseFullRange)
+        throw "Coordinate exceeds range bounds";
+      maxVal = hiRange;
+      if (Abs(pg[i].X) > maxVal || Abs(pg[i].Y) > maxVal)
+        throw "Coordinate exceeds range bounds";
+      m_UseFullRange = true;
+    }
+
+    if (i == 0 || PointsEqual(p[j], pg[i])) continue;
+    else if (j > 0 && SlopesEqual(p[j-1], p[j], pg[i], m_UseFullRange))
+    {
+      if (PointsEqual(p[j-1], pg[i])) j--;
+    } else j++;
+    p[j] = pg[i];
+  }
+  if (j < 2) return false;
+
+  len = j+1;
+  for (;;)
+  {
+    //nb: test for point equality before testing slopes ...
+    if (PointsEqual(p[j], p[0])) j--;
+    else if (PointsEqual(p[0], p[1]) ||
+      SlopesEqual(p[j], p[0], p[1], m_UseFullRange))
+      p[0] = p[j--];
+    else if (SlopesEqual(p[j-1], p[j], p[0], m_UseFullRange)) j--;
+    else if (SlopesEqual(p[0], p[1], p[2], m_UseFullRange))
+    {
+      for (int i = 2; i <= j; ++i) p[i-1] = p[i];
+      j--;
+    }
+    //exit loop if nothing is changed or there are too few vertices ...
+    if (j == len-1 || j < 2) break;
+    len = j +1;
+  }
+  if (len < 3) return false;
+
+  //create a new edge array ...
+  TEdge *edges = new TEdge [len];
+  m_edges.push_back(edges);
+
+  //convert vertices to a double-linked-list of edges and initialize ...
+  edges[0].xcurr = p[0].X;
+  edges[0].ycurr = p[0].Y;
+  InitEdge(&edges[len-1], &edges[0], &edges[len-2], p[len-1], polyType);
+  for (int i = len-2; i > 0; --i)
+    InitEdge(&edges[i], &edges[i+1], &edges[i-1], p[i], polyType);
+  InitEdge(&edges[0], &edges[1], &edges[len-1], p[0], polyType);
+
+  //reset xcurr & ycurr and find 'eHighest' (given the Y axis coordinates
+  //increase downward so the 'highest' edge will have the smallest ytop) ...
+  TEdge *e = &edges[0];
+  TEdge *eHighest = e;
+  do
+  {
+    e->xcurr = e->xbot;
+    e->ycurr = e->ybot;
+    if (e->ytop < eHighest->ytop) eHighest = e;
+    e = e->next;
+  }
+  while ( e != &edges[0]);
+
+  //make sure eHighest is positioned so the following loop works safely ...
+  if (eHighest->windDelta > 0) eHighest = eHighest->next;
+  if (NEAR_EQUAL(eHighest->dx, HORIZONTAL)) eHighest = eHighest->next;
+
+  //finally insert each local minima ...
+  e = eHighest;
+  do {
+    e = AddBoundsToLML(e);
+  }
+  while( e != eHighest );
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::InsertLocalMinima(LocalMinima *newLm)
+{
+  if( ! m_MinimaList )
+  {
+    m_MinimaList = newLm;
+  }
+  else if( newLm->Y >= m_MinimaList->Y )
+  {
+    newLm->next = m_MinimaList;
+    m_MinimaList = newLm;
+  } else
+  {
+    LocalMinima* tmpLm = m_MinimaList;
+    while( tmpLm->next  && ( newLm->Y < tmpLm->next->Y ) )
+      tmpLm = tmpLm->next;
+    newLm->next = tmpLm->next;
+    tmpLm->next = newLm;
+  }
+}
+//------------------------------------------------------------------------------
+
+TEdge* ClipperBase::AddBoundsToLML(TEdge *e)
+{
+  //Starting at the top of one bound we progress to the bottom where there's
+  //a local minima. We then go to the top of the next bound. These two bounds
+  //form the left and right (or right and left) bounds of the local minima.
+  e->nextInLML = 0;
+  e = e->next;
+  for (;;)
+  {
+    if (NEAR_EQUAL(e->dx, HORIZONTAL))
+    {
+      //nb: proceed through horizontals when approaching from their right,
+      //    but break on horizontal minima if approaching from their left.
+      //    This ensures 'local minima' are always on the left of horizontals.
+      if (e->next->ytop < e->ytop && e->next->xbot > e->prev->xbot) break;
+      if (e->xtop != e->prev->xbot) SwapX(*e);
+      e->nextInLML = e->prev;
+    }
+    else if (e->ycurr == e->prev->ycurr) break;
+    else e->nextInLML = e->prev;
+    e = e->next;
+  }
+
+  //e and e.prev are now at a local minima ...
+  LocalMinima* newLm = new LocalMinima;
+  newLm->next = 0;
+  newLm->Y = e->prev->ybot;
+
+  if ( NEAR_EQUAL(e->dx, HORIZONTAL) ) //horizontal edges never start a left bound
+  {
+    if (e->xbot != e->prev->xbot) SwapX(*e);
+    newLm->leftBound = e->prev;
+    newLm->rightBound = e;
+  } else if (e->dx < e->prev->dx)
+  {
+    newLm->leftBound = e->prev;
+    newLm->rightBound = e;
+  } else
+  {
+    newLm->leftBound = e;
+    newLm->rightBound = e->prev;
+  }
+  newLm->leftBound->side = esLeft;
+  newLm->rightBound->side = esRight;
+  InsertLocalMinima( newLm );
+
+  for (;;)
+  {
+    if ( e->next->ytop == e->ytop && !NEAR_EQUAL(e->next->dx, HORIZONTAL) ) break;
+    e->nextInLML = e->next;
+    e = e->next;
+    if ( NEAR_EQUAL(e->dx, HORIZONTAL) && e->xbot != e->prev->xtop) SwapX(*e);
+  }
+  return e->next;
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::AddPolygons(const Polygons &ppg, PolyType polyType)
+{
+  bool result = true;
+  for (Polygons::size_type i = 0; i < ppg.size(); ++i)
+    if (AddPolygon(ppg[i], polyType)) result = false;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::Clear()
+{
+  DisposeLocalMinimaList();
+  for (EdgeList::size_type i = 0; i < m_edges.size(); ++i) delete [] m_edges[i];
+  m_edges.clear();
+  m_UseFullRange = false;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::Reset()
+{
+  m_CurrentLM = m_MinimaList;
+  if( !m_CurrentLM ) return; //ie nothing to process
+
+  //reset all edges ...
+  LocalMinima* lm = m_MinimaList;
+  while( lm )
+  {
+    TEdge* e = lm->leftBound;
+    while( e )
+    {
+      e->xcurr = e->xbot;
+      e->ycurr = e->ybot;
+      e->side = esLeft;
+      e->outIdx = -1;
+      e = e->nextInLML;
+    }
+    e = lm->rightBound;
+    while( e )
+    {
+      e->xcurr = e->xbot;
+      e->ycurr = e->ybot;
+      e->side = esRight;
+      e->outIdx = -1;
+      e = e->nextInLML;
+    }
+    lm = lm->next;
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::DisposeLocalMinimaList()
+{
+  while( m_MinimaList )
+  {
+    LocalMinima* tmpLm = m_MinimaList->next;
+    delete m_MinimaList;
+    m_MinimaList = tmpLm;
+  }
+  m_CurrentLM = 0;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::PopLocalMinima()
+{
+  if( ! m_CurrentLM ) return;
+  m_CurrentLM = m_CurrentLM->next;
+}
+//------------------------------------------------------------------------------
+
+IntRect ClipperBase::GetBounds()
+{
+  IntRect result;
+  LocalMinima* lm = m_MinimaList;
+  if (!lm)
+  {
+    result.left = result.top = result.right = result.bottom = 0;
+    return result;
+  }
+  result.left = lm->leftBound->xbot;
+  result.top = lm->leftBound->ybot;
+  result.right = lm->leftBound->xbot;
+  result.bottom = lm->leftBound->ybot;
+  while (lm)
+  {
+    if (lm->leftBound->ybot > result.bottom)
+      result.bottom = lm->leftBound->ybot;
+    TEdge* e = lm->leftBound;
+    for (;;) {
+      TEdge* bottomE = e;
+      while (e->nextInLML)
+      {
+        if (e->xbot < result.left) result.left = e->xbot;
+        if (e->xbot > result.right) result.right = e->xbot;
+        e = e->nextInLML;
+      }
+      if (e->xbot < result.left) result.left = e->xbot;
+      if (e->xbot > result.right) result.right = e->xbot;
+      if (e->xtop < result.left) result.left = e->xtop;
+      if (e->xtop > result.right) result.right = e->xtop;
+      if (e->ytop < result.top) result.top = e->ytop;
+
+      if (bottomE == lm->leftBound) e = lm->rightBound;
+      else break;
+    }
+    lm = lm->next;
+  }
+  return result;
+}
+
+
+//------------------------------------------------------------------------------
+// TClipper methods ...
