Merge pull request #1 from PaddlePaddle/develop

update-2020-7-17

deploy/ios_demo/ocr_demo/pdocr/ocr_clipper.cpp

+/*******************************************************************************
+*                                                                              *
+* Author    :  Angus Johnson                                                   *
+* Version   :  6.4.2                                                           *
+* Date      :  27 February 2017                                                *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2017                                         *
+*                                                                              *
+* License:                                                                     *
+* Use, modification & distribution is subject to Boost Software License Ver 1. *
+* http://www.boost.org/LICENSE_1_0.txt                                         *
+*                                                                              *
+* Attributions:                                                                *
+* The code in this library is an extension of Bala Vatti's clipping algorithm: *
+* "A generic solution to polygon clipping"                                     *
+* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
+* http://portal.acm.org/citation.cfm?id=129906                                 *
+*                                                                              *
+* Computer graphics and geometric modeling: implementation and algorithms      *
+* By Max K. Agoston                                                            *
+* Springer; 1 edition (January 4, 2005)                                        *
+* http://books.google.com/books?q=vatti+clipping+agoston                       *
+*                                                                              *
+* See also:                                                                    *
+* "Polygon Offsetting by Computing Winding Numbers"                            *
+* Paper no. DETC2005-85513 pp. 565-575                                         *
+* ASME 2005 International Design Engineering Technical Conferences             *
+* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
+* September 24-28, 2005 , Long Beach, California, USA                          *
+* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
+*                                                                              *
+*******************************************************************************/
+
+/*******************************************************************************
+*                                                                              *
+* This is a translation of the Delphi Clipper library and the naming style     *
+* used has retained a Delphi flavour.                                          *
+*                                                                              *
+*******************************************************************************/
+
+#include "ocr_clipper.hpp"
+#include <cmath>
+#include <vector>
+#include <algorithm>
+#include <stdexcept>
+#include <cstring>
+#include <cstdlib>
+#include <ostream>
+#include <functional>
+
+namespace ClipperLib {
+
+static double const pi = 3.141592653589793238;
+static double const two_pi = pi *2;
+static double const def_arc_tolerance = 0.25;
+
+enum Direction { dRightToLeft, dLeftToRight };
+
+static int const Unassigned = -1;  //edge not currently 'owning' a solution
+static int const Skip = -2;        //edge that would otherwise close a path
+
+#define HORIZONTAL (-1.0E+40)
+#define TOLERANCE (1.0e-20)
+#define NEAR_ZERO(val) (((val) > -TOLERANCE) && ((val) < TOLERANCE))
+
+struct TEdge {
+  IntPoint Bot;
+  IntPoint Curr; //current (updated for every new scanbeam)
+  IntPoint Top;
+  double Dx;
+  PolyType PolyTyp;
+  EdgeSide Side; //side only refers to current side of solution poly
+  int WindDelta; //1 or -1 depending on winding direction
+  int WindCnt;
+  int WindCnt2; //winding count of the opposite polytype
+  int OutIdx;
+  TEdge *Next;
+  TEdge *Prev;
+  TEdge *NextInLML;
+  TEdge *NextInAEL;
+  TEdge *PrevInAEL;
+  TEdge *NextInSEL;
+  TEdge *PrevInSEL;
+};
+
+struct IntersectNode {
+  TEdge          *Edge1;
+  TEdge          *Edge2;
+  IntPoint        Pt;
+};
+
+struct LocalMinimum {
+  cInt          Y;
+  TEdge        *LeftBound;
+  TEdge        *RightBound;
+};
+
+struct OutPt;
+
+//OutRec: contains a path in the clipping solution. Edges in the AEL will
+//carry a pointer to an OutRec when they are part of the clipping solution.
+struct OutRec {
+  int       Idx;
+  bool      IsHole;
+  bool      IsOpen;
+  OutRec   *FirstLeft;  //see comments in clipper.pas
+  PolyNode *PolyNd;
+  OutPt    *Pts;
+  OutPt    *BottomPt;
+};
+
+struct OutPt {
+  int       Idx;
+  IntPoint  Pt;
+  OutPt    *Next;
+  OutPt    *Prev;
+};
+
+struct Join {
+  OutPt    *OutPt1;
+  OutPt    *OutPt2;
+  IntPoint  OffPt;
+};
+
+struct LocMinSorter
+{
+  inline bool operator()(const LocalMinimum& locMin1, const LocalMinimum& locMin2)
+  {
+    return locMin2.Y < locMin1.Y;
+  }
+};
+
+//------------------------------------------------------------------------------
+//------------------------------------------------------------------------------
+
+inline cInt Round(double val)
+{
+  if ((val < 0)) return static_cast<cInt>(val - 0.5); 
+  else return static_cast<cInt>(val + 0.5);
+}
+//------------------------------------------------------------------------------
+
+inline cInt Abs(cInt val)
+{
+  return val < 0 ? -val : val;
+}
+
+//------------------------------------------------------------------------------
+// PolyTree methods ...
+//------------------------------------------------------------------------------
+
+void PolyTree::Clear()
+{
+    for (PolyNodes::size_type i = 0; i < AllNodes.size(); ++i)
+      delete AllNodes[i];
+    AllNodes.resize(0); 
+    Childs.resize(0);
+}
+//------------------------------------------------------------------------------
+
+PolyNode* PolyTree::GetFirst() const
+{
+  if (!Childs.empty())
+      return Childs[0];
+  else
+      return 0;
+}
+//------------------------------------------------------------------------------
+
+int PolyTree::Total() const
+{
+  int result = (int)AllNodes.size();
+  //with negative offsets, ignore the hidden outer polygon ...
+  if (result > 0 && Childs[0] != AllNodes[0]) result--;
+  return result;
+}
+
+//------------------------------------------------------------------------------
+// PolyNode methods ...
+//------------------------------------------------------------------------------
+
+PolyNode::PolyNode(): Parent(0), Index(0), m_IsOpen(false)
+{
+}
+//------------------------------------------------------------------------------
+
+int PolyNode::ChildCount() const
+{
+  return (int)Childs.size();
+}
+//------------------------------------------------------------------------------
+
+void PolyNode::AddChild(PolyNode& child)
+{
+  unsigned cnt = (unsigned)Childs.size();
+  Childs.push_back(&child);
+  child.Parent = this;
+  child.Index = cnt;
+}
+//------------------------------------------------------------------------------
+
+PolyNode* PolyNode::GetNext() const
+{ 
+  if (!Childs.empty()) 
+      return Childs[0]; 
+  else
+      return GetNextSiblingUp();    
+}  
+//------------------------------------------------------------------------------
+
+PolyNode* PolyNode::GetNextSiblingUp() const
+{ 
+  if (!Parent) //protects against PolyTree.GetNextSiblingUp()
+      return 0;
+  else if (Index == Parent->Childs.size() - 1)
+      return Parent->GetNextSiblingUp();
+  else
+      return Parent->Childs[Index + 1];
+}  
+//------------------------------------------------------------------------------
+
+bool PolyNode::IsHole() const
+{ 
+  bool result = true;
+  PolyNode* node = Parent;
+  while (node)
+  {
+      result = !result;
+      node = node->Parent;
+  }
+  return result;
+}  
+//------------------------------------------------------------------------------
+
+bool PolyNode::IsOpen() const
+{ 
+  return m_IsOpen;
+}  
+//------------------------------------------------------------------------------
+
+#ifndef use_int32
+
+//------------------------------------------------------------------------------
+// Int128 class (enables safe math on signed 64bit integers)
+// eg Int128 val1((long64)9223372036854775807); //ie 2^63 -1
+//    Int128 val2((long64)9223372036854775807);
+//    Int128 val3 = val1 * val2;
+//    val3.AsString => "85070591730234615847396907784232501249" (8.5e+37)
+//------------------------------------------------------------------------------
+
+class Int128
+{
+  public:
+    ulong64 lo;
+    long64 hi;
+
+    Int128(long64 _lo = 0)
+    {
+      lo = (ulong64)_lo;   
+      if (_lo < 0)  hi = -1; else hi = 0; 
+    }
+
+
+    Int128(const Int128 &val): lo(val.lo), hi(val.hi){}
+
+    Int128(const long64& _hi, const ulong64& _lo): lo(_lo), hi(_hi){}
+    
+    Int128& operator = (const long64 &val)
+    {
+      lo = (ulong64)val;
+      if (val < 0) hi = -1; else hi = 0;
+      return *this;
+    }
+
+    bool operator == (const Int128 &val) const
+      {return (hi == val.hi && lo == val.lo);}
+
+    bool operator != (const Int128 &val) const
+      { return !(*this == val);}
+
+    bool operator > (const Int128 &val) const
+    {
+      if (hi != val.hi)
+        return hi > val.hi;
+      else
+        return lo > val.lo;
+    }
+
+    bool operator < (const Int128 &val) const
+    {
+      if (hi != val.hi)
+        return hi < val.hi;
+      else
+        return lo < val.lo;
+    }
+
+    bool operator >= (const Int128 &val) const
+      { return !(*this < val);}
+
+    bool operator <= (const Int128 &val) const
+      { return !(*this > val);}
+
+    Int128& operator += (const Int128 &rhs)
+    {
+      hi += rhs.hi;
+      lo += rhs.lo;
+      if (lo < rhs.lo) hi++;
+      return *this;
+    }
+
+    Int128 operator + (const Int128 &rhs) const
+    {
+      Int128 result(*this);
+      result+= rhs;
+      return result;
+    }
+
+    Int128& operator -= (const Int128 &rhs)
+    {
+      *this += -rhs;
+      return *this;
+    }
+
+    Int128 operator - (const Int128 &rhs) const
+    {
+      Int128 result(*this);
+      result -= rhs;
+      return result;
+    }
+
+    Int128 operator-() const //unary negation
+    {
+      if (lo == 0)
+        return Int128(-hi, 0);
+      else
+        return Int128(~hi, ~lo + 1);
+    }
+
+    operator double() const
+    {
+      const double shift64 = 18446744073709551616.0; //2^64
+      if (hi < 0)
+      {
+        if (lo == 0) return (double)hi * shift64;
+        else return -(double)(~lo + ~hi * shift64);
+      }
+      else
+        return (double)(lo + hi * shift64);
+    }
+
+};
+//------------------------------------------------------------------------------
+
+Int128 Int128Mul (long64 lhs, long64 rhs)
+{
+  bool negate = (lhs < 0) != (rhs < 0);
+
+  if (lhs < 0) lhs = -lhs;
+  ulong64 int1Hi = ulong64(lhs) >> 32;
+  ulong64 int1Lo = ulong64(lhs & 0xFFFFFFFF);
+
+  if (rhs < 0) rhs = -rhs;
+  ulong64 int2Hi = ulong64(rhs) >> 32;
+  ulong64 int2Lo = ulong64(rhs & 0xFFFFFFFF);
+
+  //nb: see comments in clipper.pas
+  ulong64 a = int1Hi * int2Hi;
+  ulong64 b = int1Lo * int2Lo;
+  ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;
+
+  Int128 tmp;
+  tmp.hi = long64(a + (c >> 32));
+  tmp.lo = long64(c << 32);
+  tmp.lo += long64(b);
+  if (tmp.lo < b) tmp.hi++;
+  if (negate) tmp = -tmp;
+  return tmp;
+};
+#endif
+
+//------------------------------------------------------------------------------
+// Miscellaneous global functions
+//------------------------------------------------------------------------------
+
+bool Orientation(const Path &poly)
+{
+    return Area(poly) >= 0;
+}
+//------------------------------------------------------------------------------
+
+double Area(const Path &poly)
+{
+  int size = (int)poly.size();
+  if (size < 3) return 0;
+
+  double a = 0;
+  for (int i = 0, j = size -1; i < size; ++i)
+  {
+    a += ((double)poly[j].X + poly[i].X) * ((double)poly[j].Y - poly[i].Y);
+    j = i;
+  }
+  return -a * 0.5;
+}
+//------------------------------------------------------------------------------
+
+double Area(const OutPt *op)
+{
+  const OutPt *startOp = op;
+  if (!op) return 0;
+  double a = 0;
+  do {
+    a +=  (double)(op->Prev->Pt.X + op->Pt.X) * (double)(op->Prev->Pt.Y - op->Pt.Y);
+    op = op->Next;
+  } while (op != startOp);
+  return a * 0.5;
+}
+//------------------------------------------------------------------------------
+
+double Area(const OutRec &outRec)
+{
+  return Area(outRec.Pts);
+}
+//------------------------------------------------------------------------------
+
+bool PointIsVertex(const IntPoint &Pt, OutPt *pp)
+{
+  OutPt *pp2 = pp;
+  do
+  {
+    if (pp2->Pt == Pt) return true;
+    pp2 = pp2->Next;
+  }
+  while (pp2 != pp);
+  return false;
+}
+//------------------------------------------------------------------------------
+
+//See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
+//http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
+int PointInPolygon(const IntPoint &pt, const Path &path)
+{
+  //returns 0 if false, +1 if true, -1 if pt ON polygon boundary
+  int result = 0;
+  size_t cnt = path.size();
+  if (cnt < 3) return 0;
+  IntPoint ip = path[0];
+  for(size_t i = 1; i <= cnt; ++i)
+  {
+    IntPoint ipNext = (i == cnt ? path[0] : path[i]);
+    if (ipNext.Y == pt.Y)
+    {
+        if ((ipNext.X == pt.X) || (ip.Y == pt.Y && 
+          ((ipNext.X > pt.X) == (ip.X < pt.X)))) return -1;
+    }
+    if ((ip.Y < pt.Y) != (ipNext.Y < pt.Y))
+    {
+      if (ip.X >= pt.X)
+      {
+        if (ipNext.X > pt.X) result = 1 - result;
+        else
+        {
+          double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) - 
+            (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
+          if (!d) return -1;
+          if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
+        }
+      } else
+      {
+        if (ipNext.X > pt.X)
+        {
+          double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) - 
+            (double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
+          if (!d) return -1;
+          if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
+        }
+      }
+    }
+    ip = ipNext;
+  } 
+  return result;
+}
+//------------------------------------------------------------------------------
+
+int PointInPolygon (const IntPoint &pt, OutPt *op)
+{
+  //returns 0 if false, +1 if true, -1 if pt ON polygon boundary
+  int result = 0;
+  OutPt* startOp = op;
+  for(;;)
+  {
+    if (op->Next->Pt.Y == pt.Y)
+    {
+        if ((op->Next->Pt.X == pt.X) || (op->Pt.Y == pt.Y && 
+          ((op->Next->Pt.X > pt.X) == (op->Pt.X < pt.X)))) return -1;
+    }
+    if ((op->Pt.Y < pt.Y) != (op->Next->Pt.Y < pt.Y))
+    {
+      if (op->Pt.X >= pt.X)
+      {
+        if (op->Next->Pt.X > pt.X) result = 1 - result;
+        else
+        {
+          double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) - 
+            (double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
+          if (!d) return -1;
+          if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
+        }
+      } else
+      {
+        if (op->Next->Pt.X > pt.X)
+        {
+          double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) - 
+            (double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
+          if (!d) return -1;
+          if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
+        }
+      }
+    } 
+    op = op->Next;
+    if (startOp == op) break;
+  } 
+  return result;
+}
+//------------------------------------------------------------------------------
+
+bool Poly2ContainsPoly1(OutPt *OutPt1, OutPt *OutPt2)
+{
+  OutPt* op = OutPt1;
+  do
+  {
+    //nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
+    int res = PointInPolygon(op->Pt, OutPt2);
+    if (res >= 0) return res > 0;
+    op = op->Next; 
+  }
+  while (op != OutPt1);
+  return true; 
+}
+//----------------------------------------------------------------------
+
+bool SlopesEqual(const TEdge &e1, const TEdge &e2, bool UseFullInt64Range)
+{
+#ifndef use_int32
+  if (UseFullInt64Range)
+    return Int128Mul(e1.Top.Y - e1.Bot.Y, e2.Top.X - e2.Bot.X) == 
+    Int128Mul(e1.Top.X - e1.Bot.X, e2.Top.Y - e2.Bot.Y);
+  else 
+#endif
+    return (e1.Top.Y - e1.Bot.Y) * (e2.Top.X - e2.Bot.X) == 
+    (e1.Top.X - e1.Bot.X) * (e2.Top.Y - e2.Bot.Y);
+}
+//------------------------------------------------------------------------------
+
+bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
+  const IntPoint pt3, bool UseFullInt64Range)
+{
+#ifndef use_int32
+  if (UseFullInt64Range)
+    return Int128Mul(pt1.Y-pt2.Y, pt2.X-pt3.X) == Int128Mul(pt1.X-pt2.X, pt2.Y-pt3.Y);
+  else 
+#endif
+    return (pt1.Y-pt2.Y)*(pt2.X-pt3.X) == (pt1.X-pt2.X)*(pt2.Y-pt3.Y);
+}
+//------------------------------------------------------------------------------
+
+bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
+  const IntPoint pt3, const IntPoint pt4, bool UseFullInt64Range)
+{
+#ifndef use_int32
+  if (UseFullInt64Range)
+    return Int128Mul(pt1.Y-pt2.Y, pt3.X-pt4.X) == Int128Mul(pt1.X-pt2.X, pt3.Y-pt4.Y);
+  else 
+#endif
+    return (pt1.Y-pt2.Y)*(pt3.X-pt4.X) == (pt1.X-pt2.X)*(pt3.Y-pt4.Y);
+}
+//------------------------------------------------------------------------------
+
+inline bool IsHorizontal(TEdge &e)
+{
+  return e.Dx == HORIZONTAL;
+}
+//------------------------------------------------------------------------------
+
+inline double GetDx(const IntPoint pt1, const IntPoint pt2)
+{
+  return (pt1.Y == pt2.Y) ?
+    HORIZONTAL : (double)(pt2.X - pt1.X) / (pt2.Y - pt1.Y);
+}
+//---------------------------------------------------------------------------
+
+inline void SetDx(TEdge &e)
+{
+  cInt dy  = (e.Top.Y - e.Bot.Y);
+  if (dy == 0) e.Dx = HORIZONTAL;
+  else e.Dx = (double)(e.Top.X - e.Bot.X) / dy;
+}
+//---------------------------------------------------------------------------
+
+inline void SwapSides(TEdge &Edge1, TEdge &Edge2)
+{
+  EdgeSide Side =  Edge1.Side;
+  Edge1.Side = Edge2.Side;
+  Edge2.Side = Side;
+}
+//------------------------------------------------------------------------------
+
+inline void SwapPolyIndexes(TEdge &Edge1, TEdge &Edge2)
+{
+  int OutIdx =  Edge1.OutIdx;
+  Edge1.OutIdx = Edge2.OutIdx;
+  Edge2.OutIdx = OutIdx;
+}
+//------------------------------------------------------------------------------
+
+inline cInt TopX(TEdge &edge, const cInt currentY)
+{
+  return ( currentY == edge.Top.Y ) ?
+    edge.Top.X : edge.Bot.X + Round(edge.Dx *(currentY - edge.Bot.Y));
+}
+//------------------------------------------------------------------------------
+
+void IntersectPoint(TEdge &Edge1, TEdge &Edge2, IntPoint &ip)
+{
+#ifdef use_xyz  
+  ip.Z = 0;
+#endif
+
+  double b1, b2;
+  if (Edge1.Dx == Edge2.Dx)
+  {
+    ip.Y = Edge1.Curr.Y;
+    ip.X = TopX(Edge1, ip.Y);
+    return;
+  }
+  else if (Edge1.Dx == 0)
+  {
+    ip.X = Edge1.Bot.X;
+    if (IsHorizontal(Edge2))
+      ip.Y = Edge2.Bot.Y;
+    else
+    {
+      b2 = Edge2.Bot.Y - (Edge2.Bot.X / Edge2.Dx);
+      ip.Y = Round(ip.X / Edge2.Dx + b2);
+    }
+  }
+  else if (Edge2.Dx == 0)
+  {
+    ip.X = Edge2.Bot.X;
+    if (IsHorizontal(Edge1))
+      ip.Y = Edge1.Bot.Y;
+    else
+    {
+      b1 = Edge1.Bot.Y - (Edge1.Bot.X / Edge1.Dx);
+      ip.Y = Round(ip.X / Edge1.Dx + b1);
+    }
+  } 
+  else 
+  {
+    b1 = Edge1.Bot.X - Edge1.Bot.Y * Edge1.Dx;
+    b2 = Edge2.Bot.X - Edge2.Bot.Y * Edge2.Dx;
+    double q = (b2-b1) / (Edge1.Dx - Edge2.Dx);
+    ip.Y = Round(q);
+    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
+      ip.X = Round(Edge1.Dx * q + b1);
+    else 
+      ip.X = Round(Edge2.Dx * q + b2);
+  }
+
+  if (ip.Y < Edge1.Top.Y || ip.Y < Edge2.Top.Y) 
+  {
+    if (Edge1.Top.Y > Edge2.Top.Y)
+      ip.Y = Edge1.Top.Y;
+    else
+      ip.Y = Edge2.Top.Y;
+    if (std::fabs(Edge1.Dx) < std::fabs(Edge2.Dx))
+      ip.X = TopX(Edge1, ip.Y);
+    else
+      ip.X = TopX(Edge2, ip.Y);
+  } 
+  //finally, don't allow 'ip' to be BELOW curr.Y (ie bottom of scanbeam) ...