+//------------------------------------------------------------------------------
+
+Clipper::Clipper() : ClipperBase() //constructor
+{
+  m_Scanbeam = 0;
+  m_ActiveEdges = 0;
+  m_SortedEdges = 0;
+  m_IntersectNodes = 0;
+  m_ExecuteLocked = false;
+  m_UseFullRange = false;
+  m_ReverseOutput = false;
+}
+//------------------------------------------------------------------------------
+
+Clipper::~Clipper() //destructor
+{
+  Clear();
+  DisposeScanbeamList();
+}
+//------------------------------------------------------------------------------
+
+void Clipper::Clear()
+{
+  if (m_edges.size() == 0) return; //avoids problems with ClipperBase destructor
+  DisposeAllPolyPts();
+  ClipperBase::Clear();
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DisposeScanbeamList()
+{
+  while ( m_Scanbeam ) {
+  Scanbeam* sb2 = m_Scanbeam->next;
+  delete m_Scanbeam;
+  m_Scanbeam = sb2;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::Reset()
+{
+  ClipperBase::Reset();
+  m_Scanbeam = 0;
+  m_ActiveEdges = 0;
+  m_SortedEdges = 0;
+  LocalMinima* lm = m_MinimaList;
+  while (lm)
+  {
+    InsertScanbeam(lm->Y);
+    InsertScanbeam(lm->leftBound->ytop);
+    lm = lm->next;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::Execute(ClipType clipType, Polygons &solution,
+    PolyFillType subjFillType, PolyFillType clipFillType)
+{
+  if( m_ExecuteLocked ) return false;
+  m_ExecuteLocked = true;
+  solution.resize(0);
+  m_SubjFillType = subjFillType;
+  m_ClipFillType = clipFillType;
+  m_ClipType = clipType;
+  bool succeeded = ExecuteInternal(false);
+  if (succeeded) BuildResult(solution);
+  m_ExecuteLocked = false;
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::Execute(ClipType clipType, ExPolygons &solution,
+    PolyFillType subjFillType, PolyFillType clipFillType)
+{
+  if( m_ExecuteLocked ) return false;
+  m_ExecuteLocked = true;
+  solution.resize(0);
+  m_SubjFillType = subjFillType;
+  m_ClipFillType = clipFillType;
+  m_ClipType = clipType;
+  bool succeeded = ExecuteInternal(true);
+  if (succeeded) BuildResultEx(solution);
+  m_ExecuteLocked = false;
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+bool PolySort(OutRec *or1, OutRec *or2)
+{
+  if (or1 == or2) return false;
+  if (!or1->pts || !or2->pts)
+  {
+    if (or1->pts != or2->pts)
+    {
+      if (or1->pts) return true; else return false;
+    }
+    else return false;
+  }
+  int i1, i2;
+  if (or1->isHole)
+    i1 = or1->FirstLeft->idx; else
+    i1 = or1->idx;
+  if (or2->isHole)
+    i2 = or2->FirstLeft->idx; else
+    i2 = or2->idx;
+  int result = i1 - i2;
+  if (result == 0 && (or1->isHole != or2->isHole))
+  {
+    if (or1->isHole) return false;
+    else return true;
+  }
+  else return result < 0;
+}
+//------------------------------------------------------------------------------
+
+OutRec* FindAppendLinkEnd(OutRec *outRec)
+{
+  while (outRec->AppendLink) outRec = outRec->AppendLink;
+  return outRec;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::FixHoleLinkage(OutRec *outRec)
+{
+  OutRec *tmp;
+  if (outRec->bottomPt)
+    tmp = m_PolyOuts[outRec->bottomPt->idx]->FirstLeft;
+  else
+    tmp = outRec->FirstLeft;
+  if (outRec == tmp) throw clipperException("HoleLinkage error");
+
+  if (tmp)
+  {
+    if (tmp->AppendLink) tmp = FindAppendLinkEnd(tmp);
+    if (tmp == outRec) tmp = 0;
+    else if (tmp->isHole)
+    {
+      FixHoleLinkage(tmp);
+      tmp = tmp->FirstLeft;
+    }
+  }
+  outRec->FirstLeft = tmp;
+  if (!tmp) outRec->isHole = false;
+  outRec->AppendLink = 0;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::ExecuteInternal(bool fixHoleLinkages)
+{
+  bool succeeded;
+  try {
+    Reset();
+    if (!m_CurrentLM ) return true;
+    long64 botY = PopScanbeam();
+    do {
+      InsertLocalMinimaIntoAEL(botY);
+      ClearHorzJoins();
+      ProcessHorizontals();
+      long64 topY = PopScanbeam();
+      succeeded = ProcessIntersections(botY, topY);
+      if (!succeeded) break;
+      ProcessEdgesAtTopOfScanbeam(topY);
+      botY = topY;
+    } while( m_Scanbeam );
+  }
+  catch(...) {
+    succeeded = false;
+  }
+
+  if (succeeded)
+  {
+    //tidy up output polygons and fix orientations where necessary ...
+    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    {
+      OutRec *outRec = m_PolyOuts[i];
+      if (!outRec->pts) continue;
+      FixupOutPolygon(*outRec);
+      if (!outRec->pts) continue;
+      if (outRec->isHole && fixHoleLinkages) FixHoleLinkage(outRec);
+      if (outRec->isHole ==
+        (m_ReverseOutput ^ Orientation(outRec, m_UseFullRange)))
+          ReversePolyPtLinks(*outRec->pts);
+    }
+
+    JoinCommonEdges(fixHoleLinkages);
+    if (fixHoleLinkages)
+      std::sort(m_PolyOuts.begin(), m_PolyOuts.end(), PolySort);
+  }
+
+  ClearJoins();
+  ClearHorzJoins();
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::InsertScanbeam(const long64 Y)
+{
+  if( !m_Scanbeam )
+  {
+    m_Scanbeam = new Scanbeam;
+    m_Scanbeam->next = 0;
+    m_Scanbeam->Y = Y;
+  }
+  else if(  Y > m_Scanbeam->Y )
+  {
+    Scanbeam* newSb = new Scanbeam;
+    newSb->Y = Y;
+    newSb->next = m_Scanbeam;
+    m_Scanbeam = newSb;
+  } else
+  {
+    Scanbeam* sb2 = m_Scanbeam;
+    while( sb2->next  && ( Y <= sb2->next->Y ) ) sb2 = sb2->next;
+    if(  Y == sb2->Y ) return; //ie ignores duplicates
+    Scanbeam* newSb = new Scanbeam;
+    newSb->Y = Y;
+    newSb->next = sb2->next;
+    sb2->next = newSb;
+  }
+}
+//------------------------------------------------------------------------------
+
+long64 Clipper::PopScanbeam()
+{
+  long64 Y = m_Scanbeam->Y;
+  Scanbeam* sb2 = m_Scanbeam;
+  m_Scanbeam = m_Scanbeam->next;
+  delete sb2;
+  return Y;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DisposeAllPolyPts(){
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    DisposeOutRec(i);
+  m_PolyOuts.clear();
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DisposeOutRec(PolyOutList::size_type index, bool ignorePts)
+{
+  OutRec *outRec = m_PolyOuts[index];
+  if (!ignorePts && 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->polyType != edge.polyType ) e = e->prevInAEL;
+  if ( !e )
+  {
+    edge.windCnt = edge.windDelta;
+    edge.windCnt2 = 0;
+    e = m_ActiveEdges; //ie get ready to calc windCnt2
+  } else if ( IsEvenOddFillType(edge) )
+  {
+    //EvenOdd filling ...
+    edge.windCnt = 1;
+    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 )
+    {
+      if (Abs(e->windCnt) > 1)
+      {
+        if (e->windDelta * edge.windDelta < 0) edge.windCnt = e->windCnt;
+        else edge.windCnt = e->windCnt + edge.windDelta;
+      } else
+        edge.windCnt = e->windCnt + e->windDelta + edge.windDelta;
+    } else
+    {
+      if ( Abs(e->windCnt) > 1 && e->windDelta * edge.windDelta < 0)
+        edge.windCnt = e->windCnt;
+      else if ( e->windCnt + edge.windDelta == 0 )
+        edge.windCnt = e->windCnt;
+      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 )
+    {
+      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.polyType == ptSubject)
+    return m_SubjFillType == pftEvenOdd; else
+    return m_ClipFillType == pftEvenOdd;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsEvenOddAltFillType(const TEdge& edge) const
+{
+  if (edge.polyType == ptSubject)
+    return m_ClipFillType == pftEvenOdd; else
+    return m_SubjFillType == pftEvenOdd;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsContributing(const TEdge& edge) const
+{
+  PolyFillType pft, pft2;
+  if (edge.polyType == ptSubject)
+  {
+    pft = m_SubjFillType;
+    pft2 = m_ClipFillType;
+  } else
+  {
+    pft = m_ClipFillType;
+    pft2 = m_SubjFillType;
+  }
+
+  switch(pft)
+  {
+    case pftEvenOdd: 
+    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);
+      }
+    case ctUnion:
+      switch(pft2)
+      {
+        case pftEvenOdd: 
+        case pftNonZero: 
+          return (edge.windCnt2 == 0);
+        case pftPositive: 
+          return (edge.windCnt2 <= 0);
+        default: 
+          return (edge.windCnt2 >= 0);
+      }
+    case ctDifference:
+      if (edge.polyType == 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);
+        }
+    default:
+      return true;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &pt)
+{
+  if( NEAR_EQUAL(e2->dx, HORIZONTAL) || ( e1->dx > e2->dx ) )
+  {
+    AddOutPt( e1, e2, pt );
+    e2->outIdx = e1->outIdx;
+    e1->side = esLeft;
+    e2->side = esRight;
+  } else
+  {
+    AddOutPt( e2, e1, pt );
+    e1->outIdx = e2->outIdx;
+    e1->side = esRight;
+    e2->side = esLeft;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &pt)
+{
+  AddOutPt( e1, 0, pt );
+  if( e1->outIdx == e2->outIdx )
+  {
+    e1->outIdx = -1;
+    e2->outIdx = -1;
+  }
+  else
+    AppendPolygon( e1, e2 );
+}
+//------------------------------------------------------------------------------
+
+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;
+  if (!m_ActiveEdges) return;
+  m_SortedEdges->prevInSEL = 0;
+  e = e->nextInAEL;
+  while ( e )
+  {
+    e->prevInSEL = e->prevInAEL;
+    e->prevInSEL->nextInSEL = e;
+    e->nextInSEL = 0;
+    e = e->nextInAEL;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddJoin(TEdge *e1, TEdge *e2, int e1OutIdx, int e2OutIdx)
+{
+  JoinRec* jr = new JoinRec;
+  if (e1OutIdx >= 0)
+    jr->poly1Idx = e1OutIdx; else
+    jr->poly1Idx = e1->outIdx;
+  jr->pt1a = IntPoint(e1->xcurr, e1->ycurr);
+  jr->pt1b = IntPoint(e1->xtop, e1->ytop);
+  if (e2OutIdx >= 0)
+    jr->poly2Idx = e2OutIdx; else
+    jr->poly2Idx = e2->outIdx;
+  jr->pt2a = IntPoint(e2->xcurr, e2->ycurr);
+  jr->pt2b = IntPoint(e2->xtop, e2->ytop);
+  m_Joins.push_back(jr);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ClearJoins()
+{
+  for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
+    delete m_Joins[i];
+  m_Joins.resize(0);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddHorzJoin(TEdge *e, int idx)
+{
+  HorzJoinRec* hj = new HorzJoinRec;
+  hj->edge = e;
+  hj->savedIdx = idx;
+  m_HorizJoins.push_back(hj);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ClearHorzJoins()
+{
+  for (HorzJoinList::size_type i = 0; i < m_HorizJoins.size(); i++)
+    delete m_HorizJoins[i];
+  m_HorizJoins.resize(0);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::InsertLocalMinimaIntoAEL( const long64 botY)
+{
+  while(  m_CurrentLM  && ( m_CurrentLM->Y == botY ) )
+  {
+    TEdge* lb = m_CurrentLM->leftBound;
+    TEdge* rb = m_CurrentLM->rightBound;
+
+    InsertEdgeIntoAEL( lb );
+    InsertScanbeam( lb->ytop );
+    InsertEdgeIntoAEL( rb );
+
+    if (IsEvenOddFillType(*lb))
+    {
+      lb->windDelta = 1;
+      rb->windDelta = 1;
+    }
+    else
+    {
+      rb->windDelta = -lb->windDelta;
+    }
+    SetWindingCount( *lb );
+    rb->windCnt = lb->windCnt;
+    rb->windCnt2 = lb->windCnt2;
+
+    if( NEAR_EQUAL(rb->dx, HORIZONTAL) )
+    {
+      //nb: only rightbounds can have a horizontal bottom edge
+      AddEdgeToSEL( rb );
+      InsertScanbeam( rb->nextInLML->ytop );
+    }
+    else
+      InsertScanbeam( rb->ytop );
+
+    if( IsContributing(*lb) )
+      AddLocalMinPoly( lb, rb, IntPoint(lb->xcurr, m_CurrentLM->Y) );
+
+    //if output polygons share an edge, they'll need joining later ...
+    if (lb->outIdx >= 0 && lb->prevInAEL &&
+      lb->prevInAEL->outIdx >= 0 && lb->prevInAEL->xcurr == lb->xbot &&
+       SlopesEqual(*lb, *lb->prevInAEL, m_UseFullRange))
+         AddJoin(lb, lb->prevInAEL);
+
+    //if any output polygons share an edge, they'll need joining later ...
+    if (rb->outIdx >= 0)
+    {
+      if (NEAR_EQUAL(rb->dx, HORIZONTAL))
+      {
+        for (HorzJoinList::size_type i = 0; i < m_HorizJoins.size(); ++i)
+        {
+          IntPoint pt, pt2; //returned by GetOverlapSegment() but unused here.
+          HorzJoinRec* hj = m_HorizJoins[i];
+          //if horizontals rb and hj.edge overlap, flag for joining later ...
+          if (GetOverlapSegment(IntPoint(hj->edge->xbot, hj->edge->ybot),
+            IntPoint(hj->edge->xtop, hj->edge->ytop),
+            IntPoint(rb->xbot, rb->ybot),
+            IntPoint(rb->xtop, rb->ytop), pt, pt2))
+              AddJoin(hj->edge, rb, hj->savedIdx);
+        }
+      }
+    }
+
+    if( lb->nextInAEL != rb )
+    {
+      if (rb->outIdx >= 0 && rb->prevInAEL->outIdx >= 0 &&
+        SlopesEqual(*rb->prevInAEL, *rb, m_UseFullRange))
+          AddJoin(rb, rb->prevInAEL);
+
+      TEdge* e = lb->nextInAEL;
+      IntPoint pt = IntPoint(lb->xcurr, lb->ycurr);
+      while( e != rb )
+      {
+        if(!e) throw clipperException("InsertLocalMinimaIntoAEL: missing rightbound!");
+        //nb: For calculating winding counts etc, IntersectEdges() assumes
+        //that param1 will be to the right of param2 ABOVE the intersection ...
+        IntersectEdges( rb , e , pt , ipNone); //order important here
+        e = e->nextInAEL;
+      }
+    }
+    PopLocalMinima();
+  }
+}
+//------------------------------------------------------------------------------
+
+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;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::IntersectEdges(TEdge *e1, TEdge *e2,
+     const IntPoint &pt, IntersectProtects protects)
+{
+  //e1 will be to the left of e2 BELOW the intersection. Therefore e1 is before
+  //e2 in AEL except when e1 is being inserted at the intersection point ...
+  bool e1stops = !(ipLeft & protects) &&  !e1->nextInLML &&
+    e1->xtop == pt.X && e1->ytop == pt.Y;
+  bool e2stops = !(ipRight & protects) &&  !e2->nextInLML &&
+    e2->xtop == pt.X && e2->ytop == pt.Y;
+  bool e1Contributing = ( e1->outIdx >= 0 );
+  bool e2contributing = ( e2->outIdx >= 0 );
+
+  //update winding counts...
+  //assumes that e1 will be to the right of e2 ABOVE the intersection
+  if ( e1->polyType == e2->polyType )
+  {
+    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->polyType == ptSubject)
+  {
+    e1FillType = m_SubjFillType;
+    e1FillType2 = m_ClipFillType;
+  } else
+  {
+    e1FillType = m_ClipFillType;
+    e1FillType2 = m_SubjFillType;
+  }
+  if (e2->polyType == ptSubject)
+  {
+    e2FillType = m_SubjFillType;
+    e2FillType2 = m_ClipFillType;
+  } else
+  {
+    e2FillType = m_ClipFillType;
+    e2FillType2 = m_SubjFillType;
+  }
+
+  long64 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 ( e1stops || e2stops || 
+      (e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
+      (e1->polyType != e2->polyType && m_ClipType != ctXor) )
+        AddLocalMaxPoly(e1, e2, pt); 
+    else
+        DoBothEdges( e1, e2, pt );
+  }
+  else if ( e1Contributing )
+  {
+    if ((e2Wc == 0 || e2Wc == 1) && 
+      (m_ClipType != ctIntersection || 
+      e2->polyType == ptSubject || (e2->windCnt2 != 0))) 
+        DoEdge1(e1, e2, pt);
+  }
+  else if ( e2contributing )
+  {
+    if ((e1Wc == 0 || e1Wc == 1) && 
+      (m_ClipType != ctIntersection || 
+      e1->polyType == ptSubject || (e1->windCnt2 != 0))) 
+        DoEdge2(e1, e2, pt);
+  } 
+  else if ( (e1Wc == 0 || e1Wc == 1) && 
+    (e2Wc == 0 || e2Wc == 1) && !e1stops && !e2stops )
+  {
+    //neither edge is currently contributing ...
+
+    long64 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->polyType != e2->polyType)
+        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->polyType == ptClip && e2->polyType == ptClip && 
+              e1Wc2 > 0 && e2Wc2 > 0) || 
+              (e1->polyType == ptSubject && e2->polyType == ptSubject && 
+              e1Wc2 <= 0 && e2Wc2 <= 0)) 
+                AddLocalMinPoly(e1, e2, pt);
+          break;
+        case ctXor:
+          AddLocalMinPoly(e1, e2, pt);
+      }
+    else
+      SwapSides( *e1, *e2 );
+  }
+
+  if(  (e1stops != e2stops) &&
+    ( (e1stops && (e1->outIdx >= 0)) || (e2stops && (e2->outIdx >= 0)) ) )
+  {
+    SwapSides( *e1, *e2 );
+    SwapPolyIndexes( *e1, *e2 );
+  }
+
+  //finally, delete any non-contributing maxima edges  ...
+  if( e1stops ) DeleteFromAEL( e1 );
+  if( e2stops ) DeleteFromAEL( e2 );
+}
+//------------------------------------------------------------------------------
+
+void Clipper::SetHoleState(TEdge *e, OutRec *outRec)
+{
+  bool isHole = false;
+  TEdge *e2 = e->prevInAEL;
+  while (e2)
+  {
+    if (e2->outIdx >= 0)
+    {
+      isHole = !isHole;
+      if (! outRec->FirstLeft)
+        outRec->FirstLeft = m_PolyOuts[e2->outIdx];
+    }
+    e2 = e2->prevInAEL;
+  }
+  if (isHole) outRec->isHole = true;
+}
+//------------------------------------------------------------------------------
+
+bool GetNextNonDupOutPt(OutPt* pp, OutPt*& next)
+{
+  next = pp->next;
+  while (next != pp && PointsEqual(pp->pt, next->pt))
+    next = next->next;
+  return next != pp;
+}
+//------------------------------------------------------------------------------
+
+bool GetPrevNonDupOutPt(OutPt* pp, OutPt*& prev)
+{
+  prev = pp->prev;
+  while (prev != pp && PointsEqual(pp->pt, prev->pt))
+    prev = prev->prev;
+  return prev != pp;
+}
+//------------------------------------------------------------------------------
+
+OutRec* GetLowermostRec(OutRec *outRec1, OutRec *outRec2)
+{
+  //work out which polygon fragment has the correct hole state ...
+  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 (outRec1->bottomE2 == 0) return outRec2;
+  else if (outRec2->bottomE2 == 0) return outRec1;
+  else
+  {
+    long64 y1 = std::max(outRec1->bottomE1->ybot, outRec1->bottomE2->ybot);
+    long64 y2 = std::max(outRec2->bottomE1->ybot, outRec2->bottomE2->ybot);
+    if (y2 == y1 || (y1 > outPt1->pt.Y && y2 > outPt1->pt.Y))
+    {
+      double dx1 = std::max(outRec1->bottomE1->dx, outRec1->bottomE2->dx);
+      double dx2 = std::max(outRec2->bottomE1->dx, outRec2->bottomE2->dx);
+      if (dx2 > dx1) return outRec2; else return outRec1;
+    }
+    else if (y2 > y1) return outRec2;
+    else return outRec1;
+  }
+}
+//------------------------------------------------------------------------------
+
+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 = GetLowermostRec(outRec1, outRec2);
+
+  //fixup hole status ...