+  if (ip.Y > Edge1.Curr.Y)
+  {
+    ip.Y = Edge1.Curr.Y;
+    //use the more vertical edge to derive X ...
+    if (std::fabs(Edge1.Dx) > std::fabs(Edge2.Dx))
+      ip.X = TopX(Edge2, ip.Y); else
+      ip.X = TopX(Edge1, ip.Y);
+  }
+}
+//------------------------------------------------------------------------------
+
+void ReversePolyPtLinks(OutPt *pp)
+{
+  if (!pp) return;
+  OutPt *pp1, *pp2;
+  pp1 = pp;
+  do {
+  pp2 = pp1->Next;
+  pp1->Next = pp1->Prev;
+  pp1->Prev = pp2;
+  pp1 = pp2;
+  } while( pp1 != pp );
+}
+//------------------------------------------------------------------------------
+
+void DisposeOutPts(OutPt*& pp)
+{
+  if (pp == 0) return;
+    pp->Prev->Next = 0;
+  while( pp )
+  {
+    OutPt *tmpPp = pp;
+    pp = pp->Next;
+    delete tmpPp;
+  }
+}
+//------------------------------------------------------------------------------
+
+inline void InitEdge(TEdge* e, TEdge* eNext, TEdge* ePrev, const IntPoint& Pt)
+{
+  std::memset(e, 0, sizeof(TEdge));
+  e->Next = eNext;
+  e->Prev = ePrev;
+  e->Curr = Pt;
+  e->OutIdx = Unassigned;
+}
+//------------------------------------------------------------------------------
+
+void InitEdge2(TEdge& e, PolyType Pt)
+{
+  if (e.Curr.Y >= e.Next->Curr.Y)
+  {
+    e.Bot = e.Curr;
+    e.Top = e.Next->Curr;
+  } else
+  {
+    e.Top = e.Curr;
+    e.Bot = e.Next->Curr;
+  }
+  SetDx(e);
+  e.PolyTyp = Pt;
+}
+//------------------------------------------------------------------------------
+
+TEdge* RemoveEdge(TEdge* e)
+{
+  //removes e from double_linked_list (but without removing from memory)
+  e->Prev->Next = e->Next;
+  e->Next->Prev = e->Prev;
+  TEdge* result = e->Next;
+  e->Prev = 0; //flag as removed (see ClipperBase.Clear)
+  return result;
+}
+//------------------------------------------------------------------------------
+
+inline void ReverseHorizontal(TEdge &e)
+{
+  //swap horizontal edges' Top and Bottom x's so they follow the natural
+  //progression of the bounds - ie so their xbots will align with the
+  //adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
+  std::swap(e.Top.X, e.Bot.X);
+#ifdef use_xyz  
+  std::swap(e.Top.Z, e.Bot.Z);
+#endif
+}
+//------------------------------------------------------------------------------
+
+void SwapPoints(IntPoint &pt1, IntPoint &pt2)
+{
+  IntPoint tmp = pt1;
+  pt1 = pt2;
+  pt2 = tmp;
+}
+//------------------------------------------------------------------------------
+
+bool GetOverlapSegment(IntPoint pt1a, IntPoint pt1b, IntPoint pt2a,
+  IntPoint pt2b, IntPoint &pt1, IntPoint &pt2)
+{
+  //precondition: segments are Collinear.
+  if (Abs(pt1a.X - pt1b.X) > Abs(pt1a.Y - pt1b.Y))
+  {
+    if (pt1a.X > pt1b.X) SwapPoints(pt1a, pt1b);
+    if (pt2a.X > pt2b.X) SwapPoints(pt2a, pt2b);
+    if (pt1a.X > pt2a.X) pt1 = pt1a; else pt1 = pt2a;
+    if (pt1b.X < pt2b.X) pt2 = pt1b; else pt2 = pt2b;
+    return pt1.X < pt2.X;
+  } else
+  {
+    if (pt1a.Y < pt1b.Y) SwapPoints(pt1a, pt1b);
+    if (pt2a.Y < pt2b.Y) SwapPoints(pt2a, pt2b);
+    if (pt1a.Y < pt2a.Y) pt1 = pt1a; else pt1 = pt2a;
+    if (pt1b.Y > pt2b.Y) pt2 = pt1b; else pt2 = pt2b;
+    return pt1.Y > pt2.Y;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool FirstIsBottomPt(const OutPt* btmPt1, const OutPt* btmPt2)
+{
+  OutPt *p = btmPt1->Prev;
+  while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Prev;
+  double dx1p = std::fabs(GetDx(btmPt1->Pt, p->Pt));
+  p = btmPt1->Next;
+  while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Next;
+  double dx1n = std::fabs(GetDx(btmPt1->Pt, p->Pt));
+
+  p = btmPt2->Prev;
+  while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Prev;
+  double dx2p = std::fabs(GetDx(btmPt2->Pt, p->Pt));
+  p = btmPt2->Next;
+  while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Next;
+  double dx2n = std::fabs(GetDx(btmPt2->Pt, p->Pt));
+
+  if (std::max(dx1p, dx1n) == std::max(dx2p, dx2n) &&
+    std::min(dx1p, dx1n) == std::min(dx2p, dx2n))
+      return Area(btmPt1) > 0; //if otherwise identical use orientation
+  else
+    return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
+}
+//------------------------------------------------------------------------------
+
+OutPt* GetBottomPt(OutPt *pp)
+{
+  OutPt* dups = 0;
+  OutPt* p = pp->Next;
+  while (p != pp)
+  {
+    if (p->Pt.Y > pp->Pt.Y)
+    {
+      pp = p;
+      dups = 0;
+    }
+    else if (p->Pt.Y == pp->Pt.Y && p->Pt.X <= pp->Pt.X)
+    {
+      if (p->Pt.X < pp->Pt.X)
+      {
+        dups = 0;
+        pp = p;
+      } else
+      {
+        if (p->Next != pp && p->Prev != pp) dups = p;
+      }
+    }
+    p = p->Next;
+  }
+  if (dups)
+  {
+    //there appears to be at least 2 vertices at BottomPt so ...
+    while (dups != p)
+    {
+      if (!FirstIsBottomPt(p, dups)) pp = dups;
+      dups = dups->Next;
+      while (dups->Pt != pp->Pt) dups = dups->Next;
+    }
+  }
+  return pp;
+}
+//------------------------------------------------------------------------------
+
+bool Pt2IsBetweenPt1AndPt3(const IntPoint pt1,
+  const IntPoint pt2, const IntPoint pt3)
+{
+  if ((pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2))
+    return false;
+  else if (pt1.X != pt3.X)
+    return (pt2.X > pt1.X) == (pt2.X < pt3.X);
+  else
+    return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
+}
+//------------------------------------------------------------------------------
+
+bool HorzSegmentsOverlap(cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b)
+{
+  if (seg1a > seg1b) std::swap(seg1a, seg1b);
+  if (seg2a > seg2b) std::swap(seg2a, seg2b);
+  return (seg1a < seg2b) && (seg2a < seg1b);
+}
+
+//------------------------------------------------------------------------------
+// ClipperBase class methods ...
+//------------------------------------------------------------------------------
+
+ClipperBase::ClipperBase() //constructor
+{
+  m_CurrentLM = m_MinimaList.begin(); //begin() == end() here
+  m_UseFullRange = false;
+}
+//------------------------------------------------------------------------------
+
+ClipperBase::~ClipperBase() //destructor
+{
+  Clear();
+}
+//------------------------------------------------------------------------------
+
+void RangeTest(const IntPoint& Pt, bool& useFullRange)
+{
+  if (useFullRange)
+  {
+    if (Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange) 
+      throw clipperException("Coordinate outside allowed range");
+  }
+  else if (Pt.X > loRange|| Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange) 
+  {
+    useFullRange = true;
+    RangeTest(Pt, useFullRange);
+  }
+}
+//------------------------------------------------------------------------------
+
+TEdge* FindNextLocMin(TEdge* E)
+{
+  for (;;)
+  {
+    while (E->Bot != E->Prev->Bot || E->Curr == E->Top) E = E->Next;
+    if (!IsHorizontal(*E) && !IsHorizontal(*E->Prev)) break;
+    while (IsHorizontal(*E->Prev)) E = E->Prev;
+    TEdge* E2 = E;
+    while (IsHorizontal(*E)) E = E->Next;
+    if (E->Top.Y == E->Prev->Bot.Y) continue; //ie just an intermediate horz.
+    if (E2->Prev->Bot.X < E->Bot.X) E = E2;
+    break;
+  }
+  return E;
+}
+//------------------------------------------------------------------------------
+
+TEdge* ClipperBase::ProcessBound(TEdge* E, bool NextIsForward)
+{
+  TEdge *Result = E;
+  TEdge *Horz = 0;
+
+  if (E->OutIdx == Skip)
+  {
+    //if edges still remain in the current bound beyond the skip edge then
+    //create another LocMin and call ProcessBound once more
+    if (NextIsForward)
+    {
+      while (E->Top.Y == E->Next->Bot.Y) E = E->Next;
+      //don't include top horizontals when parsing a bound a second time,
+      //they will be contained in the opposite bound ...
+      while (E != Result && IsHorizontal(*E)) E = E->Prev;
+    }
+    else
+    {
+      while (E->Top.Y == E->Prev->Bot.Y) E = E->Prev;
+      while (E != Result && IsHorizontal(*E)) E = E->Next;
+    }
+
+    if (E == Result)
+    {
+      if (NextIsForward) Result = E->Next;
+      else Result = E->Prev;
+    }
+    else
+    {
+      //there are more edges in the bound beyond result starting with E
+      if (NextIsForward)
+        E = Result->Next;
+      else
+        E = Result->Prev;
+      MinimaList::value_type locMin;
+      locMin.Y = E->Bot.Y;
+      locMin.LeftBound = 0;
+      locMin.RightBound = E;
+      E->WindDelta = 0;
+      Result = ProcessBound(E, NextIsForward);
+      m_MinimaList.push_back(locMin);
+    }
+    return Result;
+  }
+
+  TEdge *EStart;
+
+  if (IsHorizontal(*E))
+  {
+    //We need to be careful with open paths because this may not be a
+    //true local minima (ie E may be following a skip edge).
+    //Also, consecutive horz. edges may start heading left before going right.
+    if (NextIsForward) 
+      EStart = E->Prev;
+    else 
+      EStart = E->Next;
+    if (IsHorizontal(*EStart)) //ie an adjoining horizontal skip edge
+      {
+        if (EStart->Bot.X != E->Bot.X && EStart->Top.X != E->Bot.X)
+          ReverseHorizontal(*E);
+      }
+      else if (EStart->Bot.X != E->Bot.X)
+        ReverseHorizontal(*E);
+  }
+  
+  EStart = E;
+  if (NextIsForward)
+  {
+    while (Result->Top.Y == Result->Next->Bot.Y && Result->Next->OutIdx != Skip)
+      Result = Result->Next;
+    if (IsHorizontal(*Result) && Result->Next->OutIdx != Skip)
+    {
+      //nb: at the top of a bound, horizontals are added to the bound
+      //only when the preceding edge attaches to the horizontal's left vertex
+      //unless a Skip edge is encountered when that becomes the top divide
+      Horz = Result;
+      while (IsHorizontal(*Horz->Prev)) Horz = Horz->Prev;
+      if (Horz->Prev->Top.X > Result->Next->Top.X) Result = Horz->Prev;
+    }
+    while (E != Result) 
+    {
+      E->NextInLML = E->Next;
+      if (IsHorizontal(*E) && E != EStart &&
+        E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
+      E = E->Next;
+    }
+    if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Prev->Top.X) 
+      ReverseHorizontal(*E);
+    Result = Result->Next; //move to the edge just beyond current bound
+  } else
+  {
+    while (Result->Top.Y == Result->Prev->Bot.Y && Result->Prev->OutIdx != Skip) 
+      Result = Result->Prev;
+    if (IsHorizontal(*Result) && Result->Prev->OutIdx != Skip)
+    {
+      Horz = Result;
+      while (IsHorizontal(*Horz->Next)) Horz = Horz->Next;
+      if (Horz->Next->Top.X == Result->Prev->Top.X ||
+          Horz->Next->Top.X > Result->Prev->Top.X) Result = Horz->Next;
+    }
+
+    while (E != Result)
+    {
+      E->NextInLML = E->Prev;
+      if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X) 
+        ReverseHorizontal(*E);
+      E = E->Prev;
+    }
+    if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X) 
+      ReverseHorizontal(*E);
+    Result = Result->Prev; //move to the edge just beyond current bound
+  }
+
+  return Result;
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::AddPath(const Path &pg, PolyType PolyTyp, bool Closed)
+{
+#ifdef use_lines
+  if (!Closed && PolyTyp == ptClip)
+    throw clipperException("AddPath: Open paths must be subject.");
+#else
+  if (!Closed)
+    throw clipperException("AddPath: Open paths have been disabled.");
+#endif
+
+  int highI = (int)pg.size() -1;
+  if (Closed) while (highI > 0 && (pg[highI] == pg[0])) --highI;
+  while (highI > 0 && (pg[highI] == pg[highI -1])) --highI;
+  if ((Closed && highI < 2) || (!Closed && highI < 1)) return false;
+
+  //create a new edge array ...
+  TEdge *edges = new TEdge [highI +1];
+
+  bool IsFlat = true;
+  //1. Basic (first) edge initialization ...
+  try
+  {
+    edges[1].Curr = pg[1];
+    RangeTest(pg[0], m_UseFullRange);
+    RangeTest(pg[highI], m_UseFullRange);
+    InitEdge(&edges[0], &edges[1], &edges[highI], pg[0]);
+    InitEdge(&edges[highI], &edges[0], &edges[highI-1], pg[highI]);
+    for (int i = highI - 1; i >= 1; --i)
+    {
+      RangeTest(pg[i], m_UseFullRange);
+      InitEdge(&edges[i], &edges[i+1], &edges[i-1], pg[i]);
+    }
+  }
+  catch(...)
+  {
+    delete [] edges;
+    throw; //range test fails
+  }
+  TEdge *eStart = &edges[0];
+
+  //2. Remove duplicate vertices, and (when closed) collinear edges ...
+  TEdge *E = eStart, *eLoopStop = eStart;
+  for (;;)
+  {
+    //nb: allows matching start and end points when not Closed ...
+    if (E->Curr == E->Next->Curr && (Closed || E->Next != eStart))
+    {
+      if (E == E->Next) break;
+      if (E == eStart) eStart = E->Next;
+      E = RemoveEdge(E);
+      eLoopStop = E;
+      continue;
+    }
+    if (E->Prev == E->Next) 
+      break; //only two vertices
+    else if (Closed &&
+      SlopesEqual(E->Prev->Curr, E->Curr, E->Next->Curr, m_UseFullRange) && 
+      (!m_PreserveCollinear ||
+      !Pt2IsBetweenPt1AndPt3(E->Prev->Curr, E->Curr, E->Next->Curr)))
+    {
+      //Collinear edges are allowed for open paths but in closed paths
+      //the default is to merge adjacent collinear edges into a single edge.
+      //However, if the PreserveCollinear property is enabled, only overlapping
+      //collinear edges (ie spikes) will be removed from closed paths.
+      if (E == eStart) eStart = E->Next;
+      E = RemoveEdge(E);
+      E = E->Prev;
+      eLoopStop = E;
+      continue;
+    }
+    E = E->Next;
+    if ((E == eLoopStop) || (!Closed && E->Next == eStart)) break;
+  }
+
+  if ((!Closed && (E == E->Next)) || (Closed && (E->Prev == E->Next)))
+  {
+    delete [] edges;
+    return false;
+  }
+
+  if (!Closed)
+  { 
+    m_HasOpenPaths = true;
+    eStart->Prev->OutIdx = Skip;
+  }
+
+  //3. Do second stage of edge initialization ...
+  E = eStart;
+  do
+  {
+    InitEdge2(*E, PolyTyp);
+    E = E->Next;
+    if (IsFlat && E->Curr.Y != eStart->Curr.Y) IsFlat = false;
+  }
+  while (E != eStart);
+
+  //4. Finally, add edge bounds to LocalMinima list ...
+
+  //Totally flat paths must be handled differently when adding them
+  //to LocalMinima list to avoid endless loops etc ...
+  if (IsFlat) 
+  {
+    if (Closed) 
+    {
+      delete [] edges;
+      return false;
+    }
+    E->Prev->OutIdx = Skip;
+    MinimaList::value_type locMin;
+    locMin.Y = E->Bot.Y;
+    locMin.LeftBound = 0;
+    locMin.RightBound = E;
+    locMin.RightBound->Side = esRight;
+    locMin.RightBound->WindDelta = 0;
+    for (;;)
+    {
+      if (E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
+      if (E->Next->OutIdx == Skip) break;
+      E->NextInLML = E->Next;
+      E = E->Next;
+    }
+    m_MinimaList.push_back(locMin);
+    m_edges.push_back(edges);
+	  return true;
+  }
+
+  m_edges.push_back(edges);
+  bool leftBoundIsForward;
+  TEdge* EMin = 0;
+
+  //workaround to avoid an endless loop in the while loop below when
+  //open paths have matching start and end points ...
+  if (E->Prev->Bot == E->Prev->Top) E = E->Next;
+
+  for (;;)
+  {
+    E = FindNextLocMin(E);
+    if (E == EMin) break;
+    else if (!EMin) EMin = E;
+
+    //E and E.Prev now share a local minima (left aligned if horizontal).
+    //Compare their slopes to find which starts which bound ...
+    MinimaList::value_type locMin;
+    locMin.Y = E->Bot.Y;
+    if (E->Dx < E->Prev->Dx) 
+    {
+      locMin.LeftBound = E->Prev;
+      locMin.RightBound = E;
+      leftBoundIsForward = false; //Q.nextInLML = Q.prev
+    } else
+    {
+      locMin.LeftBound = E;
+      locMin.RightBound = E->Prev;
+      leftBoundIsForward = true; //Q.nextInLML = Q.next
+    }
+
+    if (!Closed) locMin.LeftBound->WindDelta = 0;
+    else if (locMin.LeftBound->Next == locMin.RightBound)
+      locMin.LeftBound->WindDelta = -1;
+    else locMin.LeftBound->WindDelta = 1;
+    locMin.RightBound->WindDelta = -locMin.LeftBound->WindDelta;
+
+    E = ProcessBound(locMin.LeftBound, leftBoundIsForward);
+    if (E->OutIdx == Skip) E = ProcessBound(E, leftBoundIsForward);
+
+    TEdge* E2 = ProcessBound(locMin.RightBound, !leftBoundIsForward);
+    if (E2->OutIdx == Skip) E2 = ProcessBound(E2, !leftBoundIsForward);
+
+    if (locMin.LeftBound->OutIdx == Skip)
+      locMin.LeftBound = 0;
+    else if (locMin.RightBound->OutIdx == Skip)
+      locMin.RightBound = 0;
+    m_MinimaList.push_back(locMin);
+    if (!leftBoundIsForward) E = E2;
+  }
+  return true;
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed)
+{
+  bool result = false;
+  for (Paths::size_type i = 0; i < ppg.size(); ++i)
+    if (AddPath(ppg[i], PolyTyp, Closed)) result = true;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::Clear()
+{
+  DisposeLocalMinimaList();
+  for (EdgeList::size_type i = 0; i < m_edges.size(); ++i)
+  {
+    TEdge* edges = m_edges[i];
+    delete [] edges;
+  }
+  m_edges.clear();
+  m_UseFullRange = false;
+  m_HasOpenPaths = false;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::Reset()
+{
+  m_CurrentLM = m_MinimaList.begin();
+  if (m_CurrentLM == m_MinimaList.end()) return; //ie nothing to process
+  std::sort(m_MinimaList.begin(), m_MinimaList.end(), LocMinSorter());
+
+  m_Scanbeam = ScanbeamList(); //clears/resets priority_queue
+  //reset all edges ...
+  for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
+  {
+    InsertScanbeam(lm->Y);
+    TEdge* e = lm->LeftBound;
+    if (e)
+    {
+      e->Curr = e->Bot;
+      e->Side = esLeft;
+      e->OutIdx = Unassigned;
+    }
+
+    e = lm->RightBound;
+    if (e)
+    {
+      e->Curr = e->Bot;
+      e->Side = esRight;
+      e->OutIdx = Unassigned;
+    }
+  }
+  m_ActiveEdges = 0;
+  m_CurrentLM = m_MinimaList.begin();
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::DisposeLocalMinimaList()
+{
+  m_MinimaList.clear();
+  m_CurrentLM = m_MinimaList.begin();
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::PopLocalMinima(cInt Y, const LocalMinimum *&locMin)
+{
+  if (m_CurrentLM == m_MinimaList.end() || (*m_CurrentLM).Y != Y) return false;
+  locMin = &(*m_CurrentLM);
+  ++m_CurrentLM;
+  return true;
+}
+//------------------------------------------------------------------------------
+
+IntRect ClipperBase::GetBounds()
+{
+  IntRect result;
+  MinimaList::iterator lm = m_MinimaList.begin();
+  if (lm == m_MinimaList.end())
+  {
+    result.left = result.top = result.right = result.bottom = 0;
+    return result;
+  }
+  result.left = lm->LeftBound->Bot.X;
+  result.top = lm->LeftBound->Bot.Y;
+  result.right = lm->LeftBound->Bot.X;
+  result.bottom = lm->LeftBound->Bot.Y;
+  while (lm != m_MinimaList.end())
+  {
+    //todo - needs fixing for open paths
+    result.bottom = std::max(result.bottom, lm->LeftBound->Bot.Y);
+    TEdge* e = lm->LeftBound;
+    for (;;) {
+      TEdge* bottomE = e;
+      while (e->NextInLML)
+      {
+        if (e->Bot.X < result.left) result.left = e->Bot.X;
+        if (e->Bot.X > result.right) result.right = e->Bot.X;
+        e = e->NextInLML;
+      }
+      result.left = std::min(result.left, e->Bot.X);
+      result.right = std::max(result.right, e->Bot.X);
+      result.left = std::min(result.left, e->Top.X);
+      result.right = std::max(result.right, e->Top.X);
+      result.top = std::min(result.top, e->Top.Y);
+      if (bottomE == lm->LeftBound) e = lm->RightBound;
+      else break;
+    }
+    ++lm;
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::InsertScanbeam(const cInt Y)
+{
+  m_Scanbeam.push(Y);
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::PopScanbeam(cInt &Y)
+{
+  if (m_Scanbeam.empty()) return false;
+  Y = m_Scanbeam.top();
+  m_Scanbeam.pop();
+  while (!m_Scanbeam.empty() && Y == m_Scanbeam.top()) { m_Scanbeam.pop(); } // Pop duplicates.
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::DisposeAllOutRecs(){
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    DisposeOutRec(i);
+  m_PolyOuts.clear();
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::DisposeOutRec(PolyOutList::size_type index)
+{
+  OutRec *outRec = m_PolyOuts[index];
+  if (outRec->Pts) DisposeOutPts(outRec->Pts);
+  delete outRec;
+  m_PolyOuts[index] = 0;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::DeleteFromAEL(TEdge *e)
+{
+  TEdge* AelPrev = e->PrevInAEL;
+  TEdge* AelNext = e->NextInAEL;
+  if (!AelPrev &&  !AelNext && (e != m_ActiveEdges)) return; //already deleted
+  if (AelPrev) AelPrev->NextInAEL = AelNext;
+  else m_ActiveEdges = AelNext;
+  if (AelNext) AelNext->PrevInAEL = AelPrev;
+  e->NextInAEL = 0;
+  e->PrevInAEL = 0;
+}
+//------------------------------------------------------------------------------
+
+OutRec* ClipperBase::CreateOutRec()
+{
+  OutRec* result = new OutRec;
+  result->IsHole = false;
+  result->IsOpen = false;
+  result->FirstLeft = 0;
+  result->Pts = 0;
+  result->BottomPt = 0;
+  result->PolyNd = 0;
+  m_PolyOuts.push_back(result);
+  result->Idx = (int)m_PolyOuts.size() - 1;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::SwapPositionsInAEL(TEdge *Edge1, TEdge *Edge2)
+{
+  //check that one or other edge hasn't already been removed from AEL ...
+  if (Edge1->NextInAEL == Edge1->PrevInAEL ||
+    Edge2->NextInAEL == Edge2->PrevInAEL) return;
+
+  if (Edge1->NextInAEL == Edge2)
+  {
+    TEdge* Next = Edge2->NextInAEL;
+    if (Next) Next->PrevInAEL = Edge1;
+    TEdge* Prev = Edge1->PrevInAEL;
+    if (Prev) Prev->NextInAEL = Edge2;
+    Edge2->PrevInAEL = Prev;
+    Edge2->NextInAEL = Edge1;
+    Edge1->PrevInAEL = Edge2;
+    Edge1->NextInAEL = Next;
+  }
+  else if (Edge2->NextInAEL == Edge1)
+  {
+    TEdge* Next = Edge1->NextInAEL;
+    if (Next) Next->PrevInAEL = Edge2;
+    TEdge* Prev = Edge2->PrevInAEL;
+    if (Prev) Prev->NextInAEL = Edge1;
+    Edge1->PrevInAEL = Prev;
+    Edge1->NextInAEL = Edge2;
+    Edge2->PrevInAEL = Edge1;
+    Edge2->NextInAEL = Next;
+  }
+  else
+  {
+    TEdge* Next = Edge1->NextInAEL;
+    TEdge* Prev = Edge1->PrevInAEL;
+    Edge1->NextInAEL = Edge2->NextInAEL;
+    if (Edge1->NextInAEL) Edge1->NextInAEL->PrevInAEL = Edge1;
+    Edge1->PrevInAEL = Edge2->PrevInAEL;
+    if (Edge1->PrevInAEL) Edge1->PrevInAEL->NextInAEL = Edge1;
+    Edge2->NextInAEL = Next;
+    if (Edge2->NextInAEL) Edge2->NextInAEL->PrevInAEL = Edge2;
+    Edge2->PrevInAEL = Prev;
+    if (Edge2->PrevInAEL) Edge2->PrevInAEL->NextInAEL = Edge2;
+  }
+
+  if (!Edge1->PrevInAEL) m_ActiveEdges = Edge1;
+  else if (!Edge2->PrevInAEL) m_ActiveEdges = Edge2;
+}
+//------------------------------------------------------------------------------
+
+void ClipperBase::UpdateEdgeIntoAEL(TEdge *&e)
+{
+  if (!e->NextInLML) 
+    throw clipperException("UpdateEdgeIntoAEL: invalid call");
+
+  e->NextInLML->OutIdx = e->OutIdx;
+  TEdge* AelPrev = e->PrevInAEL;
+  TEdge* AelNext = e->NextInAEL;
+  if (AelPrev) AelPrev->NextInAEL = e->NextInLML;
+  else m_ActiveEdges = e->NextInLML;
+  if (AelNext) AelNext->PrevInAEL = e->NextInLML;
+  e->NextInLML->Side = e->Side;
+  e->NextInLML->WindDelta = e->WindDelta;
+  e->NextInLML->WindCnt = e->WindCnt;
+  e->NextInLML->WindCnt2 = e->WindCnt2;
+  e = e->NextInLML;
+  e->Curr = e->Bot;
+  e->PrevInAEL = AelPrev;
+  e->NextInAEL = AelNext;
+  if (!IsHorizontal(*e)) InsertScanbeam(e->Top.Y);
+}
+//------------------------------------------------------------------------------
+
+bool ClipperBase::LocalMinimaPending()
+{
+  return (m_CurrentLM != m_MinimaList.end());
+}
+
+//------------------------------------------------------------------------------
+// TClipper methods ...
+//------------------------------------------------------------------------------
+
+Clipper::Clipper(int initOptions) : ClipperBase() //constructor
+{
+  m_ExecuteLocked = false;
+  m_UseFullRange = false;
+  m_ReverseOutput = ((initOptions & ioReverseSolution) != 0);
+  m_StrictSimple = ((initOptions & ioStrictlySimple) != 0);
+  m_PreserveCollinear = ((initOptions & ioPreserveCollinear) != 0);
+  m_HasOpenPaths = false;
+#ifdef use_xyz  
+  m_ZFill = 0;
+#endif
+}
+//------------------------------------------------------------------------------
+
+#ifdef use_xyz  
+void Clipper::ZFillFunction(ZFillCallback zFillFunc)
+{  
+  m_ZFill = zFillFunc;
+}
+//------------------------------------------------------------------------------
+#endif
+
+bool Clipper::Execute(ClipType clipType, Paths &solution, PolyFillType fillType)
+{
+    return Execute(clipType, solution, fillType, fillType);
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::Execute(ClipType clipType, PolyTree &polytree, PolyFillType fillType)
+{
+    return Execute(clipType, polytree, fillType, fillType);
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::Execute(ClipType clipType, Paths &solution,
+    PolyFillType subjFillType, PolyFillType clipFillType)
+{
+  if( m_ExecuteLocked ) return false;
+  if (m_HasOpenPaths)
+    throw clipperException("Error: PolyTree struct is needed for open path clipping.");
+  m_ExecuteLocked = true;
+  solution.resize(0);
+  m_SubjFillType = subjFillType;
+  m_ClipFillType = clipFillType;
+  m_ClipType = clipType;
+  m_UsingPolyTree = false;
+  bool succeeded = ExecuteInternal();
+  if (succeeded) BuildResult(solution);
+  DisposeAllOutRecs();
+  m_ExecuteLocked = false;
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::Execute(ClipType clipType, PolyTree& polytree,
+    PolyFillType subjFillType, PolyFillType clipFillType)
+{
+  if( m_ExecuteLocked ) return false;
+  m_ExecuteLocked = true;
+  m_SubjFillType = subjFillType;
+  m_ClipFillType = clipFillType;
+  m_ClipType = clipType;
+  m_UsingPolyTree = true;
+  bool succeeded = ExecuteInternal();
+  if (succeeded) BuildResult2(polytree);
+  DisposeAllOutRecs();
+  m_ExecuteLocked = false;
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::FixHoleLinkage(OutRec &outrec)
+{
+  //skip OutRecs that (a) contain outermost polygons or
+  //(b) already have the correct owner/child linkage ...
+  if (!outrec.FirstLeft ||                
+      (outrec.IsHole != outrec.FirstLeft->IsHole &&
+      outrec.FirstLeft->Pts)) return;
+
+  OutRec* orfl = outrec.FirstLeft;
+  while (orfl && ((orfl->IsHole == outrec.IsHole) || !orfl->Pts))
+      orfl = orfl->FirstLeft;
+  outrec.FirstLeft = orfl;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::ExecuteInternal()
+{
+  bool succeeded = true;
+  try {
+    Reset();
+    m_Maxima = MaximaList();
+    m_SortedEdges = 0;
+
+    succeeded = true;
+    cInt botY, topY;
+    if (!PopScanbeam(botY)) return false;
+    InsertLocalMinimaIntoAEL(botY);
+    while (PopScanbeam(topY) || LocalMinimaPending())
+    {
+      ProcessHorizontals();
+	    ClearGhostJoins();
+      if (!ProcessIntersections(topY))
+      {
+        succeeded = false;
+        break;
+      }
+      ProcessEdgesAtTopOfScanbeam(topY);
+      botY = topY;
+      InsertLocalMinimaIntoAEL(botY);
+    }
+  }
+  catch(...) 
+  {
+    succeeded = false;
+  }
+
+  if (succeeded)
+  {
+    //fix orientations ...
+    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    {
+      OutRec *outRec = m_PolyOuts[i];
+      if (!outRec->Pts || outRec->IsOpen) continue;
+      if ((outRec->IsHole ^ m_ReverseOutput) == (Area(*outRec) > 0))
+        ReversePolyPtLinks(outRec->Pts);
+    }
+
+    if (!m_Joins.empty()) JoinCommonEdges();
+
+    //unfortunately FixupOutPolygon() must be done after JoinCommonEdges()
+    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+    {
+      OutRec *outRec = m_PolyOuts[i];
+      if (!outRec->Pts) continue;
+      if (outRec->IsOpen)
+        FixupOutPolyline(*outRec);
+      else
+        FixupOutPolygon(*outRec);
+    }
+
+    if (m_StrictSimple) DoSimplePolygons();
+  }
+
+  ClearJoins();
+  ClearGhostJoins();
+  return succeeded;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::SetWindingCount(TEdge &edge)
+{
+  TEdge *e = edge.PrevInAEL;
+  //find the edge of the same polytype that immediately preceeds 'edge' in AEL
+  while (e  && ((e->PolyTyp != edge.PolyTyp) || (e->WindDelta == 0))) e = e->PrevInAEL;
+  if (!e)
+  {
+    if (edge.WindDelta == 0)
+    {
+      PolyFillType pft = (edge.PolyTyp == ptSubject ? m_SubjFillType : m_ClipFillType);
+      edge.WindCnt = (pft == pftNegative ? -1 : 1);
+    }
+    else
+      edge.WindCnt = edge.WindDelta;
+    edge.WindCnt2 = 0;
+    e = m_ActiveEdges; //ie get ready to calc WindCnt2
+  }   
+  else if (edge.WindDelta == 0 && m_ClipType != ctUnion)
+  {
+    edge.WindCnt = 1;
+    edge.WindCnt2 = e->WindCnt2;
+    e = e->NextInAEL; //ie get ready to calc WindCnt2
+  }
+  else if (IsEvenOddFillType(edge))
+  {
+    //EvenOdd filling ...
+    if (edge.WindDelta == 0)
+    {
+      //are we inside a subj polygon ...
+      bool Inside = true;
+      TEdge *e2 = e->PrevInAEL;
+      while (e2)
+      {
+        if (e2->PolyTyp == e->PolyTyp && e2->WindDelta != 0) 
+          Inside = !Inside;
+        e2 = e2->PrevInAEL;
+      }
+      edge.WindCnt = (Inside ? 0 : 1);
+    }
+    else
+    {
+      edge.WindCnt = edge.WindDelta;
+    }
+    edge.WindCnt2 = e->WindCnt2;
+    e = e->NextInAEL; //ie get ready to calc WindCnt2
+  } 
+  else
+  {
+    //nonZero, Positive or Negative filling ...
+    if (e->WindCnt * e->WindDelta < 0)
+    {
+      //prev edge is 'decreasing' WindCount (WC) toward zero
+      //so we're outside the previous polygon ...
+      if (Abs(e->WindCnt) > 1)
+      {
+        //outside prev poly but still inside another.
+        //when reversing direction of prev poly use the same WC 
+        if (e->WindDelta * edge.WindDelta < 0) edge.WindCnt = e->WindCnt;
+        //otherwise continue to 'decrease' WC ...
+        else edge.WindCnt = e->WindCnt + edge.WindDelta;
+      } 
+      else
+        //now outside all polys of same polytype so set own WC ...
+        edge.WindCnt = (edge.WindDelta == 0 ? 1 : edge.WindDelta);
+    } else
+    {
+      //prev edge is 'increasing' WindCount (WC) away from zero
+      //so we're inside the previous polygon ...
+      if (edge.WindDelta == 0) 
+        edge.WindCnt = (e->WindCnt < 0 ? e->WindCnt - 1 : e->WindCnt + 1);
+      //if wind direction is reversing prev then use same WC
+      else if (e->WindDelta * edge.WindDelta < 0) edge.WindCnt = e->WindCnt;
+      //otherwise add to WC ...
+      else edge.WindCnt = e->WindCnt + edge.WindDelta;
+    }
+    edge.WindCnt2 = e->WindCnt2;
+    e = e->NextInAEL; //ie get ready to calc WindCnt2
+  }
+
+  //update WindCnt2 ...
+  if (IsEvenOddAltFillType(edge))
+  {
+    //EvenOdd filling ...
+    while (e != &edge)
+    {
+      if (e->WindDelta != 0)
+        edge.WindCnt2 = (edge.WindCnt2 == 0 ? 1 : 0);
+      e = e->NextInAEL;
+    }
+  } else
+  {
+    //nonZero, Positive or Negative filling ...
+    while ( e != &edge )
+    {
+      edge.WindCnt2 += e->WindDelta;
+      e = e->NextInAEL;
+    }
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsEvenOddFillType(const TEdge& edge) const
+{
+  if (edge.PolyTyp == ptSubject)
+    return m_SubjFillType == pftEvenOdd; else
+    return m_ClipFillType == pftEvenOdd;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsEvenOddAltFillType(const TEdge& edge) const
+{
+  if (edge.PolyTyp == ptSubject)
+    return m_ClipFillType == pftEvenOdd; else
+    return m_SubjFillType == pftEvenOdd;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::IsContributing(const TEdge& edge) const
+{
+  PolyFillType pft, pft2;
+  if (edge.PolyTyp == ptSubject)
+  {
+    pft = m_SubjFillType;
+    pft2 = m_ClipFillType;
+  } else
+  {
+    pft = m_ClipFillType;
+    pft2 = m_SubjFillType;
+  }
+
+  switch(pft)
+  {
+    case pftEvenOdd: 
+      //return false if a subj line has been flagged as inside a subj polygon
+      if (edge.WindDelta == 0 && edge.WindCnt != 1) return false;
+      break;
+    case pftNonZero:
+      if (Abs(edge.WindCnt) != 1) return false;
+      break;
+    case pftPositive: 
+      if (edge.WindCnt != 1) return false;
+      break;
+    default: //pftNegative
+      if (edge.WindCnt != -1) return false;
+  }
+
+  switch(m_ClipType)
+  {
+    case ctIntersection:
+      switch(pft2)
+      {
+        case pftEvenOdd: 
+        case pftNonZero: 
+          return (edge.WindCnt2 != 0);
+        case pftPositive: 
+          return (edge.WindCnt2 > 0);
+        default: 
+          return (edge.WindCnt2 < 0);
+      }
+      break;
+    case ctUnion:
+      switch(pft2)
+      {
+        case pftEvenOdd: 
+        case pftNonZero: 
+          return (edge.WindCnt2 == 0);
+        case pftPositive: 
+          return (edge.WindCnt2 <= 0);
+        default: 
+          return (edge.WindCnt2 >= 0);
+      }
+      break;
+    case ctDifference:
+      if (edge.PolyTyp == ptSubject)
+        switch(pft2)
+        {
+          case pftEvenOdd: 
+          case pftNonZero: 
+            return (edge.WindCnt2 == 0);
+          case pftPositive: 
+            return (edge.WindCnt2 <= 0);
+          default: 
+            return (edge.WindCnt2 >= 0);
+        }
+      else
+        switch(pft2)
+        {
+          case pftEvenOdd: 
+          case pftNonZero: 
+            return (edge.WindCnt2 != 0);
+          case pftPositive: 
+            return (edge.WindCnt2 > 0);
+          default: 
+            return (edge.WindCnt2 < 0);
+        }
+      break;
+    case ctXor:
+      if (edge.WindDelta == 0) //XOr always contributing unless open
+        switch(pft2)
+        {
+          case pftEvenOdd: 
+          case pftNonZero: 
+            return (edge.WindCnt2 == 0);
+          case pftPositive: 
+            return (edge.WindCnt2 <= 0);
+          default: 
+            return (edge.WindCnt2 >= 0);
+        }
+      else 
+        return true;
+      break;
+    default:
+      return true;
+  }
+}
+//------------------------------------------------------------------------------
+
+OutPt* Clipper::AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
+{
+  OutPt* result;
+  TEdge *e, *prevE;
+  if (IsHorizontal(*e2) || ( e1->Dx > e2->Dx ))
+  {
+    result = AddOutPt(e1, Pt);
+    e2->OutIdx = e1->OutIdx;
+    e1->Side = esLeft;
+    e2->Side = esRight;
+    e = e1;
+    if (e->PrevInAEL == e2)
+      prevE = e2->PrevInAEL; 
+    else
+      prevE = e->PrevInAEL;
+  } else
+  {
+    result = AddOutPt(e2, Pt);
+    e1->OutIdx = e2->OutIdx;
+    e1->Side = esRight;
+    e2->Side = esLeft;
+    e = e2;
+    if (e->PrevInAEL == e1)
+        prevE = e1->PrevInAEL;
+    else
+        prevE = e->PrevInAEL;
+  }
+
+  if (prevE && prevE->OutIdx >= 0 && prevE->Top.Y < Pt.Y && e->Top.Y < Pt.Y) 
+  {
+    cInt xPrev = TopX(*prevE, Pt.Y);
+    cInt xE = TopX(*e, Pt.Y);
+    if (xPrev == xE && (e->WindDelta != 0) && (prevE->WindDelta != 0) &&
+      SlopesEqual(IntPoint(xPrev, Pt.Y), prevE->Top, IntPoint(xE, Pt.Y), e->Top, m_UseFullRange))
+    {
+      OutPt* outPt = AddOutPt(prevE, Pt);
+      AddJoin(result, outPt, e->Top);
+    }
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &Pt)
+{
+  AddOutPt( e1, Pt );
+  if (e2->WindDelta == 0) AddOutPt(e2, Pt);
+  if( e1->OutIdx == e2->OutIdx )
+  {
+    e1->OutIdx = Unassigned;
+    e2->OutIdx = Unassigned;
+  }
+  else if (e1->OutIdx < e2->OutIdx) 
+    AppendPolygon(e1, e2); 
+  else 
+    AppendPolygon(e2, e1);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddEdgeToSEL(TEdge *edge)
+{
+  //SEL pointers in PEdge are reused to build a list of horizontal edges.