+  if (holeStateRec == outRec2)
+    outRec1->isHole = outRec2->isHole;
+  else
+    outRec2->isHole = outRec1->isHole;
+
+  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;
+  }
+
+  if (holeStateRec == outRec2)
+  {
+    outRec1->bottomPt = outRec2->bottomPt;
+    outRec1->bottomPt->idx = outRec1->idx;
+    outRec1->bottomE1 = outRec2->bottomE1;
+    outRec1->bottomE2 = outRec2->bottomE2;
+
+    if (outRec2->FirstLeft != outRec1)
+      outRec1->FirstLeft = outRec2->FirstLeft;
+  }
+  outRec2->pts = 0;
+  outRec2->bottomPt = 0;
+  outRec2->AppendLink = outRec1;
+  int OKIdx = e1->outIdx;
+  int ObsoleteIdx = e2->outIdx;
+
+  e1->outIdx = -1; //nb: safe because we only get here via AddLocalMaxPoly
+  e2->outIdx = -1;
+
+  TEdge* e = m_ActiveEdges;
+  while( e )
+  {
+    if( e->outIdx == ObsoleteIdx )
+    {
+      e->outIdx = OKIdx;
+      e->side = side;
+      break;
+    }
+    e = e->nextInAEL;
+  }
+
+  for (JoinList::size_type i = 0; i < m_Joins.size(); ++i)
+  {
+      if (m_Joins[i]->poly1Idx == ObsoleteIdx) m_Joins[i]->poly1Idx = OKIdx;
+      if (m_Joins[i]->poly2Idx == ObsoleteIdx) m_Joins[i]->poly2Idx = OKIdx;
+  }
+
+  for (HorzJoinList::size_type i = 0; i < m_HorizJoins.size(); ++i)
+  {
+      if (m_HorizJoins[i]->savedIdx == ObsoleteIdx)
+        m_HorizJoins[i]->savedIdx = OKIdx;
+  }
+
+}
+//------------------------------------------------------------------------------
+
+OutRec* Clipper::CreateOutRec()
+{
+  OutRec* result = new OutRec;
+  result->isHole = false;
+  result->FirstLeft = 0;
+  result->AppendLink = 0;
+  result->pts = 0;
+  result->bottomPt = 0;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddOutPt(TEdge *e, TEdge *altE, const IntPoint &pt)
+{
+  bool ToFront = (e->side == esLeft);
+  if(  e->outIdx < 0 )
+  {
+    OutRec *outRec = CreateOutRec();
+    m_PolyOuts.push_back(outRec);
+    outRec->idx = (int)m_PolyOuts.size()-1;
+    e->outIdx = outRec->idx;
+    OutPt* op = new OutPt;
+    outRec->pts = op;
+    outRec->bottomE1 = e;
+    outRec->bottomE2 = altE;
+    outRec->bottomPt = op;
+    op->pt = pt;
+    op->idx = outRec->idx;
+    op->next = op;
+    op->prev = op;
+    SetHoleState(e, outRec);
+  } else
+  {
+    OutRec *outRec = m_PolyOuts[e->outIdx];
+    OutPt* op = outRec->pts;
+    if ((ToFront && PointsEqual(pt, op->pt)) ||
+      (!ToFront && PointsEqual(pt, op->prev->pt))) return;
+    OutPt* op2 = new OutPt;
+    op2->pt = pt;
+    op2->idx = outRec->idx;
+    if (op2->pt.Y == outRec->bottomPt->pt.Y &&
+      op2->pt.X < outRec->bottomPt->pt.X)
+    {
+      outRec->bottomPt = op2;
+      outRec->bottomE1 = e;
+      outRec->bottomE2 = altE;
+    }
+    op2->next = op;
+    op2->prev = op->prev;
+    op2->prev->next = op2;
+    op->prev = op2;
+    if (ToFront) outRec->pts = op2;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessHorizontals()
+{
+  TEdge* horzEdge = m_SortedEdges;
+  while( horzEdge )
+  {
+    DeleteFromSEL( horzEdge );
+    ProcessHorizontal( horzEdge );
+    horzEdge = m_SortedEdges;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsTopHorz(const long64 XPos)
+{
+  TEdge* e = m_SortedEdges;
+  while( e )
+  {
+    if(  ( XPos >= std::min(e->xcurr, e->xtop) ) &&
+      ( XPos <= std::max(e->xcurr, e->xtop) ) ) return false;
+    e = e->nextInSEL;
+  }
+  return true;
+}
+//------------------------------------------------------------------------------
+
+bool IsMinima(TEdge *e)
+{
+  return e  && (e->prev->nextInLML != e) && (e->next->nextInLML != e);
+}
+//------------------------------------------------------------------------------
+
+bool IsMaxima(TEdge *e, const long64 Y)
+{
+  return e && e->ytop == Y && !e->nextInLML;
+}
+//------------------------------------------------------------------------------
+
+bool IsIntermediate(TEdge *e, const long64 Y)
+{
+  return e->ytop == Y && e->nextInLML;
+}
+//------------------------------------------------------------------------------
+
+TEdge *GetMaximaPair(TEdge *e)
+{
+  if( !IsMaxima(e->next, e->ytop) || e->next->xtop != e->xtop )
+    return e->prev; else
+    return e->next;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::SwapPositionsInAEL(TEdge *edge1, TEdge *edge2)
+{
+  if(  !edge1->nextInAEL &&  !edge1->prevInAEL ) return;
+  if(  !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)
+{
+  if( dir == dLeftToRight ) return e->nextInAEL;
+  else return e->prevInAEL;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessHorizontal(TEdge *horzEdge)
+{
+  Direction dir;
+  long64 horzLeft, horzRight;
+
+  if( horzEdge->xcurr < horzEdge->xtop )
+  {
+    horzLeft = horzEdge->xcurr;
+    horzRight = horzEdge->xtop;
+    dir = dLeftToRight;
+  } else
+  {
+    horzLeft = horzEdge->xtop;
+    horzRight = horzEdge->xcurr;
+    dir = dRightToLeft;
+  }
+
+  TEdge* eMaxPair;
+  if( horzEdge->nextInLML ) eMaxPair = 0;
+  else eMaxPair = GetMaximaPair(horzEdge);
+
+  TEdge* e = GetNextInAEL( horzEdge , dir );
+  while( e )
+  {
+    TEdge* eNext = GetNextInAEL( e, dir );
+
+    if (eMaxPair ||
+      ((dir == dLeftToRight) && (e->xcurr <= horzRight)) ||
+      ((dir == dRightToLeft) && (e->xcurr >= horzLeft)))
+    {
+      //ok, so far it looks like we're still in range of the horizontal edge
+      if ( e->xcurr == horzEdge->xtop && !eMaxPair )
+      {
+        if (SlopesEqual(*e, *horzEdge->nextInLML, m_UseFullRange))
+        {
+          //if output polygons share an edge, they'll need joining later ...
+          if (horzEdge->outIdx >= 0 && e->outIdx >= 0)
+            AddJoin(horzEdge->nextInLML, e, horzEdge->outIdx);
+          break; //we've reached the end of the horizontal line
+        }
+        else if (e->dx < horzEdge->nextInLML->dx)
+        //we really have got to the end of the intermediate horz edge so quit.
+        //nb: More -ve slopes follow more +ve slopes ABOVE the horizontal.
+          break;
+      }
+
+      if( e == eMaxPair )
+      {
+        //horzEdge is evidently a maxima horizontal and we've arrived at its end.
+        if (dir == dLeftToRight)
+          IntersectEdges(horzEdge, e, IntPoint(e->xcurr, horzEdge->ycurr), ipNone);
+        else
+          IntersectEdges(e, horzEdge, IntPoint(e->xcurr, horzEdge->ycurr), ipNone);
+        if (eMaxPair->outIdx >= 0) throw clipperException("ProcessHorizontal error");
+        return;
+      }
+      else if( NEAR_EQUAL(e->dx, HORIZONTAL) &&  !IsMinima(e) && !(e->xcurr > e->xtop) )
+      {
+        //An overlapping horizontal edge. Overlapping horizontal edges are
+        //processed as if layered with the current horizontal edge (horizEdge)
+        //being infinitesimally lower that the next (e). Therfore, we
+        //intersect with e only if e.xcurr is within the bounds of horzEdge ...
+        if( dir == dLeftToRight )
+          IntersectEdges( horzEdge , e, IntPoint(e->xcurr, horzEdge->ycurr),
+            (IsTopHorz( e->xcurr ))? ipLeft : ipBoth );
+        else
+          IntersectEdges( e, horzEdge, IntPoint(e->xcurr, horzEdge->ycurr),
+            (IsTopHorz( e->xcurr ))? ipRight : ipBoth );
+      }
+      else if( dir == dLeftToRight )
+      {
+        IntersectEdges( horzEdge, e, IntPoint(e->xcurr, horzEdge->ycurr),
+          (IsTopHorz( e->xcurr ))? ipLeft : ipBoth );
+      }
+      else
+      {
+        IntersectEdges( e, horzEdge, IntPoint(e->xcurr, horzEdge->ycurr),
+          (IsTopHorz( e->xcurr ))? ipRight : ipBoth );
+      }
+      SwapPositionsInAEL( horzEdge, e );
+    }
+    else if( (dir == dLeftToRight && e->xcurr > horzRight  && m_SortedEdges) ||
+     (dir == dRightToLeft && e->xcurr < horzLeft && m_SortedEdges) ) break;
+    e = eNext;
+  } //end while
+
+  if( horzEdge->nextInLML )
+  {
+    if( horzEdge->outIdx >= 0 )
+      AddOutPt( horzEdge, 0, IntPoint(horzEdge->xtop, horzEdge->ytop));
+    UpdateEdgeIntoAEL( horzEdge );
+  }
+  else
+  {
+    if ( horzEdge->outIdx >= 0 )
+      IntersectEdges( horzEdge, eMaxPair,
+      IntPoint(horzEdge->xtop, horzEdge->ycurr), ipBoth);
+    if (eMaxPair->outIdx >= 0) throw clipperException("ProcessHorizontal error");
+    DeleteFromAEL(eMaxPair);
+    DeleteFromAEL(horzEdge);
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::UpdateEdgeIntoAEL(TEdge *&e)
+{
+  if( !e->nextInLML ) throw
+    clipperException("UpdateEdgeIntoAEL: invalid call");
+  TEdge* AelPrev = e->prevInAEL;
+  TEdge* AelNext = e->nextInAEL;
+  e->nextInLML->outIdx = e->outIdx;
+  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->prevInAEL = AelPrev;
+  e->nextInAEL = AelNext;
+  if( !NEAR_EQUAL(e->dx, HORIZONTAL) ) InsertScanbeam( e->ytop );
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::ProcessIntersections(const long64 botY, const long64 topY)
+{
+  if( !m_ActiveEdges ) return true;
+  try {
+    BuildIntersectList(botY, topY);
+    if ( !m_IntersectNodes) return true;
+    if ( FixupIntersections() ) ProcessIntersectList();
+    else return false;
+  }
+  catch(...) {
+    m_SortedEdges = 0;
+    DisposeIntersectNodes();
+    throw clipperException("ProcessIntersections error");
+  }
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DisposeIntersectNodes()
+{
+  while ( m_IntersectNodes )
+  {
+    IntersectNode* iNode = m_IntersectNodes->next;
+    delete m_IntersectNodes;
+    m_IntersectNodes = iNode;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildIntersectList(const long64 botY, const long64 topY)
+{
+  if ( !m_ActiveEdges ) return;
+
+  //prepare for sorting ...
+  TEdge* e = m_ActiveEdges;
+  e->tmpX = TopX( *e, topY );
+  m_SortedEdges = e;
+  m_SortedEdges->prevInSEL = 0;
+  e = e->nextInAEL;
+  while( e )
+  {
+    e->prevInSEL = e->prevInAEL;
+    e->prevInSEL->nextInSEL = e;
+    e->nextInSEL = 0;
+    e->tmpX = TopX( *e, topY );
+    e = e->nextInAEL;
+  }
+
+  //bubblesort ...