+  //However, we don't need to worry about order with horizontal edge processing.
+  if( !m_SortedEdges )
+  {
+    m_SortedEdges = edge;
+    edge->PrevInSEL = 0;
+    edge->NextInSEL = 0;
+  }
+  else
+  {
+    edge->NextInSEL = m_SortedEdges;
+    edge->PrevInSEL = 0;
+    m_SortedEdges->PrevInSEL = edge;
+    m_SortedEdges = edge;
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::PopEdgeFromSEL(TEdge *&edge)
+{
+  if (!m_SortedEdges) return false;
+  edge = m_SortedEdges;
+  DeleteFromSEL(m_SortedEdges);
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::CopyAELToSEL()
+{
+  TEdge* e = m_ActiveEdges;
+  m_SortedEdges = e;
+  while ( e )
+  {
+    e->PrevInSEL = e->PrevInAEL;
+    e->NextInSEL = e->NextInAEL;
+    e = e->NextInAEL;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddJoin(OutPt *op1, OutPt *op2, const IntPoint OffPt)
+{
+  Join* j = new Join;
+  j->OutPt1 = op1;
+  j->OutPt2 = op2;
+  j->OffPt = OffPt;
+  m_Joins.push_back(j);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ClearJoins()
+{
+  for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
+    delete m_Joins[i];
+  m_Joins.resize(0);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ClearGhostJoins()
+{
+  for (JoinList::size_type i = 0; i < m_GhostJoins.size(); i++)
+    delete m_GhostJoins[i];
+  m_GhostJoins.resize(0);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AddGhostJoin(OutPt *op, const IntPoint OffPt)
+{
+  Join* j = new Join;
+  j->OutPt1 = op;
+  j->OutPt2 = 0;
+  j->OffPt = OffPt;
+  m_GhostJoins.push_back(j);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::InsertLocalMinimaIntoAEL(const cInt botY)
+{
+  const LocalMinimum *lm;
+  while (PopLocalMinima(botY, lm))
+  {
+    TEdge* lb = lm->LeftBound;
+    TEdge* rb = lm->RightBound;
+    
+    OutPt *Op1 = 0;
+    if (!lb)
+    {
+      //nb: don't insert LB into either AEL or SEL
+      InsertEdgeIntoAEL(rb, 0);
+      SetWindingCount(*rb);
+      if (IsContributing(*rb))
+        Op1 = AddOutPt(rb, rb->Bot); 
+    } 
+    else if (!rb)
+    {
+      InsertEdgeIntoAEL(lb, 0);
+      SetWindingCount(*lb);
+      if (IsContributing(*lb))
+        Op1 = AddOutPt(lb, lb->Bot);
+      InsertScanbeam(lb->Top.Y);
+    }
+    else
+    {
+      InsertEdgeIntoAEL(lb, 0);
+      InsertEdgeIntoAEL(rb, lb);
+      SetWindingCount( *lb );
+      rb->WindCnt = lb->WindCnt;
+      rb->WindCnt2 = lb->WindCnt2;
+      if (IsContributing(*lb))
+        Op1 = AddLocalMinPoly(lb, rb, lb->Bot);      
+      InsertScanbeam(lb->Top.Y);
+    }
+
+     if (rb)
+     {
+		 if (IsHorizontal(*rb))
+		 {
+			 AddEdgeToSEL(rb);
+			 if (rb->NextInLML) 
+				 InsertScanbeam(rb->NextInLML->Top.Y);
+		 }
+		 else InsertScanbeam( rb->Top.Y );
+     }
+
+    if (!lb || !rb) continue;
+
+    //if any output polygons share an edge, they'll need joining later ...
+    if (Op1 && IsHorizontal(*rb) && 
+      m_GhostJoins.size() > 0 && (rb->WindDelta != 0))
+    {
+      for (JoinList::size_type i = 0; i < m_GhostJoins.size(); ++i)
+      {
+        Join* jr = m_GhostJoins[i];
+        //if the horizontal Rb and a 'ghost' horizontal overlap, then convert
+        //the 'ghost' join to a real join ready for later ...
+        if (HorzSegmentsOverlap(jr->OutPt1->Pt.X, jr->OffPt.X, rb->Bot.X, rb->Top.X))
+          AddJoin(jr->OutPt1, Op1, jr->OffPt);
+      }
+    }
+
+    if (lb->OutIdx >= 0 && lb->PrevInAEL && 
+      lb->PrevInAEL->Curr.X == lb->Bot.X &&
+      lb->PrevInAEL->OutIdx >= 0 &&
+      SlopesEqual(lb->PrevInAEL->Bot, lb->PrevInAEL->Top, lb->Curr, lb->Top, m_UseFullRange) &&
+      (lb->WindDelta != 0) && (lb->PrevInAEL->WindDelta != 0))
+    {
+        OutPt *Op2 = AddOutPt(lb->PrevInAEL, lb->Bot);
+        AddJoin(Op1, Op2, lb->Top);
+    }
+
+    if(lb->NextInAEL != rb)
+    {
+
+      if (rb->OutIdx >= 0 && rb->PrevInAEL->OutIdx >= 0 &&
+        SlopesEqual(rb->PrevInAEL->Curr, rb->PrevInAEL->Top, rb->Curr, rb->Top, m_UseFullRange) &&
+        (rb->WindDelta != 0) && (rb->PrevInAEL->WindDelta != 0))
+      {
+          OutPt *Op2 = AddOutPt(rb->PrevInAEL, rb->Bot);
+          AddJoin(Op1, Op2, rb->Top);
+      }
+
+      TEdge* e = lb->NextInAEL;
+      if (e)
+      {
+        while( e != rb )
+        {
+          //nb: For calculating winding counts etc, IntersectEdges() assumes
+          //that param1 will be to the Right of param2 ABOVE the intersection ...
+          IntersectEdges(rb , e , lb->Curr); //order important here
+          e = e->NextInAEL;
+        }
+      }
+    }
+    
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DeleteFromSEL(TEdge *e)
+{
+  TEdge* SelPrev = e->PrevInSEL;
+  TEdge* SelNext = e->NextInSEL;
+  if( !SelPrev &&  !SelNext && (e != m_SortedEdges) ) return; //already deleted
+  if( SelPrev ) SelPrev->NextInSEL = SelNext;
+  else m_SortedEdges = SelNext;
+  if( SelNext ) SelNext->PrevInSEL = SelPrev;
+  e->NextInSEL = 0;
+  e->PrevInSEL = 0;
+}
+//------------------------------------------------------------------------------
+
+#ifdef use_xyz
+void Clipper::SetZ(IntPoint& pt, TEdge& e1, TEdge& e2)
+{
+  if (pt.Z != 0 || !m_ZFill) return;
+  else if (pt == e1.Bot) pt.Z = e1.Bot.Z;
+  else if (pt == e1.Top) pt.Z = e1.Top.Z;
+  else if (pt == e2.Bot) pt.Z = e2.Bot.Z;
+  else if (pt == e2.Top) pt.Z = e2.Top.Z;
+  else (*m_ZFill)(e1.Bot, e1.Top, e2.Bot, e2.Top, pt); 
+}
+//------------------------------------------------------------------------------
+#endif
+
+void Clipper::IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &Pt)
+{
+  bool e1Contributing = ( e1->OutIdx >= 0 );
+  bool e2Contributing = ( e2->OutIdx >= 0 );
+
+#ifdef use_xyz
+        SetZ(Pt, *e1, *e2);
+#endif
+
+#ifdef use_lines
+  //if either edge is on an OPEN path ...
+  if (e1->WindDelta == 0 || e2->WindDelta == 0)
+  {
+    //ignore subject-subject open path intersections UNLESS they
+    //are both open paths, AND they are both 'contributing maximas' ...
+	if (e1->WindDelta == 0 && e2->WindDelta == 0) return;
+
+    //if intersecting a subj line with a subj poly ...
+    else if (e1->PolyTyp == e2->PolyTyp && 
+      e1->WindDelta != e2->WindDelta && m_ClipType == ctUnion)
+    {
+      if (e1->WindDelta == 0)
+      {
+        if (e2Contributing)
+        {
+          AddOutPt(e1, Pt);
+          if (e1Contributing) e1->OutIdx = Unassigned;
+        }
+      }
+      else
+      {
+        if (e1Contributing)
+        {
+          AddOutPt(e2, Pt);
+          if (e2Contributing) e2->OutIdx = Unassigned;
+        }
+      }
+    }
+    else if (e1->PolyTyp != e2->PolyTyp)
+    {
+      //toggle subj open path OutIdx on/off when Abs(clip.WndCnt) == 1 ...
+      if ((e1->WindDelta == 0) && abs(e2->WindCnt) == 1 && 
+        (m_ClipType != ctUnion || e2->WindCnt2 == 0))
+      {
+        AddOutPt(e1, Pt);
+        if (e1Contributing) e1->OutIdx = Unassigned;
+      }
+      else if ((e2->WindDelta == 0) && (abs(e1->WindCnt) == 1) && 
+        (m_ClipType != ctUnion || e1->WindCnt2 == 0))
+      {
+        AddOutPt(e2, Pt);
+        if (e2Contributing) e2->OutIdx = Unassigned;
+      }
+    }
+    return;
+  }
+#endif
+
+  //update winding counts...
+  //assumes that e1 will be to the Right of e2 ABOVE the intersection
+  if ( e1->PolyTyp == e2->PolyTyp )
+  {
+    if ( IsEvenOddFillType( *e1) )
+    {
+      int oldE1WindCnt = e1->WindCnt;
+      e1->WindCnt = e2->WindCnt;
+      e2->WindCnt = oldE1WindCnt;
+    } else
+    {
+      if (e1->WindCnt + e2->WindDelta == 0 ) e1->WindCnt = -e1->WindCnt;
+      else e1->WindCnt += e2->WindDelta;
+      if ( e2->WindCnt - e1->WindDelta == 0 ) e2->WindCnt = -e2->WindCnt;
+      else e2->WindCnt -= e1->WindDelta;
+    }
+  } else
+  {
+    if (!IsEvenOddFillType(*e2)) e1->WindCnt2 += e2->WindDelta;
+    else e1->WindCnt2 = ( e1->WindCnt2 == 0 ) ? 1 : 0;
+    if (!IsEvenOddFillType(*e1)) e2->WindCnt2 -= e1->WindDelta;
+    else e2->WindCnt2 = ( e2->WindCnt2 == 0 ) ? 1 : 0;
+  }
+
+  PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;
+  if (e1->PolyTyp == ptSubject)
+  {
+    e1FillType = m_SubjFillType;
+    e1FillType2 = m_ClipFillType;
+  } else
+  {
+    e1FillType = m_ClipFillType;
+    e1FillType2 = m_SubjFillType;
+  }
+  if (e2->PolyTyp == ptSubject)
+  {
+    e2FillType = m_SubjFillType;
+    e2FillType2 = m_ClipFillType;
+  } else
+  {
+    e2FillType = m_ClipFillType;
+    e2FillType2 = m_SubjFillType;
+  }
+
+  cInt e1Wc, e2Wc;
+  switch (e1FillType)
+  {
+    case pftPositive: e1Wc = e1->WindCnt; break;
+    case pftNegative: e1Wc = -e1->WindCnt; break;
+    default: e1Wc = Abs(e1->WindCnt);
+  }
+  switch(e2FillType)
+  {
+    case pftPositive: e2Wc = e2->WindCnt; break;
+    case pftNegative: e2Wc = -e2->WindCnt; break;
+    default: e2Wc = Abs(e2->WindCnt);
+  }
+
+  if ( e1Contributing && e2Contributing )
+  {
+    if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
+      (e1->PolyTyp != e2->PolyTyp && m_ClipType != ctXor) )
+    {
+      AddLocalMaxPoly(e1, e2, Pt); 
+    }
+    else
+    {
+      AddOutPt(e1, Pt);
+      AddOutPt(e2, Pt);
+      SwapSides( *e1 , *e2 );
+      SwapPolyIndexes( *e1 , *e2 );
+    }
+  }
+  else if ( e1Contributing )
+  {
+    if (e2Wc == 0 || e2Wc == 1) 
+    {
+      AddOutPt(e1, Pt);
+      SwapSides(*e1, *e2);
+      SwapPolyIndexes(*e1, *e2);
+    }
+  }
+  else if ( e2Contributing )
+  {
+    if (e1Wc == 0 || e1Wc == 1) 
+    {
+      AddOutPt(e2, Pt);
+      SwapSides(*e1, *e2);
+      SwapPolyIndexes(*e1, *e2);
+    }
+  } 
+  else if ( (e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1))
+  {
+    //neither edge is currently contributing ...
+
+    cInt e1Wc2, e2Wc2;
+    switch (e1FillType2)
+    {
+      case pftPositive: e1Wc2 = e1->WindCnt2; break;
+      case pftNegative : e1Wc2 = -e1->WindCnt2; break;
+      default: e1Wc2 = Abs(e1->WindCnt2);
+    }
+    switch (e2FillType2)
+    {
+      case pftPositive: e2Wc2 = e2->WindCnt2; break;
+      case pftNegative: e2Wc2 = -e2->WindCnt2; break;
+      default: e2Wc2 = Abs(e2->WindCnt2);
+    }
+
+    if (e1->PolyTyp != e2->PolyTyp)
+    {
+      AddLocalMinPoly(e1, e2, Pt);
+    }
+    else if (e1Wc == 1 && e2Wc == 1)
+      switch( m_ClipType ) {
+        case ctIntersection:
+          if (e1Wc2 > 0 && e2Wc2 > 0)
+            AddLocalMinPoly(e1, e2, Pt);
+          break;
+        case ctUnion:
+          if ( e1Wc2 <= 0 && e2Wc2 <= 0 )
+            AddLocalMinPoly(e1, e2, Pt);
+          break;
+        case ctDifference:
+          if (((e1->PolyTyp == ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0)) ||
+              ((e1->PolyTyp == ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0)))
+                AddLocalMinPoly(e1, e2, Pt);
+          break;
+        case ctXor:
+          AddLocalMinPoly(e1, e2, Pt);
+      }
+    else
+      SwapSides( *e1, *e2 );
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::SetHoleState(TEdge *e, OutRec *outrec)
+{
+  TEdge *e2 = e->PrevInAEL;
+  TEdge *eTmp = 0;
+  while (e2)
+  {
+    if (e2->OutIdx >= 0 && e2->WindDelta != 0)
+    {
+      if (!eTmp) eTmp = e2;
+      else if (eTmp->OutIdx == e2->OutIdx) eTmp = 0;        
+    }
+    e2 = e2->PrevInAEL;
+  }
+  if (!eTmp)
+  {
+    outrec->FirstLeft = 0;
+    outrec->IsHole = false;
+  }
+  else
+  {
+    outrec->FirstLeft = m_PolyOuts[eTmp->OutIdx];
+    outrec->IsHole = !outrec->FirstLeft->IsHole;
+  }
+}
+//------------------------------------------------------------------------------
+
+OutRec* GetLowermostRec(OutRec *outRec1, OutRec *outRec2)
+{
+  //work out which polygon fragment has the correct hole state ...
+  if (!outRec1->BottomPt) 
+    outRec1->BottomPt = GetBottomPt(outRec1->Pts);
+  if (!outRec2->BottomPt) 
+    outRec2->BottomPt = GetBottomPt(outRec2->Pts);
+  OutPt *OutPt1 = outRec1->BottomPt;
+  OutPt *OutPt2 = outRec2->BottomPt;
+  if (OutPt1->Pt.Y > OutPt2->Pt.Y) return outRec1;
+  else if (OutPt1->Pt.Y < OutPt2->Pt.Y) return outRec2;
+  else if (OutPt1->Pt.X < OutPt2->Pt.X) return outRec1;
+  else if (OutPt1->Pt.X > OutPt2->Pt.X) return outRec2;
+  else if (OutPt1->Next == OutPt1) return outRec2;
+  else if (OutPt2->Next == OutPt2) return outRec1;
+  else if (FirstIsBottomPt(OutPt1, OutPt2)) return outRec1;
+  else return outRec2;
+}
+//------------------------------------------------------------------------------
+
+bool OutRec1RightOfOutRec2(OutRec* outRec1, OutRec* outRec2)
+{
+  do
+  {
+    outRec1 = outRec1->FirstLeft;
+    if (outRec1 == outRec2) return true;
+  } while (outRec1);
+  return false;
+}
+//------------------------------------------------------------------------------
+
+OutRec* Clipper::GetOutRec(int Idx)
+{
+  OutRec* outrec = m_PolyOuts[Idx];
+  while (outrec != m_PolyOuts[outrec->Idx])
+    outrec = m_PolyOuts[outrec->Idx];
+  return outrec;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::AppendPolygon(TEdge *e1, TEdge *e2)
+{
+  //get the start and ends of both output polygons ...
+  OutRec *outRec1 = m_PolyOuts[e1->OutIdx];
+  OutRec *outRec2 = m_PolyOuts[e2->OutIdx];
+
+  OutRec *holeStateRec;
+  if (OutRec1RightOfOutRec2(outRec1, outRec2))
+    holeStateRec = outRec2;
+  else if (OutRec1RightOfOutRec2(outRec2, outRec1))
+    holeStateRec = outRec1;
+  else 
+    holeStateRec = GetLowermostRec(outRec1, outRec2);
+
+  //get the start and ends of both output polygons and
+  //join e2 poly onto e1 poly and delete pointers to e2 ...
+
+  OutPt* p1_lft = outRec1->Pts;
+  OutPt* p1_rt = p1_lft->Prev;
+  OutPt* p2_lft = outRec2->Pts;
+  OutPt* p2_rt = p2_lft->Prev;
+
+  //join e2 poly onto e1 poly and delete pointers to e2 ...
+  if(  e1->Side == esLeft )
+  {
+    if(  e2->Side == esLeft )
+    {
+      //z y x a b c
+      ReversePolyPtLinks(p2_lft);
+      p2_lft->Next = p1_lft;
+      p1_lft->Prev = p2_lft;
+      p1_rt->Next = p2_rt;
+      p2_rt->Prev = p1_rt;
+      outRec1->Pts = p2_rt;
+    } else
+    {
+      //x y z a b c
+      p2_rt->Next = p1_lft;
+      p1_lft->Prev = p2_rt;
+      p2_lft->Prev = p1_rt;
+      p1_rt->Next = p2_lft;
+      outRec1->Pts = p2_lft;
+    }
+  } else
+  {
+    if(  e2->Side == esRight )
+    {
+      //a b c z y x
+      ReversePolyPtLinks(p2_lft);
+      p1_rt->Next = p2_rt;
+      p2_rt->Prev = p1_rt;
+      p2_lft->Next = p1_lft;
+      p1_lft->Prev = p2_lft;
+    } else
+    {
+      //a b c x y z
+      p1_rt->Next = p2_lft;
+      p2_lft->Prev = p1_rt;
+      p1_lft->Prev = p2_rt;
+      p2_rt->Next = p1_lft;
+    }
+  }
+
+  outRec1->BottomPt = 0;
+  if (holeStateRec == outRec2)
+  {
+    if (outRec2->FirstLeft != outRec1)
+      outRec1->FirstLeft = outRec2->FirstLeft;
+    outRec1->IsHole = outRec2->IsHole;
+  }
+  outRec2->Pts = 0;
+  outRec2->BottomPt = 0;
+  outRec2->FirstLeft = outRec1;
+
+  int OKIdx = e1->OutIdx;
+  int ObsoleteIdx = e2->OutIdx;
+
+  e1->OutIdx = Unassigned; //nb: safe because we only get here via AddLocalMaxPoly
+  e2->OutIdx = Unassigned;
+
+  TEdge* e = m_ActiveEdges;
+  while( e )
+  {
+    if( e->OutIdx == ObsoleteIdx )
+    {
+      e->OutIdx = OKIdx;
+      e->Side = e1->Side;
+      break;
+    }
+    e = e->NextInAEL;
+  }
+
+  outRec2->Idx = outRec1->Idx;
+}
+//------------------------------------------------------------------------------
+
+OutPt* Clipper::AddOutPt(TEdge *e, const IntPoint &pt)
+{
+  if(  e->OutIdx < 0 )
+  {
+    OutRec *outRec = CreateOutRec();
+    outRec->IsOpen = (e->WindDelta == 0);
+    OutPt* newOp = new OutPt;
+    outRec->Pts = newOp;
+    newOp->Idx = outRec->Idx;
+    newOp->Pt = pt;
+    newOp->Next = newOp;
+    newOp->Prev = newOp;
+    if (!outRec->IsOpen)
+      SetHoleState(e, outRec);
+    e->OutIdx = outRec->Idx;
+    return newOp;
+  } else
+  {
+    OutRec *outRec = m_PolyOuts[e->OutIdx];
+    //OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
+    OutPt* op = outRec->Pts;
+
+	bool ToFront = (e->Side == esLeft);
+	if (ToFront && (pt == op->Pt)) return op;
+    else if (!ToFront && (pt == op->Prev->Pt)) return op->Prev;
+
+    OutPt* newOp = new OutPt;
+    newOp->Idx = outRec->Idx;
+    newOp->Pt = pt;
+    newOp->Next = op;
+    newOp->Prev = op->Prev;
+    newOp->Prev->Next = newOp;
+    op->Prev = newOp;
+    if (ToFront) outRec->Pts = newOp;
+    return newOp;
+  }
+}
+//------------------------------------------------------------------------------
+
+OutPt* Clipper::GetLastOutPt(TEdge *e)
+{
+	OutRec *outRec = m_PolyOuts[e->OutIdx];
+	if (e->Side == esLeft)
+		return outRec->Pts;
+	else
+		return outRec->Pts->Prev;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessHorizontals()
+{
+  TEdge* horzEdge;
+  while (PopEdgeFromSEL(horzEdge))
+    ProcessHorizontal(horzEdge);
+}
+//------------------------------------------------------------------------------
+
+inline bool IsMinima(TEdge *e)
+{
+  return e  && (e->Prev->NextInLML != e) && (e->Next->NextInLML != e);
+}
+//------------------------------------------------------------------------------
+
+inline bool IsMaxima(TEdge *e, const cInt Y)
+{
+  return e && e->Top.Y == Y && !e->NextInLML;
+}
+//------------------------------------------------------------------------------
+
+inline bool IsIntermediate(TEdge *e, const cInt Y)
+{
+  return e->Top.Y == Y && e->NextInLML;
+}
+//------------------------------------------------------------------------------
+
+TEdge *GetMaximaPair(TEdge *e)
+{
+  if ((e->Next->Top == e->Top) && !e->Next->NextInLML)
+    return e->Next;
+  else if ((e->Prev->Top == e->Top) && !e->Prev->NextInLML)
+    return e->Prev;
+  else return 0;
+}
+//------------------------------------------------------------------------------
+
+TEdge *GetMaximaPairEx(TEdge *e)
+{
+  //as GetMaximaPair() but returns 0 if MaxPair isn't in AEL (unless it's horizontal)
+  TEdge* result = GetMaximaPair(e);
+  if (result && (result->OutIdx == Skip ||
+    (result->NextInAEL == result->PrevInAEL && !IsHorizontal(*result)))) return 0;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::SwapPositionsInSEL(TEdge *Edge1, TEdge *Edge2)
+{
+  if(  !( Edge1->NextInSEL ) &&  !( Edge1->PrevInSEL ) ) return;
+  if(  !( Edge2->NextInSEL ) &&  !( Edge2->PrevInSEL ) ) return;
+
+  if(  Edge1->NextInSEL == Edge2 )
+  {
+    TEdge* Next = Edge2->NextInSEL;
+    if( Next ) Next->PrevInSEL = Edge1;
+    TEdge* Prev = Edge1->PrevInSEL;
+    if( Prev ) Prev->NextInSEL = Edge2;
+    Edge2->PrevInSEL = Prev;
+    Edge2->NextInSEL = Edge1;
+    Edge1->PrevInSEL = Edge2;
+    Edge1->NextInSEL = Next;
+  }
+  else if(  Edge2->NextInSEL == Edge1 )
+  {
+    TEdge* Next = Edge1->NextInSEL;
+    if( Next ) Next->PrevInSEL = Edge2;
+    TEdge* Prev = Edge2->PrevInSEL;
+    if( Prev ) Prev->NextInSEL = Edge1;
+    Edge1->PrevInSEL = Prev;
+    Edge1->NextInSEL = Edge2;
+    Edge2->PrevInSEL = Edge1;
+    Edge2->NextInSEL = Next;
+  }
+  else
+  {
+    TEdge* Next = Edge1->NextInSEL;
+    TEdge* Prev = Edge1->PrevInSEL;
+    Edge1->NextInSEL = Edge2->NextInSEL;
+    if( Edge1->NextInSEL ) Edge1->NextInSEL->PrevInSEL = Edge1;
+    Edge1->PrevInSEL = Edge2->PrevInSEL;
+    if( Edge1->PrevInSEL ) Edge1->PrevInSEL->NextInSEL = Edge1;
+    Edge2->NextInSEL = Next;
+    if( Edge2->NextInSEL ) Edge2->NextInSEL->PrevInSEL = Edge2;
+    Edge2->PrevInSEL = Prev;
+    if( Edge2->PrevInSEL ) Edge2->PrevInSEL->NextInSEL = Edge2;
+  }
+
+  if( !Edge1->PrevInSEL ) m_SortedEdges = Edge1;
+  else if( !Edge2->PrevInSEL ) m_SortedEdges = Edge2;
+}
+//------------------------------------------------------------------------------
+
+TEdge* GetNextInAEL(TEdge *e, Direction dir)
+{
+  return dir == dLeftToRight ? e->NextInAEL : e->PrevInAEL;
+}
+//------------------------------------------------------------------------------
+
+void GetHorzDirection(TEdge& HorzEdge, Direction& Dir, cInt& Left, cInt& Right)
+{
+  if (HorzEdge.Bot.X < HorzEdge.Top.X)
+  {
+    Left = HorzEdge.Bot.X;
+    Right = HorzEdge.Top.X;
+    Dir = dLeftToRight;
+  } else
+  {
+    Left = HorzEdge.Top.X;
+    Right = HorzEdge.Bot.X;
+    Dir = dRightToLeft;
+  }
+}
+//------------------------------------------------------------------------
+
+/*******************************************************************************
+* Notes: Horizontal edges (HEs) at scanline intersections (ie at the Top or    *
+* Bottom of a scanbeam) are processed as if layered. The order in which HEs    *
+* are processed doesn't matter. HEs intersect with other HE Bot.Xs only [#]    *
+* (or they could intersect with Top.Xs only, ie EITHER Bot.Xs OR Top.Xs),      *
+* and with other non-horizontal edges [*]. Once these intersections are        *
+* processed, intermediate HEs then 'promote' the Edge above (NextInLML) into   *
+* the AEL. These 'promoted' edges may in turn intersect [%] with other HEs.    *
+*******************************************************************************/
+
+void Clipper::ProcessHorizontal(TEdge *horzEdge)
+{
+  Direction dir;
+  cInt horzLeft, horzRight;
+  bool IsOpen = (horzEdge->WindDelta == 0);
+
+  GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);
+
+  TEdge* eLastHorz = horzEdge, *eMaxPair = 0;
+  while (eLastHorz->NextInLML && IsHorizontal(*eLastHorz->NextInLML)) 
+    eLastHorz = eLastHorz->NextInLML;
+  if (!eLastHorz->NextInLML)
+    eMaxPair = GetMaximaPair(eLastHorz);
+
+  MaximaList::const_iterator maxIt;
+  MaximaList::const_reverse_iterator maxRit;
+  if (m_Maxima.size() > 0)
+  {
+      //get the first maxima in range (X) ...
+      if (dir == dLeftToRight)
+      {
+          maxIt = m_Maxima.begin();
+          while (maxIt != m_Maxima.end() && *maxIt <= horzEdge->Bot.X) maxIt++;
+          if (maxIt != m_Maxima.end() && *maxIt >= eLastHorz->Top.X)
+              maxIt = m_Maxima.end();
+      }
+      else
+      {
+          maxRit = m_Maxima.rbegin();
+          while (maxRit != m_Maxima.rend() && *maxRit > horzEdge->Bot.X) maxRit++;
+          if (maxRit != m_Maxima.rend() && *maxRit <= eLastHorz->Top.X)
+              maxRit = m_Maxima.rend();
+      }
+  }
+
+  OutPt* op1 = 0;
+
+  for (;;) //loop through consec. horizontal edges
+  {
+		  
+    bool IsLastHorz = (horzEdge == eLastHorz);
+    TEdge* e = GetNextInAEL(horzEdge, dir);
+    while(e)
+    {
+
+        //this code block inserts extra coords into horizontal edges (in output
+        //polygons) whereever maxima touch these horizontal edges. This helps
+        //'simplifying' polygons (ie if the Simplify property is set).
+        if (m_Maxima.size() > 0)
+        {
+            if (dir == dLeftToRight)
+            {
+                while (maxIt != m_Maxima.end() && *maxIt < e->Curr.X) 
+                {
+                  if (horzEdge->OutIdx >= 0 && !IsOpen)
+                    AddOutPt(horzEdge, IntPoint(*maxIt, horzEdge->Bot.Y));
+                  maxIt++;
+                }
+            }
+            else
+            {
+                while (maxRit != m_Maxima.rend() && *maxRit > e->Curr.X)
+                {
+                  if (horzEdge->OutIdx >= 0 && !IsOpen)
+                    AddOutPt(horzEdge, IntPoint(*maxRit, horzEdge->Bot.Y));
+                  maxRit++;
+                }
+            }
+        };
+
+        if ((dir == dLeftToRight && e->Curr.X > horzRight) ||
+			(dir == dRightToLeft && e->Curr.X < horzLeft)) break;
+
+		//Also break if we've got to the end of an intermediate horizontal edge ...
+		//nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
+		if (e->Curr.X == horzEdge->Top.X && horzEdge->NextInLML && 
+			e->Dx < horzEdge->NextInLML->Dx) break;
+
+    if (horzEdge->OutIdx >= 0 && !IsOpen)  //note: may be done multiple times
+		{
+#ifdef use_xyz
+			if (dir == dLeftToRight) SetZ(e->Curr, *horzEdge, *e);
+			else SetZ(e->Curr, *e, *horzEdge);
+#endif      
+			op1 = AddOutPt(horzEdge, e->Curr);
+			TEdge* eNextHorz = m_SortedEdges;
+			while (eNextHorz)
+			{
+				if (eNextHorz->OutIdx >= 0 &&
+					HorzSegmentsOverlap(horzEdge->Bot.X,
+					horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
+				{
+                    OutPt* op2 = GetLastOutPt(eNextHorz);
+                    AddJoin(op2, op1, eNextHorz->Top);
+				}
+				eNextHorz = eNextHorz->NextInSEL;
+			}
+			AddGhostJoin(op1, horzEdge->Bot);
+		}
+		
+		//OK, so far we're still in range of the horizontal Edge  but make sure
+        //we're at the last of consec. horizontals when matching with eMaxPair
+        if(e == eMaxPair && IsLastHorz)
+        {
+          if (horzEdge->OutIdx >= 0)
+            AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge->Top);
+          DeleteFromAEL(horzEdge);
+          DeleteFromAEL(eMaxPair);
+          return;
+        }
+        
+		if(dir == dLeftToRight)
+        {
+          IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
+          IntersectEdges(horzEdge, e, Pt);
+        }
+        else
+        {
+          IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
+          IntersectEdges( e, horzEdge, Pt);
+        }
+        TEdge* eNext = GetNextInAEL(e, dir);
+        SwapPositionsInAEL( horzEdge, e );
+        e = eNext;
+    } //end while(e)
+
+	//Break out of loop if HorzEdge.NextInLML is not also horizontal ...
+	if (!horzEdge->NextInLML || !IsHorizontal(*horzEdge->NextInLML)) break;
+
+	UpdateEdgeIntoAEL(horzEdge);
+    if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Bot);
+    GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);
+
+  } //end for (;;)
+
+  if (horzEdge->OutIdx >= 0 && !op1)
+  {
+      op1 = GetLastOutPt(horzEdge);
+      TEdge* eNextHorz = m_SortedEdges;
+      while (eNextHorz)
+      {
+          if (eNextHorz->OutIdx >= 0 &&
+              HorzSegmentsOverlap(horzEdge->Bot.X,
+              horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
+          {
+              OutPt* op2 = GetLastOutPt(eNextHorz);
+              AddJoin(op2, op1, eNextHorz->Top);
+          }
+          eNextHorz = eNextHorz->NextInSEL;
+      }
+      AddGhostJoin(op1, horzEdge->Top);
+  }
+
+  if (horzEdge->NextInLML)
+  {
+    if(horzEdge->OutIdx >= 0)
+    {
+      op1 = AddOutPt( horzEdge, horzEdge->Top);
+      UpdateEdgeIntoAEL(horzEdge);
+      if (horzEdge->WindDelta == 0) return;
+      //nb: HorzEdge is no longer horizontal here
+      TEdge* ePrev = horzEdge->PrevInAEL;
+      TEdge* eNext = horzEdge->NextInAEL;
+      if (ePrev && ePrev->Curr.X == horzEdge->Bot.X &&
+        ePrev->Curr.Y == horzEdge->Bot.Y && ePrev->WindDelta != 0 &&
+        (ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
+        SlopesEqual(*horzEdge, *ePrev, m_UseFullRange)))
+      {
+        OutPt* op2 = AddOutPt(ePrev, horzEdge->Bot);
+        AddJoin(op1, op2, horzEdge->Top);
+      }
+      else if (eNext && eNext->Curr.X == horzEdge->Bot.X &&
+        eNext->Curr.Y == horzEdge->Bot.Y && eNext->WindDelta != 0 &&
+        eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
+        SlopesEqual(*horzEdge, *eNext, m_UseFullRange))
+      {
+        OutPt* op2 = AddOutPt(eNext, horzEdge->Bot);
+        AddJoin(op1, op2, horzEdge->Top);
+      }
+    }
+    else
+      UpdateEdgeIntoAEL(horzEdge); 
+  }
+  else
+  {
+    if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Top);
+    DeleteFromAEL(horzEdge);
+  }
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::ProcessIntersections(const cInt topY)
+{
+  if( !m_ActiveEdges ) return true;
+  try {
+    BuildIntersectList(topY);
+    size_t IlSize = m_IntersectList.size();
+    if (IlSize == 0) return true;
+    if (IlSize == 1 || FixupIntersectionOrder()) ProcessIntersectList();
+    else return false;
+  }
+  catch(...) 
+  {
+    m_SortedEdges = 0;
+    DisposeIntersectNodes();
+    throw clipperException("ProcessIntersections error");
+  }
+  m_SortedEdges = 0;
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DisposeIntersectNodes()
+{
+  for (size_t i = 0; i < m_IntersectList.size(); ++i )
+    delete m_IntersectList[i];
+  m_IntersectList.clear();
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildIntersectList(const cInt topY)
+{
+  if ( !m_ActiveEdges ) return;
+
+  //prepare for sorting ...
+  TEdge* e = m_ActiveEdges;
+  m_SortedEdges = e;
+  while( e )
+  {
+    e->PrevInSEL = e->PrevInAEL;
+    e->NextInSEL = e->NextInAEL;
+    e->Curr.X = TopX( *e, topY );
+    e = e->NextInAEL;
+  }
+
+  //bubblesort ...
+  bool isModified;
+  do
+  {
+    isModified = false;
+    e = m_SortedEdges;
+    while( e->NextInSEL )
+    {
+      TEdge *eNext = e->NextInSEL;
+      IntPoint Pt;
+      if(e->Curr.X > eNext->Curr.X)
+      {
+        IntersectPoint(*e, *eNext, Pt);
+        if (Pt.Y < topY) Pt = IntPoint(TopX(*e, topY), topY);
+        IntersectNode * newNode = new IntersectNode;
+        newNode->Edge1 = e;
+        newNode->Edge2 = eNext;
+        newNode->Pt = Pt;
+        m_IntersectList.push_back(newNode);
+
+        SwapPositionsInSEL(e, eNext);
+        isModified = true;
+      }
+      else
+        e = eNext;
+    }
+    if( e->PrevInSEL ) e->PrevInSEL->NextInSEL = 0;
+    else break;
+  }
+  while ( isModified );
+  m_SortedEdges = 0; //important
+}
+//------------------------------------------------------------------------------
+
+
+void Clipper::ProcessIntersectList()
+{
+  for (size_t i = 0; i < m_IntersectList.size(); ++i)
+  {
+    IntersectNode* iNode = m_IntersectList[i];
+    {
+      IntersectEdges( iNode->Edge1, iNode->Edge2, iNode->Pt);
+      SwapPositionsInAEL( iNode->Edge1 , iNode->Edge2 );
+    }
+    delete iNode;
+  }
+  m_IntersectList.clear();
+}
+//------------------------------------------------------------------------------
+
+bool IntersectListSort(IntersectNode* node1, IntersectNode* node2)
+{
+  return node2->Pt.Y < node1->Pt.Y;
+}
+//------------------------------------------------------------------------------
+
+inline bool EdgesAdjacent(const IntersectNode &inode)
+{
+  return (inode.Edge1->NextInSEL == inode.Edge2) ||
+    (inode.Edge1->PrevInSEL == inode.Edge2);
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::FixupIntersectionOrder()
+{
+  //pre-condition: intersections are sorted Bottom-most first.
+  //Now it's crucial that intersections are made only between adjacent edges,
+  //so to ensure this the order of intersections may need adjusting ...
+  CopyAELToSEL();
+  std::sort(m_IntersectList.begin(), m_IntersectList.end(), IntersectListSort);
+  size_t cnt = m_IntersectList.size();
+  for (size_t i = 0; i < cnt; ++i) 
+  {
+    if (!EdgesAdjacent(*m_IntersectList[i]))
+    {
+      size_t j = i + 1;
+      while (j < cnt && !EdgesAdjacent(*m_IntersectList[j])) j++;
+      if (j == cnt)  return false;
+      std::swap(m_IntersectList[i], m_IntersectList[j]);
+    }
+    SwapPositionsInSEL(m_IntersectList[i]->Edge1, m_IntersectList[i]->Edge2);
+  }
+  return true;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::DoMaxima(TEdge *e)
+{
+  TEdge* eMaxPair = GetMaximaPairEx(e);
+  if (!eMaxPair)
+  {
+    if (e->OutIdx >= 0)
+      AddOutPt(e, e->Top);
+    DeleteFromAEL(e);
+    return;
+  }
+
+  TEdge* eNext = e->NextInAEL;
+  while(eNext && eNext != eMaxPair)
+  {
+    IntersectEdges(e, eNext, e->Top);
+    SwapPositionsInAEL(e, eNext);
+    eNext = e->NextInAEL;
+  }
+
+  if(e->OutIdx == Unassigned && eMaxPair->OutIdx == Unassigned)
+  {
+    DeleteFromAEL(e);
+    DeleteFromAEL(eMaxPair);
+  }
+  else if( e->OutIdx >= 0 && eMaxPair->OutIdx >= 0 )
+  {
+    if (e->OutIdx >= 0) AddLocalMaxPoly(e, eMaxPair, e->Top);
+    DeleteFromAEL(e);
+    DeleteFromAEL(eMaxPair);
+  }
+#ifdef use_lines
+  else if (e->WindDelta == 0)
+  {
+    if (e->OutIdx >= 0) 
+    {
+      AddOutPt(e, e->Top);
+      e->OutIdx = Unassigned;
+    }
+    DeleteFromAEL(e);
+
+    if (eMaxPair->OutIdx >= 0)
+    {
+      AddOutPt(eMaxPair, e->Top);
+      eMaxPair->OutIdx = Unassigned;
+    }
+    DeleteFromAEL(eMaxPair);
+  } 
+#endif
+  else throw clipperException("DoMaxima error");
+}
+//------------------------------------------------------------------------------
+
+void Clipper::ProcessEdgesAtTopOfScanbeam(const cInt topY)
+{
+  TEdge* e = m_ActiveEdges;
+  while( e )
+  {
+    //1. process maxima, treating them as if they're 'bent' horizontal edges,
+    //   but exclude maxima with horizontal edges. nb: e can't be a horizontal.