+  bool isModified = true;
+  while( isModified && m_SortedEdges )
+  {
+    isModified = false;
+    e = m_SortedEdges;
+    while( e->nextInSEL )
+    {
+      TEdge *eNext = e->nextInSEL;
+      IntPoint pt;
+      if(e->tmpX > eNext->tmpX &&
+        IntersectPoint(*e, *eNext, pt, m_UseFullRange))
+      {
+        if (pt.Y > botY)
+        {
+            pt.Y = botY;
+            pt.X = TopX(*e, pt.Y);
+        }
+        AddIntersectNode( e, eNext, pt );
+        SwapPositionsInSEL(e, eNext);
+        isModified = true;
+      }
+      else
+        e = eNext;
+    }
+    if( e->prevInSEL ) e->prevInSEL->nextInSEL = 0;
+    else break;
+  }
+  m_SortedEdges = 0;
+}
+//------------------------------------------------------------------------------
+
+bool Process1Before2(IntersectNode &node1, IntersectNode &node2)
+{
+  bool result;
+  if (node1.pt.Y == node2.pt.Y)
+  {
+    if (node1.edge1 == node2.edge1 || node1.edge2 == node2.edge1)
+    {
+      result = node2.pt.X > node1.pt.X;
+      if (node2.edge1->dx > 0) return !result; else return result;
+    }
+    else if (node1.edge1 == node2.edge2 || node1.edge2 == node2.edge2)
+    {
+      result = node2.pt.X > node1.pt.X;
+      if (node2.edge2->dx > 0) return !result; else return result;
+    }
+    else return node2.pt.X > node1.pt.X;
+  }
+  else return node1.pt.Y > node2.pt.Y;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddIntersectNode(TEdge *e1, TEdge *e2, const IntPoint &pt)
+{
+  IntersectNode* newNode = new IntersectNode;
+  newNode->edge1 = e1;
+  newNode->edge2 = e2;
+  newNode->pt = pt;
+  newNode->next = 0;
+  if( !m_IntersectNodes ) m_IntersectNodes = newNode;
+  else if(  Process1Before2(*newNode, *m_IntersectNodes) )
+  {
+    newNode->next = m_IntersectNodes;
+    m_IntersectNodes = newNode;
+  }
+  else
+  {
+    IntersectNode* iNode = m_IntersectNodes;
+    while( iNode->next  && Process1Before2(*iNode->next, *newNode) )
+        iNode = iNode->next;
+    newNode->next = iNode->next;
+    iNode->next = newNode;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessIntersectList()
+{
+  while( m_IntersectNodes )
+  {
+    IntersectNode* iNode = m_IntersectNodes->next;
+    {
+      IntersectEdges( m_IntersectNodes->edge1 ,
+        m_IntersectNodes->edge2 , m_IntersectNodes->pt, ipBoth );
+      SwapPositionsInAEL( m_IntersectNodes->edge1 , m_IntersectNodes->edge2 );
+    }
+    delete m_IntersectNodes;
+    m_IntersectNodes = iNode;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DoMaxima(TEdge *e, long64 topY)
+{
+  TEdge* eMaxPair = GetMaximaPair(e);
+  long64 X = e->xtop;
+  TEdge* eNext = e->nextInAEL;
+  while( eNext != eMaxPair )
+  {
+    if (!eNext) throw clipperException("DoMaxima error");
+    IntersectEdges( e, eNext, IntPoint(X, topY), ipBoth );
+    eNext = eNext->nextInAEL;
+  }
+  if( e->outIdx < 0 && eMaxPair->outIdx < 0 )
+  {
+    DeleteFromAEL( e );
+    DeleteFromAEL( eMaxPair );
+  }
+  else if( e->outIdx >= 0 && eMaxPair->outIdx >= 0 )
+  {
+    IntersectEdges( e, eMaxPair, IntPoint(X, topY), ipNone );
+  }
+  else throw clipperException("DoMaxima error");
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessEdgesAtTopOfScanbeam(const long64 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.
+    if( IsMaxima(e, topY) && !NEAR_EQUAL(GetMaximaPair(e)->dx, HORIZONTAL) )
+    {
+      //'e' might be removed from AEL, as may any following edges so ...
+      TEdge* ePrior = e->prevInAEL;
+      DoMaxima(e, topY);
+      if( !ePrior ) e = m_ActiveEdges;
+      else e = ePrior->nextInAEL;
+    }
+    else
+    {
+      //2. promote horizontal edges, otherwise update xcurr and ycurr ...
+      if(  IsIntermediate(e, topY) && NEAR_EQUAL(e->nextInLML->dx, HORIZONTAL) )
+      {
+        if (e->outIdx >= 0)
+        {
+          AddOutPt(e, 0, IntPoint(e->xtop, e->ytop));
+
+          for (HorzJoinList::size_type i = 0; i < m_HorizJoins.size(); ++i)
+          {
+            IntPoint pt, pt2;
+            HorzJoinRec* hj = m_HorizJoins[i];
+            if (GetOverlapSegment(IntPoint(hj->edge->xbot, hj->edge->ybot),
+              IntPoint(hj->edge->xtop, hj->edge->ytop),
+              IntPoint(e->nextInLML->xbot, e->nextInLML->ybot),
+              IntPoint(e->nextInLML->xtop, e->nextInLML->ytop), pt, pt2))
+                AddJoin(hj->edge, e->nextInLML, hj->savedIdx, e->outIdx);
+          }
+
+          AddHorzJoin(e->nextInLML, e->outIdx);
+        }
+        UpdateEdgeIntoAEL(e);
+        AddEdgeToSEL(e);
+      } else
+      {
+        //this just simplifies horizontal processing ...
+        e->xcurr = TopX( *e, topY );
+        e->ycurr = topY;
+      }
+      e = e->nextInAEL;
+    }
+  }
+
+  //3. Process horizontals at the top of the scanbeam ...
+  ProcessHorizontals();
+
+  //4. Promote intermediate vertices ...
+  e = m_ActiveEdges;
+  while( e )
+  {
+    if( IsIntermediate( e, topY ) )
+    {
+      if( e->outIdx >= 0 ) AddOutPt(e, 0, IntPoint(e->xtop,e->ytop));
+      UpdateEdgeIntoAEL(e);
+
+      //if output polygons share an edge, they'll need joining later ...
+      if (e->outIdx >= 0 && e->prevInAEL && e->prevInAEL->outIdx >= 0 &&
+        e->prevInAEL->xcurr == e->xbot && e->prevInAEL->ycurr == e->ybot &&
+        SlopesEqual(IntPoint(e->xbot,e->ybot), IntPoint(e->xtop, e->ytop),
+          IntPoint(e->xbot,e->ybot),
+          IntPoint(e->prevInAEL->xtop, e->prevInAEL->ytop), m_UseFullRange))
+      {
+        AddOutPt(e->prevInAEL, 0, IntPoint(e->xbot, e->ybot));
+        AddJoin(e, e->prevInAEL);
+      }
+      else if (e->outIdx >= 0 && e->nextInAEL && e->nextInAEL->outIdx >= 0 &&
+        e->nextInAEL->ycurr > e->nextInAEL->ytop &&
+        e->nextInAEL->ycurr < e->nextInAEL->ybot &&
+        e->nextInAEL->xcurr == e->xbot && e->nextInAEL->ycurr == e->ybot &&
+        SlopesEqual(IntPoint(e->xbot,e->ybot), IntPoint(e->xtop, e->ytop),
+          IntPoint(e->xbot,e->ybot),
+          IntPoint(e->nextInAEL->xtop, e->nextInAEL->ytop), m_UseFullRange))
+      {
+        AddOutPt(e->nextInAEL, 0, IntPoint(e->xbot, e->ybot));
+        AddJoin(e, e->nextInAEL);
+      }
+    }
+    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.pts = outRec.bottomPt;
+  OutPt *pp = outRec.bottomPt;
+
+  for (;;)
+  {
+    if (pp->prev == pp || pp->prev == pp->next )
+    {
+      DisposeOutPts(pp);
+      outRec.pts = 0;
+      outRec.bottomPt = 0;
+      return;
+    }
+    //test for duplicate points and for same slope (cross-product) ...
+    if ( PointsEqual(pp->pt, pp->next->pt) ||
+      SlopesEqual(pp->prev->pt, pp->pt, pp->next->pt, m_UseFullRange) )
+    {
+      lastOK = 0;
+      OutPt *tmp = pp;
+      if (pp == outRec.bottomPt)
+      {
+          if (tmp->prev->pt.Y > tmp->next->pt.Y)
+            outRec.bottomPt = tmp->prev; else
+            outRec.bottomPt = tmp->next;
+          outRec.pts = outRec.bottomPt;
+          outRec.bottomPt->idx = outRec.idx;
+      }
+      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;
+    }
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildResult(Polygons &polys)
+{
+  int k = 0;
+  polys.resize(m_PolyOuts.size());
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    if (m_PolyOuts[i]->pts)
+    {
+      Polygon* pg = &polys[k];
+      pg->clear();
+      OutPt* p = m_PolyOuts[i]->pts;
+      do
+      {
+        pg->push_back(p->pt);
+        p = p->next;
+      } while (p != m_PolyOuts[i]->pts);
+      //make sure each polygon has at least 3 vertices ...
+      if (pg->size() < 3) pg->clear(); else k++;
+    }
+  }
+  polys.resize(k);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildResultEx(ExPolygons &polys)
+{
+  PolyOutList::size_type i = 0;
+  int k = 0;
+  polys.resize(0);
+  polys.reserve(m_PolyOuts.size());
+  while (i < m_PolyOuts.size() && m_PolyOuts[i]->pts)
+  {
+    ExPolygon epg;
+    OutPt* p = m_PolyOuts[i]->pts;
+    do {
+      epg.outer.push_back(p->pt);
+      p = p->next;
+    } while (p != m_PolyOuts[i]->pts);
+    i++;
+    //make sure polygons have at least 3 vertices ...
+    if (epg.outer.size() < 3) continue;
+    while (i < m_PolyOuts.size()
+      && m_PolyOuts[i]->pts && m_PolyOuts[i]->isHole)
+    {
+      Polygon pg;
+      p = m_PolyOuts[i]->pts;
+      do {
+        pg.push_back(p->pt);
+        p = p->next;
+      } while (p != m_PolyOuts[i]->pts);
+      epg.holes.push_back(pg);
+      i++;
+    }
+    polys.push_back(epg);
+    k++;
+  }
+  polys.resize(k);
+}
+//------------------------------------------------------------------------------
+
+void SwapIntersectNodes(IntersectNode &int1, IntersectNode &int2)
+{
+  TEdge *e1 = int1.edge1;
+  TEdge *e2 = int1.edge2;
+  IntPoint p = int1.pt;
+
+  int1.edge1 = int2.edge1;
+  int1.edge2 = int2.edge2;
+  int1.pt = int2.pt;
+
+  int2.edge1 = e1;
+  int2.edge2 = e2;
+  int2.pt = p;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::FixupIntersections()
+{
+  if ( !m_IntersectNodes->next ) return true;
+
+  CopyAELToSEL();
+  IntersectNode *int1 = m_IntersectNodes;
+  IntersectNode *int2 = m_IntersectNodes->next;
+  while (int2)
+  {
+    TEdge *e1 = int1->edge1;
+    TEdge *e2;
+    if (e1->prevInSEL == int1->edge2) e2 = e1->prevInSEL;
+    else if (e1->nextInSEL == int1->edge2) e2 = e1->nextInSEL;
+    else
+    {
+      //The current intersection is out of order, so try and swap it with
+      //a subsequent intersection ...
+      while (int2)
+      {
+        if (int2->edge1->nextInSEL == int2->edge2 ||
+          int2->edge1->prevInSEL == int2->edge2) break;
+        else int2 = int2->next;
+      }
+      if ( !int2 ) return false; //oops!!!
+
+      //found an intersect node that can be swapped ...
+      SwapIntersectNodes(*int1, *int2);
+      e1 = int1->edge1;
+      e2 = int1->edge2;
+    }
+    SwapPositionsInSEL(e1, e2);
+    int1 = int1->next;
+    int2 = int1->next;
+  }
+
+  m_SortedEdges = 0;
+
+  //finally, check the last intersection too ...
+  return (int1->edge1->prevInSEL == int1->edge2 ||
+    int1->edge1->nextInSEL == int1->edge2);
+}
+//------------------------------------------------------------------------------
+
+bool E2InsertsBeforeE1(TEdge &e1, TEdge &e2)
+{
+  if (e2.xcurr == e1.xcurr) return e2.dx > e1.dx;
+  else return e2.xcurr < e1.xcurr;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::InsertEdgeIntoAEL(TEdge *edge)
+{
+  edge->prevInAEL = 0;
+  edge->nextInAEL = 0;
+  if( !m_ActiveEdges )
+  {
+    m_ActiveEdges = edge;
+  }
+  else if( E2InsertsBeforeE1(*m_ActiveEdges, *edge) )
+  {
+    edge->nextInAEL = m_ActiveEdges;
+    m_ActiveEdges->prevInAEL = edge;
+    m_ActiveEdges = edge;
+  } else
+  {
+    TEdge* e = m_ActiveEdges;
+    while( e->nextInAEL  && !E2InsertsBeforeE1(*e->nextInAEL , *edge) )
+      e = e->nextInAEL;
+    edge->nextInAEL = e->nextInAEL;
+    if( e->nextInAEL ) e->nextInAEL->prevInAEL = edge;
+    edge->prevInAEL = e;
+    e->nextInAEL = edge;
+  }
+}
+//----------------------------------------------------------------------
+
+void Clipper::DoEdge1(TEdge *edge1, TEdge *edge2, const IntPoint &pt)
+{
+  AddOutPt(edge1, edge2, pt);
+  SwapSides(*edge1, *edge2);
+  SwapPolyIndexes(*edge1, *edge2);
+}
+//----------------------------------------------------------------------
+
+void Clipper::DoEdge2(TEdge *edge1, TEdge *edge2, const IntPoint &pt)
+{
+  AddOutPt(edge2, edge1, pt);
+  SwapSides(*edge1, *edge2);
+  SwapPolyIndexes(*edge1, *edge2);
+}
+//----------------------------------------------------------------------
+
+void Clipper::DoBothEdges(TEdge *edge1, TEdge *edge2, const IntPoint &pt)
+{
+  AddOutPt(edge1, edge2, pt);
+  AddOutPt(edge2, edge1, pt);
+  SwapSides( *edge1 , *edge2 );
+  SwapPolyIndexes( *edge1 , *edge2 );
+}
+//----------------------------------------------------------------------
+
+void Clipper::CheckHoleLinkages1(OutRec *outRec1, OutRec *outRec2)
+{
+  //when a polygon is split into 2 polygons, make sure any holes the original
+  //polygon contained link to the correct polygon ...
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    OutRec *orec = m_PolyOuts[i];
+    if (orec->isHole && orec->bottomPt && orec->FirstLeft == outRec1 &&
+      !PointInPolygon(orec->bottomPt->pt, outRec1->pts, m_UseFullRange))
+        orec->FirstLeft = outRec2;
+  }
+}
+//----------------------------------------------------------------------
+
+void Clipper::CheckHoleLinkages2(OutRec *outRec1, OutRec *outRec2)
+{
+  //if a hole is owned by outRec2 then make it owned by outRec1 ...
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    if (m_PolyOuts[i]->isHole && m_PolyOuts[i]->bottomPt &&
+      m_PolyOuts[i]->FirstLeft == outRec2)
+        m_PolyOuts[i]->FirstLeft = outRec1;
+}
+//----------------------------------------------------------------------
+
+void Clipper::JoinCommonEdges(bool fixHoleLinkages)
+{
+  for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
+  {
+    JoinRec* j = m_Joins[i];
+    OutRec *outRec1 = m_PolyOuts[j->poly1Idx];
+    OutPt *pp1a = outRec1->pts;
+    OutRec *outRec2 = m_PolyOuts[j->poly2Idx];
+    OutPt *pp2a = outRec2->pts;
+    IntPoint pt1 = j->pt2a, pt2 = j->pt2b;
+    IntPoint pt3 = j->pt1a, pt4 = j->pt1b;
+    if (!FindSegment(pp1a, pt1, pt2)) continue;
+    if (j->poly1Idx == j->poly2Idx)
+    {
+      //we're searching the same polygon for overlapping segments so
+      //segment 2 mustn't be the same as segment 1 ...
+      pp2a = pp1a->next;
+      if (!FindSegment(pp2a, pt3, pt4) || (pp2a == pp1a)) continue;
+    }
+    else if (!FindSegment(pp2a, pt3, pt4)) continue;
+
+    if (!GetOverlapSegment(pt1, pt2, pt3, pt4, pt1, pt2)) continue;
+
+    OutPt *p1, *p2, *p3, *p4;
+    OutPt *prev = pp1a->prev;
+    //get p1 & p2 polypts - the overlap start & endpoints on poly1
+    if (PointsEqual(pp1a->pt, pt1)) p1 = pp1a;
+    else if (PointsEqual(prev->pt, pt1)) p1 = prev;
+    else p1 = InsertPolyPtBetween(pp1a, prev, pt1);
+
+    if (PointsEqual(pp1a->pt, pt2)) p2 = pp1a;
+    else if (PointsEqual(prev->pt, pt2)) p2 = prev;
+    else if ((p1 == pp1a) || (p1 == prev))
+      p2 = InsertPolyPtBetween(pp1a, prev, pt2);
+    else if (Pt3IsBetweenPt1AndPt2(pp1a->pt, p1->pt, pt2))
+      p2 = InsertPolyPtBetween(pp1a, p1, pt2); else
+      p2 = InsertPolyPtBetween(p1, prev, pt2);
+
+    //get p3 & p4 polypts - the overlap start & endpoints on poly2
+    prev = pp2a->prev;
+    if (PointsEqual(pp2a->pt, pt1)) p3 = pp2a;
+    else if (PointsEqual(prev->pt, pt1)) p3 = prev;
+    else p3 = InsertPolyPtBetween(pp2a, prev, pt1);
+
+    if (PointsEqual(pp2a->pt, pt2)) p4 = pp2a;
+    else if (PointsEqual(prev->pt, pt2)) p4 = prev;
+    else if ((p3 == pp2a) || (p3 == prev))
+      p4 = InsertPolyPtBetween(pp2a, prev, pt2);
+    else if (Pt3IsBetweenPt1AndPt2(pp2a->pt, p3->pt, pt2))
+      p4 = InsertPolyPtBetween(pp2a, p3, pt2); else
+      p4 = InsertPolyPtBetween(p3, prev, pt2);
+
+    //p1.pt == p3.pt and p2.pt == p4.pt so join p1 to p3 and p2 to p4 ...
+    if (p1->next == p2 && p3->prev == p4)
+    {
+      p1->next = p3;
+      p3->prev = p1;
+      p2->prev = p4;
+      p4->next = p2;
+    }
+    else if (p1->prev == p2 && p3->next == p4)
+    {
+      p1->prev = p3;
+      p3->next = p1;
+      p2->next = p4;
+      p4->prev = p2;
+    }
+    else
+      continue; //an orientation is probably wrong
+
+    if (j->poly2Idx == j->poly1Idx)
+    {
+      //instead of joining two polygons, we've just created a new one by
+      //splitting one polygon into two.
+      outRec1->pts = PolygonBottom(p1);
+      outRec1->bottomPt = outRec1->pts;
+      outRec1->bottomPt->idx = outRec1->idx;
+      outRec2 = CreateOutRec();
+      m_PolyOuts.push_back(outRec2);
+      outRec2->idx = (int)m_PolyOuts.size()-1;
+      j->poly2Idx = outRec2->idx;
+      outRec2->pts = PolygonBottom(p2);
+      outRec2->bottomPt = outRec2->pts;
+      outRec2->bottomPt->idx = outRec2->idx;
+
+      if (PointInPolygon(outRec2->pts->pt, outRec1->pts, m_UseFullRange))
+      {
+        outRec2->isHole = !outRec1->isHole;
+        outRec2->FirstLeft = outRec1;
+        if (outRec2->isHole == Orientation(outRec2, m_UseFullRange))
+          ReversePolyPtLinks(*outRec2->pts);
+      } else if (PointInPolygon(outRec1->pts->pt, outRec2->pts, m_UseFullRange))
+      {
+        outRec2->isHole = outRec1->isHole;
+        outRec1->isHole = !outRec2->isHole;
+        outRec2->FirstLeft = outRec1->FirstLeft;
+        outRec1->FirstLeft = outRec2;
+        if (outRec1->isHole == Orientation(outRec1, m_UseFullRange))
+          ReversePolyPtLinks(*outRec1->pts);
+      } else
+      {
+        outRec2->isHole = outRec1->isHole;
+        outRec2->FirstLeft = outRec1->FirstLeft;
+        //make sure any contained holes now link to the correct polygon ...
+        if (fixHoleLinkages) CheckHoleLinkages1(outRec1, outRec2);
+      }
+
+      //now fixup any subsequent joins that match this polygon
+      for (JoinList::size_type k = i+1; k < m_Joins.size(); k++)
+      {
+        JoinRec* j2 = m_Joins[k];
+        if (j2->poly1Idx == j->poly1Idx && PointIsVertex(j2->pt1a, p2))
+          j2->poly1Idx = j->poly2Idx;
+        if (j2->poly2Idx == j->poly1Idx && PointIsVertex(j2->pt2a, p2))
+          j2->poly2Idx = j->poly2Idx;
+      }
+
+      //now cleanup redundant edges too ...
+      FixupOutPolygon(*outRec1);
+      FixupOutPolygon(*outRec2);
+    } else
+    {
+      //joined 2 polygons together ...
+
+      //make sure any holes contained by outRec2 now link to outRec1 ...