+    bool IsMaximaEdge = IsMaxima(e, topY);
+
+    if(IsMaximaEdge)
+    {
+      TEdge* eMaxPair = GetMaximaPairEx(e);
+      IsMaximaEdge = (!eMaxPair || !IsHorizontal(*eMaxPair));
+    }
+
+    if(IsMaximaEdge)
+    {
+      if (m_StrictSimple) m_Maxima.push_back(e->Top.X);
+      TEdge* ePrev = e->PrevInAEL;
+      DoMaxima(e);
+      if( !ePrev ) e = m_ActiveEdges;
+      else e = ePrev->NextInAEL;
+    }
+    else
+    {
+      //2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
+      if (IsIntermediate(e, topY) && IsHorizontal(*e->NextInLML))
+      {
+        UpdateEdgeIntoAEL(e);
+        if (e->OutIdx >= 0)
+          AddOutPt(e, e->Bot);
+        AddEdgeToSEL(e);
+      } 
+      else
+      {
+        e->Curr.X = TopX( *e, topY );
+        e->Curr.Y = topY;
+#ifdef use_xyz
+		e->Curr.Z = topY == e->Top.Y ? e->Top.Z : (topY == e->Bot.Y ? e->Bot.Z : 0);
+#endif
+	  }
+
+      //When StrictlySimple and 'e' is being touched by another edge, then
+      //make sure both edges have a vertex here ...
+      if (m_StrictSimple)
+      {  
+        TEdge* ePrev = e->PrevInAEL;
+        if ((e->OutIdx >= 0) && (e->WindDelta != 0) && ePrev && (ePrev->OutIdx >= 0) &&
+          (ePrev->Curr.X == e->Curr.X) && (ePrev->WindDelta != 0))
+        {
+          IntPoint pt = e->Curr;
+#ifdef use_xyz
+          SetZ(pt, *ePrev, *e);
+#endif
+          OutPt* op = AddOutPt(ePrev, pt);
+          OutPt* op2 = AddOutPt(e, pt);
+          AddJoin(op, op2, pt); //StrictlySimple (type-3) join
+        }
+      }
+
+      e = e->NextInAEL;
+    }
+  }
+
+  //3. Process horizontals at the Top of the scanbeam ...
+  m_Maxima.sort();
+  ProcessHorizontals();
+  m_Maxima.clear();
+
+  //4. Promote intermediate vertices ...
+  e = m_ActiveEdges;
+  while(e)
+  {
+    if(IsIntermediate(e, topY))
+    {
+      OutPt* op = 0;
+      if( e->OutIdx >= 0 ) 
+        op = AddOutPt(e, e->Top);
+      UpdateEdgeIntoAEL(e);
+
+      //if output polygons share an edge, they'll need joining later ...
+      TEdge* ePrev = e->PrevInAEL;
+      TEdge* eNext = e->NextInAEL;
+      if (ePrev && ePrev->Curr.X == e->Bot.X &&
+        ePrev->Curr.Y == e->Bot.Y && op &&
+        ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
+        SlopesEqual(e->Curr, e->Top, ePrev->Curr, ePrev->Top, m_UseFullRange) &&
+        (e->WindDelta != 0) && (ePrev->WindDelta != 0))
+      {
+        OutPt* op2 = AddOutPt(ePrev, e->Bot);
+        AddJoin(op, op2, e->Top);
+      }
+      else if (eNext && eNext->Curr.X == e->Bot.X &&
+        eNext->Curr.Y == e->Bot.Y && op &&
+        eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
+        SlopesEqual(e->Curr, e->Top, eNext->Curr, eNext->Top, m_UseFullRange) &&
+        (e->WindDelta != 0) && (eNext->WindDelta != 0))
+      {
+        OutPt* op2 = AddOutPt(eNext, e->Bot);
+        AddJoin(op, op2, e->Top);
+      }
+    }
+    e = e->NextInAEL;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::FixupOutPolyline(OutRec &outrec)
+{
+  OutPt *pp = outrec.Pts;
+  OutPt *lastPP = pp->Prev;
+  while (pp != lastPP)
+  {
+    pp = pp->Next;
+    if (pp->Pt == pp->Prev->Pt)
+    {
+      if (pp == lastPP) lastPP = pp->Prev;
+      OutPt *tmpPP = pp->Prev;
+      tmpPP->Next = pp->Next;
+      pp->Next->Prev = tmpPP;
+      delete pp;
+      pp = tmpPP;
+    }
+  }
+
+  if (pp == pp->Prev)
+  {
+    DisposeOutPts(pp);
+    outrec.Pts = 0;
+    return;
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::FixupOutPolygon(OutRec &outrec)
+{
+    //FixupOutPolygon() - removes duplicate points and simplifies consecutive
+    //parallel edges by removing the middle vertex.
+    OutPt *lastOK = 0;
+    outrec.BottomPt = 0;
+    OutPt *pp = outrec.Pts;
+    bool preserveCol = m_PreserveCollinear || m_StrictSimple;
+
+    for (;;)
+    {
+        if (pp->Prev == pp || pp->Prev == pp->Next)
+        {
+            DisposeOutPts(pp);
+            outrec.Pts = 0;
+            return;
+        }
+
+        //test for duplicate points and collinear edges ...
+        if ((pp->Pt == pp->Next->Pt) || (pp->Pt == pp->Prev->Pt) ||
+            (SlopesEqual(pp->Prev->Pt, pp->Pt, pp->Next->Pt, m_UseFullRange) &&
+            (!preserveCol || !Pt2IsBetweenPt1AndPt3(pp->Prev->Pt, pp->Pt, pp->Next->Pt))))
+        {
+            lastOK = 0;
+            OutPt *tmp = pp;
+            pp->Prev->Next = pp->Next;
+            pp->Next->Prev = pp->Prev;
+            pp = pp->Prev;
+            delete tmp;
+        }
+        else if (pp == lastOK) break;
+        else
+        {
+            if (!lastOK) lastOK = pp;
+            pp = pp->Next;
+        }
+    }
+    outrec.Pts = pp;
+}
+//------------------------------------------------------------------------------
+
+int PointCount(OutPt *Pts)
+{
+    if (!Pts) return 0;
+    int result = 0;
+    OutPt* p = Pts;
+    do
+    {
+        result++;
+        p = p->Next;
+    }
+    while (p != Pts);
+    return result;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildResult(Paths &polys)
+{
+  polys.reserve(m_PolyOuts.size());
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    if (!m_PolyOuts[i]->Pts) continue;
+    Path pg;
+    OutPt* p = m_PolyOuts[i]->Pts->Prev;
+    int cnt = PointCount(p);
+    if (cnt < 2) continue;
+    pg.reserve(cnt);
+    for (int i = 0; i < cnt; ++i)
+    {
+      pg.push_back(p->Pt);
+      p = p->Prev;
+    }
+    polys.push_back(pg);
+  }
+}
+//------------------------------------------------------------------------------
+
+void Clipper::BuildResult2(PolyTree& polytree)
+{
+    polytree.Clear();
+    polytree.AllNodes.reserve(m_PolyOuts.size());
+    //add each output polygon/contour to polytree ...
+    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
+    {
+        OutRec* outRec = m_PolyOuts[i];
+        int cnt = PointCount(outRec->Pts);
+        if ((outRec->IsOpen && cnt < 2) || (!outRec->IsOpen && cnt < 3)) continue;
+        FixHoleLinkage(*outRec);
+        PolyNode* pn = new PolyNode();
+        //nb: polytree takes ownership of all the PolyNodes
+        polytree.AllNodes.push_back(pn);
+        outRec->PolyNd = pn;
+        pn->Parent = 0;
+        pn->Index = 0;
+        pn->Contour.reserve(cnt);
+        OutPt *op = outRec->Pts->Prev;
+        for (int j = 0; j < cnt; j++)
+        {
+            pn->Contour.push_back(op->Pt);
+            op = op->Prev;
+        }
+    }
+
+    //fixup PolyNode links etc ...
+    polytree.Childs.reserve(m_PolyOuts.size());
+    for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
+    {
+        OutRec* outRec = m_PolyOuts[i];
+        if (!outRec->PolyNd) continue;
+        if (outRec->IsOpen) 
+        {
+          outRec->PolyNd->m_IsOpen = true;
+          polytree.AddChild(*outRec->PolyNd);
+        }
+        else if (outRec->FirstLeft && outRec->FirstLeft->PolyNd) 
+          outRec->FirstLeft->PolyNd->AddChild(*outRec->PolyNd);
+        else
+          polytree.AddChild(*outRec->PolyNd);
+    }
+}
+//------------------------------------------------------------------------------
+
+void SwapIntersectNodes(IntersectNode &int1, IntersectNode &int2)
+{
+  //just swap the contents (because fIntersectNodes is a single-linked-list)
+  IntersectNode inode = int1; //gets a copy of Int1
+  int1.Edge1 = int2.Edge1;
+  int1.Edge2 = int2.Edge2;
+  int1.Pt = int2.Pt;
+  int2.Edge1 = inode.Edge1;
+  int2.Edge2 = inode.Edge2;
+  int2.Pt = inode.Pt;
+}
+//------------------------------------------------------------------------------
+
+inline bool E2InsertsBeforeE1(TEdge &e1, TEdge &e2)
+{
+  if (e2.Curr.X == e1.Curr.X) 
+  {
+    if (e2.Top.Y > e1.Top.Y)
+      return e2.Top.X < TopX(e1, e2.Top.Y); 
+      else return e1.Top.X > TopX(e2, e1.Top.Y);
+  } 
+  else return e2.Curr.X < e1.Curr.X;
+}
+//------------------------------------------------------------------------------
+
+bool GetOverlap(const cInt a1, const cInt a2, const cInt b1, const cInt b2, 
+    cInt& Left, cInt& Right)
+{
+  if (a1 < a2)
+  {
+    if (b1 < b2) {Left = std::max(a1,b1); Right = std::min(a2,b2);}
+    else {Left = std::max(a1,b2); Right = std::min(a2,b1);}
+  } 
+  else
+  {
+    if (b1 < b2) {Left = std::max(a2,b1); Right = std::min(a1,b2);}
+    else {Left = std::max(a2,b2); Right = std::min(a1,b1);}
+  }
+  return Left < Right;
+}
+//------------------------------------------------------------------------------
+
+inline void UpdateOutPtIdxs(OutRec& outrec)
+{  
+  OutPt* op = outrec.Pts;
+  do
+  {
+    op->Idx = outrec.Idx;
+    op = op->Prev;
+  }
+  while(op != outrec.Pts);
+}
+//------------------------------------------------------------------------------
+
+void Clipper::InsertEdgeIntoAEL(TEdge *edge, TEdge* startEdge)
+{
+  if(!m_ActiveEdges)
+  {
+    edge->PrevInAEL = 0;
+    edge->NextInAEL = 0;
+    m_ActiveEdges = edge;
+  }
+  else if(!startEdge && E2InsertsBeforeE1(*m_ActiveEdges, *edge))
+  {
+      edge->PrevInAEL = 0;
+      edge->NextInAEL = m_ActiveEdges;
+      m_ActiveEdges->PrevInAEL = edge;
+      m_ActiveEdges = edge;
+  } 
+  else
+  {
+    if(!startEdge) startEdge = m_ActiveEdges;
+    while(startEdge->NextInAEL  && 
+      !E2InsertsBeforeE1(*startEdge->NextInAEL , *edge))
+        startEdge = startEdge->NextInAEL;
+    edge->NextInAEL = startEdge->NextInAEL;
+    if(startEdge->NextInAEL) startEdge->NextInAEL->PrevInAEL = edge;
+    edge->PrevInAEL = startEdge;
+    startEdge->NextInAEL = edge;
+  }
+}
+//----------------------------------------------------------------------
+
+OutPt* DupOutPt(OutPt* outPt, bool InsertAfter)
+{
+  OutPt* result = new OutPt;
+  result->Pt = outPt->Pt;
+  result->Idx = outPt->Idx;
+  if (InsertAfter)
+  {
+    result->Next = outPt->Next;
+    result->Prev = outPt;
+    outPt->Next->Prev = result;
+    outPt->Next = result;
+  } 
+  else
+  {
+    result->Prev = outPt->Prev;
+    result->Next = outPt;
+    outPt->Prev->Next = result;
+    outPt->Prev = result;
+  }
+  return result;
+}
+//------------------------------------------------------------------------------
+
+bool JoinHorz(OutPt* op1, OutPt* op1b, OutPt* op2, OutPt* op2b,
+  const IntPoint Pt, bool DiscardLeft)
+{
+  Direction Dir1 = (op1->Pt.X > op1b->Pt.X ? dRightToLeft : dLeftToRight);
+  Direction Dir2 = (op2->Pt.X > op2b->Pt.X ? dRightToLeft : dLeftToRight);
+  if (Dir1 == Dir2) return false;
+
+  //When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
+  //want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
+  //So, to facilitate this while inserting Op1b and Op2b ...
+  //when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
+  //otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
+  if (Dir1 == dLeftToRight) 
+  {
+    while (op1->Next->Pt.X <= Pt.X && 
+      op1->Next->Pt.X >= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)  
+        op1 = op1->Next;
+    if (DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
+    op1b = DupOutPt(op1, !DiscardLeft);
+    if (op1b->Pt != Pt) 
+    {
+      op1 = op1b;
+      op1->Pt = Pt;
+      op1b = DupOutPt(op1, !DiscardLeft);
+    }
+  } 
+  else
+  {
+    while (op1->Next->Pt.X >= Pt.X && 
+      op1->Next->Pt.X <= op1->Pt.X && op1->Next->Pt.Y == Pt.Y) 
+        op1 = op1->Next;
+    if (!DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
+    op1b = DupOutPt(op1, DiscardLeft);
+    if (op1b->Pt != Pt)
+    {
+      op1 = op1b;
+      op1->Pt = Pt;
+      op1b = DupOutPt(op1, DiscardLeft);
+    }
+  }
+
+  if (Dir2 == dLeftToRight)
+  {
+    while (op2->Next->Pt.X <= Pt.X && 
+      op2->Next->Pt.X >= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
+        op2 = op2->Next;
+    if (DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
+    op2b = DupOutPt(op2, !DiscardLeft);
+    if (op2b->Pt != Pt)
+    {
+      op2 = op2b;
+      op2->Pt = Pt;
+      op2b = DupOutPt(op2, !DiscardLeft);
+    };
+  } else
+  {
+    while (op2->Next->Pt.X >= Pt.X && 
+      op2->Next->Pt.X <= op2->Pt.X && op2->Next->Pt.Y == Pt.Y) 
+        op2 = op2->Next;
+    if (!DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
+    op2b = DupOutPt(op2, DiscardLeft);
+    if (op2b->Pt != Pt)
+    {
+      op2 = op2b;
+      op2->Pt = Pt;
+      op2b = DupOutPt(op2, DiscardLeft);
+    };
+  };
+
+  if ((Dir1 == dLeftToRight) == DiscardLeft)
+  {
+    op1->Prev = op2;
+    op2->Next = op1;
+    op1b->Next = op2b;
+    op2b->Prev = op1b;
+  }
+  else
+  {
+    op1->Next = op2;
+    op2->Prev = op1;
+    op1b->Prev = op2b;
+    op2b->Next = op1b;
+  }
+  return true;
+}
+//------------------------------------------------------------------------------
+
+bool Clipper::JoinPoints(Join *j, OutRec* outRec1, OutRec* outRec2)
+{
+  OutPt *op1 = j->OutPt1, *op1b;
+  OutPt *op2 = j->OutPt2, *op2b;
+
+  //There are 3 kinds of joins for output polygons ...
+  //1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
+  //along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
+  //2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
+  //location at the Bottom of the overlapping segment (& Join.OffPt is above).
+  //3. StrictSimple joins where edges touch but are not collinear and where
+  //Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
+  bool isHorizontal = (j->OutPt1->Pt.Y == j->OffPt.Y);
+
+  if (isHorizontal  && (j->OffPt == j->OutPt1->Pt) &&
+  (j->OffPt == j->OutPt2->Pt))
+  {
+    //Strictly Simple join ...
+    if (outRec1 != outRec2) return false;
+    op1b = j->OutPt1->Next;
+    while (op1b != op1 && (op1b->Pt == j->OffPt)) 
+      op1b = op1b->Next;
+    bool reverse1 = (op1b->Pt.Y > j->OffPt.Y);
+    op2b = j->OutPt2->Next;
+    while (op2b != op2 && (op2b->Pt == j->OffPt)) 
+      op2b = op2b->Next;
+    bool reverse2 = (op2b->Pt.Y > j->OffPt.Y);
+    if (reverse1 == reverse2) return false;
+    if (reverse1)
+    {
+      op1b = DupOutPt(op1, false);
+      op2b = DupOutPt(op2, true);
+      op1->Prev = op2;
+      op2->Next = op1;
+      op1b->Next = op2b;
+      op2b->Prev = op1b;
+      j->OutPt1 = op1;
+      j->OutPt2 = op1b;
+      return true;
+    } else
+    {
+      op1b = DupOutPt(op1, true);
+      op2b = DupOutPt(op2, false);
+      op1->Next = op2;
+      op2->Prev = op1;
+      op1b->Prev = op2b;
+      op2b->Next = op1b;
+      j->OutPt1 = op1;
+      j->OutPt2 = op1b;
+      return true;
+    }
+  } 
+  else if (isHorizontal)
+  {
+    //treat horizontal joins differently to non-horizontal joins since with
+    //them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
+    //may be anywhere along the horizontal edge.
+    op1b = op1;
+    while (op1->Prev->Pt.Y == op1->Pt.Y && op1->Prev != op1b && op1->Prev != op2)
+      op1 = op1->Prev;
+    while (op1b->Next->Pt.Y == op1b->Pt.Y && op1b->Next != op1 && op1b->Next != op2)
+      op1b = op1b->Next;
+    if (op1b->Next == op1 || op1b->Next == op2) return false; //a flat 'polygon'
+
+    op2b = op2;
+    while (op2->Prev->Pt.Y == op2->Pt.Y && op2->Prev != op2b && op2->Prev != op1b)
+      op2 = op2->Prev;
+    while (op2b->Next->Pt.Y == op2b->Pt.Y && op2b->Next != op2 && op2b->Next != op1)
+      op2b = op2b->Next;
+    if (op2b->Next == op2 || op2b->Next == op1) return false; //a flat 'polygon'
+
+    cInt Left, Right;
+    //Op1 --> Op1b & Op2 --> Op2b are the extremites of the horizontal edges
+    if (!GetOverlap(op1->Pt.X, op1b->Pt.X, op2->Pt.X, op2b->Pt.X, Left, Right))
+      return false;
+
+    //DiscardLeftSide: when overlapping edges are joined, a spike will created
+    //which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
+    //on the discard Side as either may still be needed for other joins ...
+    IntPoint Pt;
+    bool DiscardLeftSide;
+    if (op1->Pt.X >= Left && op1->Pt.X <= Right) 
+    {
+      Pt = op1->Pt; DiscardLeftSide = (op1->Pt.X > op1b->Pt.X);
+    } 
+    else if (op2->Pt.X >= Left&& op2->Pt.X <= Right) 
+    {
+      Pt = op2->Pt; DiscardLeftSide = (op2->Pt.X > op2b->Pt.X);
+    } 
+    else if (op1b->Pt.X >= Left && op1b->Pt.X <= Right)
+    {
+      Pt = op1b->Pt; DiscardLeftSide = op1b->Pt.X > op1->Pt.X;
+    } 
+    else
+    {
+      Pt = op2b->Pt; DiscardLeftSide = (op2b->Pt.X > op2->Pt.X);
+    }
+    j->OutPt1 = op1; j->OutPt2 = op2;
+    return JoinHorz(op1, op1b, op2, op2b, Pt, DiscardLeftSide);
+  } else
+  {
+    //nb: For non-horizontal joins ...
+    //    1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
+    //    2. Jr.OutPt1.Pt > Jr.OffPt.Y
+
+    //make sure the polygons are correctly oriented ...
+    op1b = op1->Next;
+    while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Next;
+    bool Reverse1 = ((op1b->Pt.Y > op1->Pt.Y) ||
+      !SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange));
+    if (Reverse1)
+    {
+      op1b = op1->Prev;
+      while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Prev;
+      if ((op1b->Pt.Y > op1->Pt.Y) ||
+        !SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange)) return false;
+    };
+    op2b = op2->Next;
+    while ((op2b->Pt == op2->Pt) && (op2b != op2))op2b = op2b->Next;
+    bool Reverse2 = ((op2b->Pt.Y > op2->Pt.Y) ||
+      !SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange));
+    if (Reverse2)
+    {
+      op2b = op2->Prev;
+      while ((op2b->Pt == op2->Pt) && (op2b != op2)) op2b = op2b->Prev;
+      if ((op2b->Pt.Y > op2->Pt.Y) ||
+        !SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange)) return false;
+    }
+
+    if ((op1b == op1) || (op2b == op2) || (op1b == op2b) ||
+      ((outRec1 == outRec2) && (Reverse1 == Reverse2))) return false;
+
+    if (Reverse1)
+    {
+      op1b = DupOutPt(op1, false);
+      op2b = DupOutPt(op2, true);
+      op1->Prev = op2;
+      op2->Next = op1;
+      op1b->Next = op2b;
+      op2b->Prev = op1b;
+      j->OutPt1 = op1;
+      j->OutPt2 = op1b;
+      return true;
+    } else
+    {
+      op1b = DupOutPt(op1, true);
+      op2b = DupOutPt(op2, false);
+      op1->Next = op2;
+      op2->Prev = op1;
+      op1b->Prev = op2b;
+      op2b->Next = op1b;
+      j->OutPt1 = op1;
+      j->OutPt2 = op1b;
+      return true;
+    }
+  }
+}
+//----------------------------------------------------------------------
+
+static OutRec* ParseFirstLeft(OutRec* FirstLeft)
+{
+  while (FirstLeft && !FirstLeft->Pts)
+    FirstLeft = FirstLeft->FirstLeft;
+  return FirstLeft;
+}
+//------------------------------------------------------------------------------
+
+void Clipper::FixupFirstLefts1(OutRec* OldOutRec, OutRec* NewOutRec)
+{ 
+  //tests if NewOutRec contains the polygon before reassigning FirstLeft
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    OutRec* outRec = m_PolyOuts[i];
+    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
+    if (outRec->Pts  && firstLeft == OldOutRec)
+    {
+      if (Poly2ContainsPoly1(outRec->Pts, NewOutRec->Pts))
+        outRec->FirstLeft = NewOutRec;
+    }
+  }
+}
+//----------------------------------------------------------------------
+
+void Clipper::FixupFirstLefts2(OutRec* InnerOutRec, OutRec* OuterOutRec)
+{
+  //A polygon has split into two such that one is now the inner of the other.
+  //It's possible that these polygons now wrap around other polygons, so check
+  //every polygon that's also contained by OuterOutRec's FirstLeft container
+  //(including 0) to see if they've become inner to the new inner polygon ...
+  OutRec* orfl = OuterOutRec->FirstLeft;
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    OutRec* outRec = m_PolyOuts[i];
+
+    if (!outRec->Pts || outRec == OuterOutRec || outRec == InnerOutRec)
+      continue;
+    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
+    if (firstLeft != orfl && firstLeft != InnerOutRec && firstLeft != OuterOutRec)
+      continue;
+    if (Poly2ContainsPoly1(outRec->Pts, InnerOutRec->Pts))
+      outRec->FirstLeft = InnerOutRec;
+    else if (Poly2ContainsPoly1(outRec->Pts, OuterOutRec->Pts))
+      outRec->FirstLeft = OuterOutRec;
+    else if (outRec->FirstLeft == InnerOutRec || outRec->FirstLeft == OuterOutRec)
+      outRec->FirstLeft = orfl;
+  }
+}
+//----------------------------------------------------------------------
+void Clipper::FixupFirstLefts3(OutRec* OldOutRec, OutRec* NewOutRec)
+{
+  //reassigns FirstLeft WITHOUT testing if NewOutRec contains the polygon
+  for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
+  {
+    OutRec* outRec = m_PolyOuts[i];
+    OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
+    if (outRec->Pts && firstLeft == OldOutRec)
+      outRec->FirstLeft = NewOutRec;
+  }
+}
+//----------------------------------------------------------------------
+
+void Clipper::JoinCommonEdges()
+{
+  for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
+  {
+    Join* join = m_Joins[i];
+
+    OutRec *outRec1 = GetOutRec(join->OutPt1->Idx);
+    OutRec *outRec2 = GetOutRec(join->OutPt2->Idx);
+
+    if (!outRec1->Pts || !outRec2->Pts) continue;
+    if (outRec1->IsOpen || outRec2->IsOpen) continue;
+
+    //get the polygon fragment with the correct hole state (FirstLeft)
+    //before calling JoinPoints() ...
+    OutRec *holeStateRec;
+    if (outRec1 == outRec2) holeStateRec = outRec1;
+    else if (OutRec1RightOfOutRec2(outRec1, outRec2)) holeStateRec = outRec2;
+    else if (OutRec1RightOfOutRec2(outRec2, outRec1)) holeStateRec = outRec1;
+    else holeStateRec = GetLowermostRec(outRec1, outRec2);
+
+    if (!JoinPoints(join, outRec1, outRec2)) continue;
+
+    if (outRec1 == outRec2)
+    {
+      //instead of joining two polygons, we've just created a new one by
+      //splitting one polygon into two.
+      outRec1->Pts = join->OutPt1;
+      outRec1->BottomPt = 0;
+      outRec2 = CreateOutRec();
+      outRec2->Pts = join->OutPt2;
+
+      //update all OutRec2.Pts Idx's ...
+      UpdateOutPtIdxs(*outRec2);
+
+      if (Poly2ContainsPoly1(outRec2->Pts, outRec1->Pts))
+      {
+        //outRec1 contains outRec2 ...
+        outRec2->IsHole = !outRec1->IsHole;
+        outRec2->FirstLeft = outRec1;
+
+        if (m_UsingPolyTree) FixupFirstLefts2(outRec2, outRec1);
+
+        if ((outRec2->IsHole ^ m_ReverseOutput) == (Area(*outRec2) > 0))
+          ReversePolyPtLinks(outRec2->Pts);
+            
+      } else if (Poly2ContainsPoly1(outRec1->Pts, outRec2->Pts))
+      {
+        //outRec2 contains outRec1 ...
+        outRec2->IsHole = outRec1->IsHole;
+        outRec1->IsHole = !outRec2->IsHole;
+        outRec2->FirstLeft = outRec1->FirstLeft;
+        outRec1->FirstLeft = outRec2;
+
+        if (m_UsingPolyTree) FixupFirstLefts2(outRec1, outRec2);
+
+        if ((outRec1->IsHole ^ m_ReverseOutput) == (Area(*outRec1) > 0))
+          ReversePolyPtLinks(outRec1->Pts);
+      } 
+      else
+      {
+        //the 2 polygons are completely separate ...
+        outRec2->IsHole = outRec1->IsHole;
+        outRec2->FirstLeft = outRec1->FirstLeft;
+
+        //fixup FirstLeft pointers that may need reassigning to OutRec2
+        if (m_UsingPolyTree) FixupFirstLefts1(outRec1, outRec2);
+      }
+     
+    } else
+    {
+      //joined 2 polygons together ...
+
+      outRec2->Pts = 0;
+      outRec2->BottomPt = 0;
+      outRec2->Idx = outRec1->Idx;
+
+      outRec1->IsHole = holeStateRec->IsHole;
+      if (holeStateRec == outRec2) 
+        outRec1->FirstLeft = outRec2->FirstLeft;
+      outRec2->FirstLeft = outRec1;
+
+      if (m_UsingPolyTree) FixupFirstLefts3(outRec2, outRec1);
+    }
+  }
+}
+
+//------------------------------------------------------------------------------
+// ClipperOffset support functions ...
+//------------------------------------------------------------------------------
+
+DoublePoint GetUnitNormal(const IntPoint &pt1, const IntPoint &pt2)
+{
+  if(pt2.X == pt1.X && pt2.Y == pt1.Y) 
+    return DoublePoint(0, 0);
+
+  double Dx = (double)(pt2.X - pt1.X);
+  double dy = (double)(pt2.Y - pt1.Y);
+  double f = 1 *1.0/ std::sqrt( Dx*Dx + dy*dy );
+  Dx *= f;
+  dy *= f;
+  return DoublePoint(dy, -Dx);
+}
+
+//------------------------------------------------------------------------------
+// ClipperOffset class
+//------------------------------------------------------------------------------
+
+ClipperOffset::ClipperOffset(double miterLimit, double arcTolerance)
+{
+  this->MiterLimit = miterLimit;
+  this->ArcTolerance = arcTolerance;
+  m_lowest.X = -1;
+}
+//------------------------------------------------------------------------------
+
+ClipperOffset::~ClipperOffset()
+{
+  Clear();
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::Clear()
+{
+  for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
+    delete m_polyNodes.Childs[i];
+  m_polyNodes.Childs.clear();
+  m_lowest.X = -1;
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::AddPath(const Path& path, JoinType joinType, EndType endType)
+{
+  int highI = (int)path.size() - 1;
+  if (highI < 0) return;
+  PolyNode* newNode = new PolyNode();
+  newNode->m_jointype = joinType;
+  newNode->m_endtype = endType;
+
+  //strip duplicate points from path and also get index to the lowest point ...
+  if (endType == etClosedLine || endType == etClosedPolygon)
+    while (highI > 0 && path[0] == path[highI]) highI--;
+  newNode->Contour.reserve(highI + 1);
+  newNode->Contour.push_back(path[0]);
+  int j = 0, k = 0;
+  for (int i = 1; i <= highI; i++)
+    if (newNode->Contour[j] != path[i])
+    {
+      j++;
+      newNode->Contour.push_back(path[i]);
+      if (path[i].Y > newNode->Contour[k].Y ||
+        (path[i].Y == newNode->Contour[k].Y &&
+        path[i].X < newNode->Contour[k].X)) k = j;
+    }
+  if (endType == etClosedPolygon && j < 2)
+  {
+    delete newNode;
+    return;
+  }
+  m_polyNodes.AddChild(*newNode);
+
+  //if this path's lowest pt is lower than all the others then update m_lowest
+  if (endType != etClosedPolygon) return;
+  if (m_lowest.X < 0)
+    m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
+  else
+  {
+    IntPoint ip = m_polyNodes.Childs[(int)m_lowest.X]->Contour[(int)m_lowest.Y];
+    if (newNode->Contour[k].Y > ip.Y ||
+      (newNode->Contour[k].Y == ip.Y &&
+      newNode->Contour[k].X < ip.X))
+      m_lowest = IntPoint(m_polyNodes.ChildCount() - 1, k);
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::AddPaths(const Paths& paths, JoinType joinType, EndType endType)
+{
+  for (Paths::size_type i = 0; i < paths.size(); ++i)
+    AddPath(paths[i], joinType, endType);
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::FixOrientations()
+{
+  //fixup orientations of all closed paths if the orientation of the
+  //closed path with the lowermost vertex is wrong ...
+  if (m_lowest.X >= 0 && 
+    !Orientation(m_polyNodes.Childs[(int)m_lowest.X]->Contour))
+  {
+    for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
+    {
+      PolyNode& node = *m_polyNodes.Childs[i];
+      if (node.m_endtype == etClosedPolygon ||
+        (node.m_endtype == etClosedLine && Orientation(node.Contour)))
+          ReversePath(node.Contour);
+    }
+  } else
+  {
+    for (int i = 0; i < m_polyNodes.ChildCount(); ++i)
+    {
+      PolyNode& node = *m_polyNodes.Childs[i];
+      if (node.m_endtype == etClosedLine && !Orientation(node.Contour))
+        ReversePath(node.Contour);
+    }
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::Execute(Paths& solution, double delta)
+{
+  solution.clear();
+  FixOrientations();
+  DoOffset(delta);
+  
+  //now clean up 'corners' ...
+  Clipper clpr;
+  clpr.AddPaths(m_destPolys, ptSubject, true);
+  if (delta > 0)
+  {
+    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
+  }
+  else
+  {
+    IntRect r = clpr.GetBounds();
+    Path outer(4);
+    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
+    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
+    outer[2] = IntPoint(r.right + 10, r.top - 10);
+    outer[3] = IntPoint(r.left - 10, r.top - 10);
+
+    clpr.AddPath(outer, ptSubject, true);
+    clpr.ReverseSolution(true);
+    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
+    if (solution.size() > 0) solution.erase(solution.begin());
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::Execute(PolyTree& solution, double delta)
+{
+  solution.Clear();
+  FixOrientations();
+  DoOffset(delta);
+
+  //now clean up 'corners' ...
+  Clipper clpr;
+  clpr.AddPaths(m_destPolys, ptSubject, true);
+  if (delta > 0)
+  {
+    clpr.Execute(ctUnion, solution, pftPositive, pftPositive);
+  }
+  else
+  {
+    IntRect r = clpr.GetBounds();
+    Path outer(4);
+    outer[0] = IntPoint(r.left - 10, r.bottom + 10);
+    outer[1] = IntPoint(r.right + 10, r.bottom + 10);
+    outer[2] = IntPoint(r.right + 10, r.top - 10);
+    outer[3] = IntPoint(r.left - 10, r.top - 10);
+
+    clpr.AddPath(outer, ptSubject, true);
+    clpr.ReverseSolution(true);
+    clpr.Execute(ctUnion, solution, pftNegative, pftNegative);
+    //remove the outer PolyNode rectangle ...
+    if (solution.ChildCount() == 1 && solution.Childs[0]->ChildCount() > 0)
+    {
+      PolyNode* outerNode = solution.Childs[0];
+      solution.Childs.reserve(outerNode->ChildCount());
+      solution.Childs[0] = outerNode->Childs[0];
+      solution.Childs[0]->Parent = outerNode->Parent;
+      for (int i = 1; i < outerNode->ChildCount(); ++i)
+        solution.AddChild(*outerNode->Childs[i]);
+    }
+    else
+      solution.Clear();
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::DoOffset(double delta)
+{
+  m_destPolys.clear();
+  m_delta = delta;
+
+  //if Zero offset, just copy any CLOSED polygons to m_p and return ...
+  if (NEAR_ZERO(delta)) 
+  {
+    m_destPolys.reserve(m_polyNodes.ChildCount());
+    for (int i = 0; i < m_polyNodes.ChildCount(); i++)
+    {
+      PolyNode& node = *m_polyNodes.Childs[i];
+      if (node.m_endtype == etClosedPolygon)
+        m_destPolys.push_back(node.Contour);
+    }
+    return;
+  }
+
+  //see offset_triginometry3.svg in the documentation folder ...
+  if (MiterLimit > 2) m_miterLim = 2/(MiterLimit * MiterLimit);
+  else m_miterLim = 0.5;
+
+  double y;
+  if (ArcTolerance <= 0.0) y = def_arc_tolerance;
+  else if (ArcTolerance > std::fabs(delta) * def_arc_tolerance) 
+    y = std::fabs(delta) * def_arc_tolerance;
+  else y = ArcTolerance;
+  //see offset_triginometry2.svg in the documentation folder ...
+  double steps = pi / std::acos(1 - y / std::fabs(delta));
+  if (steps > std::fabs(delta) * pi) 
+    steps = std::fabs(delta) * pi;  //ie excessive precision check
+  m_sin = std::sin(two_pi / steps);
+  m_cos = std::cos(two_pi / steps);
+  m_StepsPerRad = steps / two_pi;
+  if (delta < 0.0) m_sin = -m_sin;
+
+  m_destPolys.reserve(m_polyNodes.ChildCount() * 2);
+  for (int i = 0; i < m_polyNodes.ChildCount(); i++)
+  {
+    PolyNode& node = *m_polyNodes.Childs[i];
+    m_srcPoly = node.Contour;
+
+    int len = (int)m_srcPoly.size();
+    if (len == 0 || (delta <= 0 && (len < 3 || node.m_endtype != etClosedPolygon)))
+        continue;
+
+    m_destPoly.clear();
+    if (len == 1)
+    {
+      if (node.m_jointype == jtRound)
+      {
+        double X = 1.0, Y = 0.0;
+        for (cInt j = 1; j <= steps; j++)
+        {
+          m_destPoly.push_back(IntPoint(
+            Round(m_srcPoly[0].X + X * delta),
+            Round(m_srcPoly[0].Y + Y * delta)));
+          double X2 = X;
+          X = X * m_cos - m_sin * Y;
+          Y = X2 * m_sin + Y * m_cos;
+        }
+      }
+      else
+      {
+        double X = -1.0, Y = -1.0;
+        for (int j = 0; j < 4; ++j)
+        {
+          m_destPoly.push_back(IntPoint(
+            Round(m_srcPoly[0].X + X * delta),
+            Round(m_srcPoly[0].Y + Y * delta)));
+          if (X < 0) X = 1;
+          else if (Y < 0) Y = 1;
+          else X = -1;
+        }
+      }
+      m_destPolys.push_back(m_destPoly);
+      continue;
+    }
+    //build m_normals ...
+    m_normals.clear();
+    m_normals.reserve(len);
+    for (int j = 0; j < len - 1; ++j)
+      m_normals.push_back(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
+    if (node.m_endtype == etClosedLine || node.m_endtype == etClosedPolygon)
+      m_normals.push_back(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
+    else
+      m_normals.push_back(DoublePoint(m_normals[len - 2]));
+
+    if (node.m_endtype == etClosedPolygon)
+    {
+      int k = len - 1;
+      for (int j = 0; j < len; ++j)
+        OffsetPoint(j, k, node.m_jointype);
+      m_destPolys.push_back(m_destPoly);
+    }
+    else if (node.m_endtype == etClosedLine)
+    {
+      int k = len - 1;
+      for (int j = 0; j < len; ++j)
+        OffsetPoint(j, k, node.m_jointype);
+      m_destPolys.push_back(m_destPoly);
+      m_destPoly.clear();
+      //re-build m_normals ...
+      DoublePoint n = m_normals[len -1];
+      for (int j = len - 1; j > 0; j--)
+        m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
+      m_normals[0] = DoublePoint(-n.X, -n.Y);
+      k = 0;
+      for (int j = len - 1; j >= 0; j--)
+        OffsetPoint(j, k, node.m_jointype);
+      m_destPolys.push_back(m_destPoly);
+    }
+    else
+    {
+      int k = 0;
+      for (int j = 1; j < len - 1; ++j)
+        OffsetPoint(j, k, node.m_jointype);
+
+      IntPoint pt1;
+      if (node.m_endtype == etOpenButt)
+      {
+        int j = len - 1;
+        pt1 = IntPoint((cInt)Round(m_srcPoly[j].X + m_normals[j].X *
+          delta), (cInt)Round(m_srcPoly[j].Y + m_normals[j].Y * delta));
+        m_destPoly.push_back(pt1);
+        pt1 = IntPoint((cInt)Round(m_srcPoly[j].X - m_normals[j].X *
+          delta), (cInt)Round(m_srcPoly[j].Y - m_normals[j].Y * delta));
+        m_destPoly.push_back(pt1);
+      }
+      else
+      {
+        int j = len - 1;
+        k = len - 2;
+        m_sinA = 0;
+        m_normals[j] = DoublePoint(-m_normals[j].X, -m_normals[j].Y);
+        if (node.m_endtype == etOpenSquare)
+          DoSquare(j, k);
+        else
+          DoRound(j, k);
+      }
+
+      //re-build m_normals ...
+      for (int j = len - 1; j > 0; j--)
+        m_normals[j] = DoublePoint(-m_normals[j - 1].X, -m_normals[j - 1].Y);
+      m_normals[0] = DoublePoint(-m_normals[1].X, -m_normals[1].Y);
+
+      k = len - 1;
+      for (int j = k - 1; j > 0; --j) OffsetPoint(j, k, node.m_jointype);
+
+      if (node.m_endtype == etOpenButt)
+      {
+        pt1 = IntPoint((cInt)Round(m_srcPoly[0].X - m_normals[0].X * delta),
+          (cInt)Round(m_srcPoly[0].Y - m_normals[0].Y * delta));
+        m_destPoly.push_back(pt1);
+        pt1 = IntPoint((cInt)Round(m_srcPoly[0].X + m_normals[0].X * delta),
+          (cInt)Round(m_srcPoly[0].Y + m_normals[0].Y * delta));
+        m_destPoly.push_back(pt1);
+      }
+      else
+      {
+        k = 1;
+        m_sinA = 0;
+        if (node.m_endtype == etOpenSquare)
+          DoSquare(0, 1);
+        else
+          DoRound(0, 1);
+      }
+      m_destPolys.push_back(m_destPoly);
+    }
+  }
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::OffsetPoint(int j, int& k, JoinType jointype)
+{
+  //cross product ...
+  m_sinA = (m_normals[k].X * m_normals[j].Y - m_normals[j].X * m_normals[k].Y);
+  if (std::fabs(m_sinA * m_delta) < 1.0) 
+  {
+    //dot product ...