+      if (fixHoleLinkages) CheckHoleLinkages2(outRec1, outRec2);
+
+      //delete the obsolete pointer ...
+      int OKIdx = outRec1->idx;
+      int ObsoleteIdx = outRec2->idx;
+      outRec2->pts = 0;
+      outRec2->bottomPt = 0;
+      outRec2->AppendLink = outRec1;
+      //holes are practically always joined to outers, not vice versa ...
+      if (outRec1->isHole && !outRec2->isHole) outRec1->isHole = false;
+
+      //now fixup any subsequent Joins that match this polygon
+      for (JoinList::size_type k = i+1; k < m_Joins.size(); k++)
+      {
+        JoinRec* j2 = m_Joins[k];
+        if (j2->poly1Idx == ObsoleteIdx) j2->poly1Idx = OKIdx;
+        if (j2->poly2Idx == ObsoleteIdx) j2->poly2Idx = OKIdx;
+      }
+
+      //now cleanup redundant edges too ...
+      if (outRec1->pts)
+        FixupOutPolygon(*outRec1);
+      else
+        FixupOutPolygon(*outRec2);
+    }
+  }
+}
+//------------------------------------------------------------------------------
+
+void ReversePoints(Polygon& p)
+{
+  std::reverse(p.begin(), p.end());
+}
+//------------------------------------------------------------------------------
+
+void ReversePoints(Polygons& p)
+{
+  for (Polygons::size_type i = 0; i < p.size(); ++i)
+    ReversePoints(p[i]);
+}
+
+//------------------------------------------------------------------------------
+// OffsetPolygon functions ...
+//------------------------------------------------------------------------------
+
+struct DoublePoint
+{
+  double X;
+  double Y;
+  DoublePoint(double x = 0, double y = 0) : X(x), Y(y) {}
+};
+//------------------------------------------------------------------------------
+
+Polygon BuildArc(const IntPoint &pt,
+  const double a1, const double a2, const double r)
+{
+  int steps = std::max(6, int(std::sqrt(std::fabs(r)) * std::fabs(a2 - a1)));
+  Polygon result(steps);
+  int n = steps - 1;
+  double da = (a2 - a1) / n;
+  double a = a1;
+  for (int i = 0; i <= n; ++i)
+  {
+    result[i].X = pt.X + Round(std::cos(a)*r);
+    result[i].Y = pt.Y + Round(std::sin(a)*r);
+    a += da;
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+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);
+}
+
+//------------------------------------------------------------------------------
+//------------------------------------------------------------------------------
+
+class PolyOffsetBuilder
+{
+private:
+  Polygons m_p;
+  Polygon* m_curr_poly;
+  std::vector<DoublePoint> normals;
+  double m_delta, m_RMin, m_R;
+  size_t m_i, m_j, m_k;
+  static const int buffLength = 128;
+  JoinType m_jointype;
+ 
+public:
+
+PolyOffsetBuilder(const Polygons& in_polys, Polygons& out_polys,
+  double delta, JoinType jointype, double MiterLimit)
+{
+    //nb precondition - out_polys != ptsin_polys
+    if (NEAR_ZERO(delta))
+    {
+        out_polys = in_polys;
+        return;
+    }
+
+    this->m_p = in_polys;
+    this->m_delta = delta;
+    this->m_jointype = jointype;
+    if (MiterLimit <= 1) MiterLimit = 1;
+    m_RMin = 2/(MiterLimit*MiterLimit);
+ 
+    double deltaSq = delta*delta;
+    out_polys.clear();
+    out_polys.resize(in_polys.size());
+    for (m_i = 0; m_i < in_polys.size(); m_i++)
+    {
+        m_curr_poly = &out_polys[m_i];
+        size_t len = in_polys[m_i].size();
+        if (len > 1 && m_p[m_i][0].X == m_p[m_i][len - 1].X &&
+            m_p[m_i][0].Y == m_p[m_i][len-1].Y) len--;
+
+        //when 'shrinking' polygons - to minimize artefacts
+        //strip those polygons that have an area < pi * delta^2 ...
+        double a1 = Area(in_polys[m_i]);
+        if (delta < 0) { if (a1 > 0 && a1 < deltaSq *pi) len = 0; }
+        else if (a1 < 0 && -a1 < deltaSq *pi) len = 0; //holes have neg. area
+
+        if (len == 0 || (len < 3 && delta <= 0))
+          continue;
+        else if (len == 1)
+        {
+            Polygon arc;
+            arc = BuildArc(in_polys[m_i][len-1], 0, 2 * pi, delta);
+            out_polys[m_i] = arc;
+            continue;
+        }
+
+        //build normals ...
+        normals.clear();
+        normals.resize(len);
+        normals[len-1] = GetUnitNormal(in_polys[m_i][len-1], in_polys[m_i][0]);
+        for (m_j = 0; m_j < len -1; ++m_j)
+            normals[m_j] = GetUnitNormal(in_polys[m_i][m_j], in_polys[m_i][m_j+1]);
+        
+        m_k = len -1;
+        for (m_j = 0; m_j < len; ++m_j)
+        {
+          switch (jointype)
+          {
+            case jtMiter:
+            {
+              m_R = 1 + (normals[m_j].X*normals[m_k].X + 
+                normals[m_j].Y*normals[m_k].Y);
+              if (m_R >= m_RMin) DoMiter(); else DoSquare(MiterLimit);
+              break;
+            }
+            case jtSquare: DoSquare(); break;
+            case jtRound: DoRound(); break;
+          }
+        m_k = m_j;
+        }
+    }
+
+    //finally, clean up untidy corners using Clipper ...
+    Clipper clpr;
+    clpr.AddPolygons(out_polys, ptSubject);
+    if (delta > 0)
+    {
+        if (!clpr.Execute(ctUnion, out_polys, pftPositive, pftPositive))
+            out_polys.clear();
+    }
+    else
+    {
+        IntRect r = clpr.GetBounds();
+        Polygon 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.AddPolygon(outer, ptSubject);
+        if (clpr.Execute(ctUnion, out_polys, pftNegative, pftNegative))
+        {
+            out_polys.erase(out_polys.begin());
+            ReversePoints(out_polys);
+
+        } else
+            out_polys.clear();
+    }
+}
+//------------------------------------------------------------------------------
+
+private:
+
+void AddPoint(const IntPoint& pt)
+{
+    Polygon::size_type len = m_curr_poly->size();
+    if (len == m_curr_poly->capacity())
+        m_curr_poly->reserve(len + buffLength);
+    m_curr_poly->push_back(pt);
+}
+//------------------------------------------------------------------------------
+
+void DoSquare(double mul = 1.0)
+{
+    IntPoint pt1 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_k].X * m_delta),
+        (long64)Round(m_p[m_i][m_j].Y + normals[m_k].Y * m_delta));
+    IntPoint pt2 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_j].X * m_delta),
+        (long64)Round(m_p[m_i][m_j].Y + normals[m_j].Y * m_delta));
+    if ((normals[m_k].X * normals[m_j].Y - normals[m_j].X * normals[m_k].Y) * m_delta >= 0)
+    {
+        double a1 = std::atan2(normals[m_k].Y, normals[m_k].X);
+        double a2 = std::atan2(-normals[m_j].Y, -normals[m_j].X);
+        a1 = std::fabs(a2 - a1);
+        if (a1 > pi) a1 = pi * 2 - a1;
+        double dx = std::tan((pi - a1)/4) * std::fabs(m_delta * mul);
+        pt1 = IntPoint((long64)(pt1.X -normals[m_k].Y * dx),
+          (long64)(pt1.Y + normals[m_k].X * dx));
+        AddPoint(pt1);
+        pt2 = IntPoint((long64)(pt2.X + normals[m_j].Y * dx),
+          (long64)(pt2.Y -normals[m_j].X * dx));
+        AddPoint(pt2);
+    }
+    else
+    {
+        AddPoint(pt1);
+        AddPoint(m_p[m_i][m_j]);
+        AddPoint(pt2);
+    }
+}
+//------------------------------------------------------------------------------
+
+void DoMiter()
+{
+    if ((normals[m_k].X * normals[m_j].Y - normals[m_j].X * normals[m_k].Y) * m_delta >= 0)
+    {
+        double q = m_delta / m_R;
+        AddPoint(IntPoint((long64)Round(m_p[m_i][m_j].X + 
+            (normals[m_k].X + normals[m_j].X) * q),
+            (long64)Round(m_p[m_i][m_j].Y + (normals[m_k].Y + normals[m_j].Y) * q)));
+    }
+    else
+    {
+        IntPoint pt1 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_k].X *
+          m_delta), (long64)Round(m_p[m_i][m_j].Y + normals[m_k].Y * m_delta));
+        IntPoint pt2 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_j].X *
+          m_delta), (long64)Round(m_p[m_i][m_j].Y + normals[m_j].Y * m_delta));
+        AddPoint(pt1);
+        AddPoint(m_p[m_i][m_j]);
+        AddPoint(pt2);
+    }
+}
+//------------------------------------------------------------------------------
+
+void DoRound()
+{
+    IntPoint pt1 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_k].X * m_delta),
+        (long64)Round(m_p[m_i][m_j].Y + normals[m_k].Y * m_delta));
+    IntPoint pt2 = IntPoint((long64)Round(m_p[m_i][m_j].X + normals[m_j].X * m_delta),
+        (long64)Round(m_p[m_i][m_j].Y + normals[m_j].Y * m_delta));
+    AddPoint(pt1);
+    //round off reflex angles (ie > 180 deg) unless almost flat (ie < ~10deg).
+    if ((normals[m_k].X*normals[m_j].Y - normals[m_j].X*normals[m_k].Y) * m_delta >= 0)
+    {
+      if (normals[m_j].X * normals[m_k].X + normals[m_j].Y * normals[m_k].Y < 0.985)
+      {
+        double a1 = std::atan2(normals[m_k].Y, normals[m_k].X);
+        double a2 = std::atan2(normals[m_j].Y, normals[m_j].X);
+        if (m_delta > 0 && a2 < a1) a2 += pi *2;
+        else if (m_delta < 0 && a2 > a1) a2 -= pi *2;
+        Polygon arc = BuildArc(m_p[m_i][m_j], a1, a2, m_delta);
+        for (Polygon::size_type m = 0; m < arc.size(); m++)
+          AddPoint(arc[m]);
+      }
+    }
+    else
+      AddPoint(m_p[m_i][m_j]);
+    AddPoint(pt2);
+}
+//--------------------------------------------------------------------------
+
+}; //end PolyOffsetBuilder
+
+//------------------------------------------------------------------------------
+//------------------------------------------------------------------------------
+
+void OffsetPolygons(const Polygons &in_polys, Polygons &out_polys,
+  double delta, JoinType jointype, double MiterLimit)
+{
+  if (&out_polys == &in_polys)
+  {
+    Polygons poly2(in_polys);
+    PolyOffsetBuilder(poly2, out_polys, delta, jointype, MiterLimit);
+  }
+  else PolyOffsetBuilder(in_polys, out_polys, delta, jointype, MiterLimit);
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, IntPoint& p)
+{
+  s << p.X << ' ' << p.Y << "\n";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, Polygon &p)
+{
+  for (Polygon::size_type i = 0; i < p.size(); i++)
+    s << p[i];
+  s << "\n";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, Polygons &p)
+{
+  for (Polygons::size_type i = 0; i < p.size(); i++)
+    s << p[i];
+  s << "\n";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+} //ClipperLib namespace

contrib/clipper/clipper.hpp

@@ -0,0 +1,302 @@
+/*******************************************************************************
+*                                                                              *
+* Author    :  Angus Johnson                                                   *
+* Version   :  4.6.3                                                           *
+* Date      :  11 November 2011                                                *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2011                                         *
+*                                                                              *
+* 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              *
+*                                                                              *
+*******************************************************************************/
+
+#ifndef clipper_hpp
+#define clipper_hpp
+
+#include <vector>
+#include <stdexcept>
+#include <cstring>
+#include <cstdlib>
+#include <ostream>
+
+namespace ClipperLib {
+
+enum ClipType { ctIntersection, ctUnion, ctDifference, ctXor };
+enum PolyType { ptSubject, ptClip };
+//By far the most widely used winding rules for polygon filling are
+//EvenOdd & NonZero (GDI, GDI+, XLib, OpenGL, Cairo, AGG, Quartz, SVG, Gr32)
+//Others rules include Positive, Negative and ABS_GTR_EQ_TWO (only in OpenGL)
+//see http://glprogramming.com/red/chapter11.html
+enum PolyFillType { pftEvenOdd, pftNonZero, pftPositive, pftNegative };
+
+typedef signed long long long64;
+typedef unsigned long long ulong64;
+
+struct IntPoint {
+public:
+  long64 X;
+  long64 Y;
+  IntPoint(long64 x = 0, long64 y = 0): X(x), Y(y) {};
+  friend std::ostream& operator <<(std::ostream &s, IntPoint &p);
+};
+
+typedef std::vector< IntPoint > Polygon;
+typedef std::vector< Polygon > Polygons;
+
+std::ostream& operator <<(std::ostream &s, Polygon &p);
+std::ostream& operator <<(std::ostream &s, Polygons &p);
+
+struct ExPolygon {
+  Polygon  outer;
+  Polygons holes;
+};
+typedef std::vector< ExPolygon > ExPolygons;
+
+enum JoinType { jtSquare, jtMiter, jtRound };
+
+bool Orientation(const Polygon &poly);
+double Area(const Polygon &poly);
+void OffsetPolygons(const Polygons &in_polys, Polygons &out_polys,
+  double delta, JoinType jointype = jtSquare, double MiterLimit = 2);
+
+void ReversePoints(Polygon& p);
+void ReversePoints(Polygons& p);
+
+//used internally ...
+enum EdgeSide { esLeft, esRight };
+enum IntersectProtects { ipNone = 0, ipLeft = 1, ipRight = 2, ipBoth = 3 };
+
+struct TEdge {
+  long64 xbot;
+  long64 ybot;
+  long64 xcurr;
+  long64 ycurr;
+  long64 xtop;
+  long64 ytop;
+  double dx;
+  long64 tmpX;
+  PolyType polyType;
+  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;
+  IntersectNode  *next;
+};
+
+struct LocalMinima {
+  long64        Y;
+  TEdge        *leftBound;
+  TEdge        *rightBound;
+  LocalMinima  *next;
+};
+
+struct Scanbeam {
+  long64    Y;
+  Scanbeam *next;
+};
+
+struct OutPt; //forward declaration
+
+struct OutRec {
+  int     idx;
+  bool    isHole;
+  OutRec *FirstLeft;
+  OutRec *AppendLink;
+  OutPt  *pts;
+  OutPt  *bottomPt;
+  TEdge  *bottomE1;
+  TEdge  *bottomE2;
+};
+
+struct OutPt {
+  int     idx;
+  IntPoint pt;
+  OutPt   *next;
+  OutPt   *prev;
+};
+
+struct JoinRec {
+  IntPoint  pt1a;
+  IntPoint  pt1b;
+  int       poly1Idx;
+  IntPoint  pt2a;
+  IntPoint  pt2b;
+  int       poly2Idx;
+};
+
+struct HorzJoinRec {
+  TEdge    *edge;
+  int       savedIdx;
+};
+
+struct IntRect { long64 left; long64 top; long64 right; long64 bottom; };
+
+typedef std::vector < OutRec* > PolyOutList;
+typedef std::vector < TEdge* > EdgeList;
+typedef std::vector < JoinRec* > JoinList;
+typedef std::vector < HorzJoinRec* > HorzJoinList;
+
+//ClipperBase is the ancestor to the Clipper class. It should not be
+//instantiated directly. This class simply abstracts the conversion of sets of
+//polygon coordinates into edge objects that are stored in a LocalMinima list.
+class ClipperBase
+{
+public:
+  ClipperBase();
+  virtual ~ClipperBase();
+  bool AddPolygon(const Polygon &pg, PolyType polyType);
+  bool AddPolygons( const Polygons &ppg, PolyType polyType);
+  virtual void Clear();
+  IntRect GetBounds();
+protected:
+  void DisposeLocalMinimaList();
+  TEdge* AddBoundsToLML(TEdge *e);
+  void PopLocalMinima();
+  virtual void Reset();
+  void InsertLocalMinima(LocalMinima *newLm);
+  LocalMinima      *m_CurrentLM;
+  LocalMinima      *m_MinimaList;
+  bool              m_UseFullRange;
+  EdgeList          m_edges;
+};
+
+class Clipper : public virtual ClipperBase
+{
+public:
+  Clipper();
+  ~Clipper();
+  bool Execute(ClipType clipType,
+  Polygons &solution,
+  PolyFillType subjFillType = pftEvenOdd,
+  PolyFillType clipFillType = pftEvenOdd);
+  bool Execute(ClipType clipType,
+  ExPolygons &solution,
+  PolyFillType subjFillType = pftEvenOdd,
+  PolyFillType clipFillType = pftEvenOdd);
+  void Clear();
+  bool ReverseSolution() {return m_ReverseOutput;};
+  void ReverseSolution(bool value) {m_ReverseOutput = value;};
+protected:
+  void Reset();
+  virtual bool ExecuteInternal(bool fixHoleLinkages);
+private:
+  PolyOutList       m_PolyOuts;
+  JoinList          m_Joins;
+  HorzJoinList      m_HorizJoins;
+  ClipType          m_ClipType;
+  Scanbeam         *m_Scanbeam;
+  TEdge           *m_ActiveEdges;
+  TEdge           *m_SortedEdges;
+  IntersectNode    *m_IntersectNodes;
+  bool              m_ExecuteLocked;
+  PolyFillType      m_ClipFillType;
+  PolyFillType      m_SubjFillType;
+  bool              m_ReverseOutput;
+  void DisposeScanbeamList();
+  void SetWindingCount(TEdge& edge);
+  bool IsEvenOddFillType(const TEdge& edge) const;
+  bool IsEvenOddAltFillType(const TEdge& edge) const;
+  void InsertScanbeam(const long64 Y);
+  long64 PopScanbeam();
+  void InsertLocalMinimaIntoAEL(const long64 botY);
+  void InsertEdgeIntoAEL(TEdge *edge);
+  void AddEdgeToSEL(TEdge *edge);
+  void CopyAELToSEL();
+  void DeleteFromSEL(TEdge *e);
+  void DeleteFromAEL(TEdge *e);
+  void UpdateEdgeIntoAEL(TEdge *&e);
+  void SwapPositionsInSEL(TEdge *edge1, TEdge *edge2);
+  bool IsContributing(const TEdge& edge) const;
+  bool IsTopHorz(const long64 XPos);
+  void SwapPositionsInAEL(TEdge *edge1, TEdge *edge2);
+  void DoMaxima(TEdge *e, long64 topY);
+  void ProcessHorizontals();
+  void ProcessHorizontal(TEdge *horzEdge);
+  void AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
+  void AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
+  void AppendPolygon(TEdge *e1, TEdge *e2);
+  void DoEdge1(TEdge *edge1, TEdge *edge2, const IntPoint &pt);
+  void DoEdge2(TEdge *edge1, TEdge *edge2, const IntPoint &pt);
+  void DoBothEdges(TEdge *edge1, TEdge *edge2, const IntPoint &pt);
+  void IntersectEdges(TEdge *e1, TEdge *e2,
+    const IntPoint &pt, IntersectProtects protects);
+  OutRec* CreateOutRec();
+  void AddOutPt(TEdge *e, TEdge *altE, const IntPoint &pt);
+  void DisposeAllPolyPts();
+  void DisposeOutRec(PolyOutList::size_type index, bool ignorePts = false);
+  bool ProcessIntersections(const long64 botY, const long64 topY);
+  void AddIntersectNode(TEdge *e1, TEdge *e2, const IntPoint &pt);
+  void BuildIntersectList(const long64 botY, const long64 topY);
+  void ProcessIntersectList();
+  void ProcessEdgesAtTopOfScanbeam(const long64 topY);
+  void BuildResult(Polygons& polys);
+  void BuildResultEx(ExPolygons& polys);
+  void SetHoleState(TEdge *e, OutRec *OutRec);
+  void DisposeIntersectNodes();
+  bool FixupIntersections();
+  void FixupOutPolygon(OutRec &outRec);
+  bool IsHole(TEdge *e);
+  void FixHoleLinkage(OutRec *outRec);
+  void CheckHoleLinkages1(OutRec *outRec1, OutRec *outRec2);
+  void CheckHoleLinkages2(OutRec *outRec1, OutRec *outRec2);
+  void AddJoin(TEdge *e1, TEdge *e2, int e1OutIdx = -1, int e2OutIdx = -1);
+  void ClearJoins();
+  void AddHorzJoin(TEdge *e, int idx);
+  void ClearHorzJoins();
+  void JoinCommonEdges(bool fixHoleLinkages);
+};
+
+//------------------------------------------------------------------------------
+//------------------------------------------------------------------------------
+
+class clipperException : public std::exception
+{
+  public:
+    clipperException(const char* description): m_descr(description) {}
+    virtual ~clipperException() throw() {}
+    virtual const char* what() const throw() {return m_descr.c_str();}
+  private:
+    std::string m_descr;
+};
+//------------------------------------------------------------------------------
+
+} //ClipperLib namespace
+
+#endif //clipper_hpp
+
+