+    double cosA = (m_normals[k].X * m_normals[j].X + m_normals[j].Y * m_normals[k].Y ); 
+    if (cosA > 0) // angle => 0 degrees
+    {
+      m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
+        Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
+      return; 
+    }
+    //else angle => 180 degrees   
+  }
+  else if (m_sinA > 1.0) m_sinA = 1.0;
+  else if (m_sinA < -1.0) m_sinA = -1.0;
+
+  if (m_sinA * m_delta < 0)
+  {
+    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[k].X * m_delta),
+      Round(m_srcPoly[j].Y + m_normals[k].Y * m_delta)));
+    m_destPoly.push_back(m_srcPoly[j]);
+    m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
+      Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
+  }
+  else
+    switch (jointype)
+    {
+      case jtMiter:
+        {
+          double r = 1 + (m_normals[j].X * m_normals[k].X +
+            m_normals[j].Y * m_normals[k].Y);
+          if (r >= m_miterLim) DoMiter(j, k, r); else DoSquare(j, k);
+          break;
+        }
+      case jtSquare: DoSquare(j, k); break;
+      case jtRound: DoRound(j, k); break;
+    }
+  k = j;
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::DoSquare(int j, int k)
+{
+  double dx = std::tan(std::atan2(m_sinA,
+      m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
+  m_destPoly.push_back(IntPoint(
+      Round(m_srcPoly[j].X + m_delta * (m_normals[k].X - m_normals[k].Y * dx)),
+      Round(m_srcPoly[j].Y + m_delta * (m_normals[k].Y + m_normals[k].X * dx))));
+  m_destPoly.push_back(IntPoint(
+      Round(m_srcPoly[j].X + m_delta * (m_normals[j].X + m_normals[j].Y * dx)),
+      Round(m_srcPoly[j].Y + m_delta * (m_normals[j].Y - m_normals[j].X * dx))));
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::DoMiter(int j, int k, double r)
+{
+  double q = m_delta / r;
+  m_destPoly.push_back(IntPoint(Round(m_srcPoly[j].X + (m_normals[k].X + m_normals[j].X) * q),
+      Round(m_srcPoly[j].Y + (m_normals[k].Y + m_normals[j].Y) * q)));
+}
+//------------------------------------------------------------------------------
+
+void ClipperOffset::DoRound(int j, int k)
+{
+  double a = std::atan2(m_sinA,
+  m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
+  int steps = std::max((int)Round(m_StepsPerRad * std::fabs(a)), 1);
+
+  double X = m_normals[k].X, Y = m_normals[k].Y, X2;
+  for (int i = 0; i < steps; ++i)
+  {
+    m_destPoly.push_back(IntPoint(
+        Round(m_srcPoly[j].X + X * m_delta),
+        Round(m_srcPoly[j].Y + Y * m_delta)));
+    X2 = X;
+    X = X * m_cos - m_sin * Y;
+    Y = X2 * m_sin + Y * m_cos;
+  }
+  m_destPoly.push_back(IntPoint(
+  Round(m_srcPoly[j].X + m_normals[j].X * m_delta),
+  Round(m_srcPoly[j].Y + m_normals[j].Y * m_delta)));
+}
+
+//------------------------------------------------------------------------------
+// Miscellaneous public functions
+//------------------------------------------------------------------------------
+
+void Clipper::DoSimplePolygons()
+{
+  PolyOutList::size_type i = 0;
+  while (i < m_PolyOuts.size()) 
+  {
+    OutRec* outrec = m_PolyOuts[i++];
+    OutPt* op = outrec->Pts;
+    if (!op || outrec->IsOpen) continue;
+    do //for each Pt in Polygon until duplicate found do ...
+    {
+      OutPt* op2 = op->Next;
+      while (op2 != outrec->Pts) 
+      {
+        if ((op->Pt == op2->Pt) && op2->Next != op && op2->Prev != op) 
+        {
+          //split the polygon into two ...
+          OutPt* op3 = op->Prev;
+          OutPt* op4 = op2->Prev;
+          op->Prev = op4;
+          op4->Next = op;
+          op2->Prev = op3;
+          op3->Next = op2;
+
+          outrec->Pts = op;
+          OutRec* outrec2 = CreateOutRec();
+          outrec2->Pts = op2;
+          UpdateOutPtIdxs(*outrec2);
+          if (Poly2ContainsPoly1(outrec2->Pts, outrec->Pts))
+          {
+            //OutRec2 is contained by OutRec1 ...
+            outrec2->IsHole = !outrec->IsHole;
+            outrec2->FirstLeft = outrec;
+            if (m_UsingPolyTree) FixupFirstLefts2(outrec2, outrec);
+          }
+          else
+            if (Poly2ContainsPoly1(outrec->Pts, outrec2->Pts))
+          {
+            //OutRec1 is contained by OutRec2 ...
+            outrec2->IsHole = outrec->IsHole;
+            outrec->IsHole = !outrec2->IsHole;
+            outrec2->FirstLeft = outrec->FirstLeft;
+            outrec->FirstLeft = outrec2;
+            if (m_UsingPolyTree) FixupFirstLefts2(outrec, outrec2);
+            }
+            else
+          {
+            //the 2 polygons are separate ...
+            outrec2->IsHole = outrec->IsHole;
+            outrec2->FirstLeft = outrec->FirstLeft;
+            if (m_UsingPolyTree) FixupFirstLefts1(outrec, outrec2);
+            }
+          op2 = op; //ie get ready for the Next iteration
+        }
+        op2 = op2->Next;
+      }
+      op = op->Next;
+    }
+    while (op != outrec->Pts);
+  }
+}
+//------------------------------------------------------------------------------
+
+void ReversePath(Path& p)
+{
+  std::reverse(p.begin(), p.end());
+}
+//------------------------------------------------------------------------------
+
+void ReversePaths(Paths& p)
+{
+  for (Paths::size_type i = 0; i < p.size(); ++i)
+    ReversePath(p[i]);
+}
+//------------------------------------------------------------------------------
+
+void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType)
+{
+  Clipper c;
+  c.StrictlySimple(true);
+  c.AddPath(in_poly, ptSubject, true);
+  c.Execute(ctUnion, out_polys, fillType, fillType);
+}
+//------------------------------------------------------------------------------
+
+void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType)
+{
+  Clipper c;
+  c.StrictlySimple(true);
+  c.AddPaths(in_polys, ptSubject, true);
+  c.Execute(ctUnion, out_polys, fillType, fillType);
+}
+//------------------------------------------------------------------------------
+
+void SimplifyPolygons(Paths &polys, PolyFillType fillType)
+{
+  SimplifyPolygons(polys, polys, fillType);
+}
+//------------------------------------------------------------------------------
+
+inline double DistanceSqrd(const IntPoint& pt1, const IntPoint& pt2)
+{
+  double Dx = ((double)pt1.X - pt2.X);
+  double dy = ((double)pt1.Y - pt2.Y);
+  return (Dx*Dx + dy*dy);
+}
+//------------------------------------------------------------------------------
+
+double DistanceFromLineSqrd(
+  const IntPoint& pt, const IntPoint& ln1, const IntPoint& ln2)
+{
+  //The equation of a line in general form (Ax + By + C = 0)
+  //given 2 points (x�,y�) & (x�,y�) is ...
+  //(y� - y�)x + (x� - x�)y + (y� - y�)x� - (x� - x�)y� = 0
+  //A = (y� - y�); B = (x� - x�); C = (y� - y�)x� - (x� - x�)y�
+  //perpendicular distance of point (x�,y�) = (Ax� + By� + C)/Sqrt(A� + B�)
+  //see http://en.wikipedia.org/wiki/Perpendicular_distance
+  double A = double(ln1.Y - ln2.Y);
+  double B = double(ln2.X - ln1.X);
+  double C = A * ln1.X  + B * ln1.Y;
+  C = A * pt.X + B * pt.Y - C;
+  return (C * C) / (A * A + B * B);
+}
+//---------------------------------------------------------------------------
+
+bool SlopesNearCollinear(const IntPoint& pt1, 
+    const IntPoint& pt2, const IntPoint& pt3, double distSqrd)
+{
+  //this function is more accurate when the point that's geometrically
+  //between the other 2 points is the one that's tested for distance.
+  //ie makes it more likely to pick up 'spikes' ...
+	if (Abs(pt1.X - pt2.X) > Abs(pt1.Y - pt2.Y))
+	{
+    if ((pt1.X > pt2.X) == (pt1.X < pt3.X))
+      return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
+    else if ((pt2.X > pt1.X) == (pt2.X < pt3.X))
+      return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
+		else
+	    return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
+	}
+	else
+	{
+    if ((pt1.Y > pt2.Y) == (pt1.Y < pt3.Y))
+      return DistanceFromLineSqrd(pt1, pt2, pt3) < distSqrd;
+    else if ((pt2.Y > pt1.Y) == (pt2.Y < pt3.Y))
+      return DistanceFromLineSqrd(pt2, pt1, pt3) < distSqrd;
+		else
+      return DistanceFromLineSqrd(pt3, pt1, pt2) < distSqrd;
+	}
+}
+//------------------------------------------------------------------------------
+
+bool PointsAreClose(IntPoint pt1, IntPoint pt2, double distSqrd)
+{
+    double Dx = (double)pt1.X - pt2.X;
+    double dy = (double)pt1.Y - pt2.Y;
+    return ((Dx * Dx) + (dy * dy) <= distSqrd);
+}
+//------------------------------------------------------------------------------
+
+OutPt* ExcludeOp(OutPt* op)
+{
+  OutPt* result = op->Prev;
+  result->Next = op->Next;
+  op->Next->Prev = result;
+  result->Idx = 0;
+  return result;
+}
+//------------------------------------------------------------------------------
+
+void CleanPolygon(const Path& in_poly, Path& out_poly, double distance)
+{
+  //distance = proximity in units/pixels below which vertices
+  //will be stripped. Default ~= sqrt(2).
+  
+  size_t size = in_poly.size();
+  
+  if (size == 0) 
+  {
+    out_poly.clear();
+    return;
+  }
+
+  OutPt* outPts = new OutPt[size];
+  for (size_t i = 0; i < size; ++i)
+  {
+    outPts[i].Pt = in_poly[i];
+    outPts[i].Next = &outPts[(i + 1) % size];
+    outPts[i].Next->Prev = &outPts[i];
+    outPts[i].Idx = 0;
+  }
+
+  double distSqrd = distance * distance;
+  OutPt* op = &outPts[0];
+  while (op->Idx == 0 && op->Next != op->Prev) 
+  {
+    if (PointsAreClose(op->Pt, op->Prev->Pt, distSqrd))
+    {
+      op = ExcludeOp(op);
+      size--;
+    } 
+    else if (PointsAreClose(op->Prev->Pt, op->Next->Pt, distSqrd))
+    {
+      ExcludeOp(op->Next);
+      op = ExcludeOp(op);
+      size -= 2;
+    }
+    else if (SlopesNearCollinear(op->Prev->Pt, op->Pt, op->Next->Pt, distSqrd))
+    {
+      op = ExcludeOp(op);
+      size--;
+    }
+    else
+    {
+      op->Idx = 1;
+      op = op->Next;
+    }
+  }
+
+  if (size < 3) size = 0;
+  out_poly.resize(size);
+  for (size_t i = 0; i < size; ++i)
+  {
+    out_poly[i] = op->Pt;
+    op = op->Next;
+  }
+  delete [] outPts;
+}
+//------------------------------------------------------------------------------
+
+void CleanPolygon(Path& poly, double distance)
+{
+  CleanPolygon(poly, poly, distance);
+}
+//------------------------------------------------------------------------------
+
+void CleanPolygons(const Paths& in_polys, Paths& out_polys, double distance)
+{
+  out_polys.resize(in_polys.size());
+  for (Paths::size_type i = 0; i < in_polys.size(); ++i)
+    CleanPolygon(in_polys[i], out_polys[i], distance);
+}
+//------------------------------------------------------------------------------
+
+void CleanPolygons(Paths& polys, double distance)
+{
+  CleanPolygons(polys, polys, distance);
+}
+//------------------------------------------------------------------------------
+
+void Minkowski(const Path& poly, const Path& path, 
+  Paths& solution, bool isSum, bool isClosed)
+{
+  int delta = (isClosed ? 1 : 0);
+  size_t polyCnt = poly.size();
+  size_t pathCnt = path.size();
+  Paths pp;
+  pp.reserve(pathCnt);
+  if (isSum)
+    for (size_t i = 0; i < pathCnt; ++i)
+    {
+      Path p;
+      p.reserve(polyCnt);
+      for (size_t j = 0; j < poly.size(); ++j)
+        p.push_back(IntPoint(path[i].X + poly[j].X, path[i].Y + poly[j].Y));
+      pp.push_back(p);
+    }
+  else
+    for (size_t i = 0; i < pathCnt; ++i)
+    {
+      Path p;
+      p.reserve(polyCnt);
+      for (size_t j = 0; j < poly.size(); ++j)
+        p.push_back(IntPoint(path[i].X - poly[j].X, path[i].Y - poly[j].Y));
+      pp.push_back(p);
+    }
+
+  solution.clear();
+  solution.reserve((pathCnt + delta) * (polyCnt + 1));
+  for (size_t i = 0; i < pathCnt - 1 + delta; ++i)
+    for (size_t j = 0; j < polyCnt; ++j)
+    {
+      Path quad;
+      quad.reserve(4);
+      quad.push_back(pp[i % pathCnt][j % polyCnt]);
+      quad.push_back(pp[(i + 1) % pathCnt][j % polyCnt]);
+      quad.push_back(pp[(i + 1) % pathCnt][(j + 1) % polyCnt]);
+      quad.push_back(pp[i % pathCnt][(j + 1) % polyCnt]);
+      if (!Orientation(quad)) ReversePath(quad);
+      solution.push_back(quad);
+    }
+}
+//------------------------------------------------------------------------------
+
+void MinkowskiSum(const Path& pattern, const Path& path, Paths& solution, bool pathIsClosed)
+{
+  Minkowski(pattern, path, solution, true, pathIsClosed);
+  Clipper c;
+  c.AddPaths(solution, ptSubject, true);
+  c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
+}
+//------------------------------------------------------------------------------
+
+void TranslatePath(const Path& input, Path& output, const IntPoint delta)
+{
+  //precondition: input != output
+  output.resize(input.size());
+  for (size_t i = 0; i < input.size(); ++i)
+    output[i] = IntPoint(input[i].X + delta.X, input[i].Y + delta.Y);
+}
+//------------------------------------------------------------------------------
+
+void MinkowskiSum(const Path& pattern, const Paths& paths, Paths& solution, bool pathIsClosed)
+{
+  Clipper c;
+  for (size_t i = 0; i < paths.size(); ++i)
+  {
+    Paths tmp;
+    Minkowski(pattern, paths[i], tmp, true, pathIsClosed);
+    c.AddPaths(tmp, ptSubject, true);
+    if (pathIsClosed)
+    {
+      Path tmp2;
+      TranslatePath(paths[i], tmp2, pattern[0]);
+      c.AddPath(tmp2, ptClip, true);
+    }
+  }
+    c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
+}
+//------------------------------------------------------------------------------
+
+void MinkowskiDiff(const Path& poly1, const Path& poly2, Paths& solution)
+{
+  Minkowski(poly1, poly2, solution, false, true);
+  Clipper c;
+  c.AddPaths(solution, ptSubject, true);
+  c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
+}
+//------------------------------------------------------------------------------
+
+enum NodeType {ntAny, ntOpen, ntClosed};
+
+void AddPolyNodeToPaths(const PolyNode& polynode, NodeType nodetype, Paths& paths)
+{
+  bool match = true;
+  if (nodetype == ntClosed) match = !polynode.IsOpen();
+  else if (nodetype == ntOpen) return;
+
+  if (!polynode.Contour.empty() && match)
+    paths.push_back(polynode.Contour);
+  for (int i = 0; i < polynode.ChildCount(); ++i)
+    AddPolyNodeToPaths(*polynode.Childs[i], nodetype, paths);
+}
+//------------------------------------------------------------------------------
+
+void PolyTreeToPaths(const PolyTree& polytree, Paths& paths)
+{
+  paths.resize(0); 
+  paths.reserve(polytree.Total());
+  AddPolyNodeToPaths(polytree, ntAny, paths);
+}
+//------------------------------------------------------------------------------
+
+void ClosedPathsFromPolyTree(const PolyTree& polytree, Paths& paths)
+{
+  paths.resize(0); 
+  paths.reserve(polytree.Total());
+  AddPolyNodeToPaths(polytree, ntClosed, paths);
+}
+//------------------------------------------------------------------------------
+
+void OpenPathsFromPolyTree(PolyTree& polytree, Paths& paths)
+{
+  paths.resize(0); 
+  paths.reserve(polytree.Total());
+  //Open paths are top level only, so ...
+  for (int i = 0; i < polytree.ChildCount(); ++i)
+    if (polytree.Childs[i]->IsOpen())
+      paths.push_back(polytree.Childs[i]->Contour);
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, const IntPoint &p)
+{
+  s << "(" << p.X << "," << p.Y << ")";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, const Path &p)
+{
+  if (p.empty()) return s;
+  Path::size_type last = p.size() -1;
+  for (Path::size_type i = 0; i < last; i++)
+    s << "(" << p[i].X << "," << p[i].Y << "), ";
+  s << "(" << p[last].X << "," << p[last].Y << ")\n";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+std::ostream& operator <<(std::ostream &s, const Paths &p)
+{
+  for (Paths::size_type i = 0; i < p.size(); i++)
+    s << p[i];
+  s << "\n";
+  return s;
+}
+//------------------------------------------------------------------------------
+
+} //ClipperLib namespace

deploy/ios_demo/ocr_demo/pdocr/ocr_clipper.hpp

+/*******************************************************************************
+*                                                                              *
+* Author    :  Angus Johnson                                                   *
+* Version   :  6.4.2                                                           *
+* Date      :  27 February 2017                                                *
+* Website   :  http://www.angusj.com                                           *
+* Copyright :  Angus Johnson 2010-2017                                         *
+*                                                                              *
+* License:                                                                     *
+* Use, modification & distribution is subject to Boost Software License Ver 1. *
+* http://www.boost.org/LICENSE_1_0.txt                                         *
+*                                                                              *
+* Attributions:                                                                *
+* The code in this library is an extension of Bala Vatti's clipping algorithm: *
+* "A generic solution to polygon clipping"                                     *
+* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
+* http://portal.acm.org/citation.cfm?id=129906                                 *
+*                                                                              *
+* Computer graphics and geometric modeling: implementation and algorithms      *
+* By Max K. Agoston                                                            *
+* Springer; 1 edition (January 4, 2005)                                        *
+* http://books.google.com/books?q=vatti+clipping+agoston                       *
+*                                                                              *
+* See also:                                                                    *
+* "Polygon Offsetting by Computing Winding Numbers"                            *
+* Paper no. DETC2005-85513 pp. 565-575                                         *
+* ASME 2005 International Design Engineering Technical Conferences             *
+* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
+* September 24-28, 2005 , Long Beach, California, USA                          *
+* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
+*                                                                              *
+*******************************************************************************/
+
+#ifndef clipper_hpp
+#define clipper_hpp
+
+#define CLIPPER_VERSION "6.4.2"
+
+//use_int32: When enabled 32bit ints are used instead of 64bit ints. This
+//improve performance but coordinate values are limited to the range +/- 46340
+//#define use_int32
+
+//use_xyz: adds a Z member to IntPoint. Adds a minor cost to perfomance.
+//#define use_xyz
+
+//use_lines: Enables line clipping. Adds a very minor cost to performance.
+#define use_lines
+
+//use_deprecated: Enables temporary support for the obsolete functions
+//#define use_deprecated  
+
+#include <vector>
+#include <list>
+#include <set>
+#include <stdexcept>
+#include <cstring>
+#include <cstdlib>
+#include <ostream>
+#include <functional>
+#include <queue>
+
+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
+};
+
+#ifdef use_int32
+typedef int cInt;
+static cInt const loRange = 0x7FFF;
+static cInt const hiRange = 0x7FFF;
+#else
+typedef signed long long cInt;
+static cInt const loRange = 0x3FFFFFFF;
+static cInt const hiRange = 0x3FFFFFFFFFFFFFFFLL;
+typedef signed long long long64;     //used by Int128 class
+typedef unsigned long long ulong64;
+
+#endif
+
+struct IntPoint {
+    cInt X;
+    cInt Y;
+#ifdef use_xyz
+    cInt Z;
+    IntPoint(cInt x = 0, cInt y = 0, cInt z = 0): X(x), Y(y), Z(z) {};
+#else
+
+    IntPoint(cInt x = 0, cInt y = 0) : X(x), Y(y) {};
+#endif
+
+    friend inline bool operator==(const IntPoint &a, const IntPoint &b) {
+        return a.X == b.X && a.Y == b.Y;
+    }
+
+    friend inline bool operator!=(const IntPoint &a, const IntPoint &b) {
+        return a.X != b.X || a.Y != b.Y;
+    }
+};
+//------------------------------------------------------------------------------
+
+typedef std::vector <IntPoint> Path;
+typedef std::vector <Path> Paths;
+
+inline Path &operator<<(Path &poly, const IntPoint &p) {
+    poly.push_back(p);
+    return poly;
+}
+
+inline Paths &operator<<(Paths &polys, const Path &p) {
+    polys.push_back(p);
+    return polys;
+}
+
+std::ostream &operator<<(std::ostream &s, const IntPoint &p);
+
+std::ostream &operator<<(std::ostream &s, const Path &p);
+
+std::ostream &operator<<(std::ostream &s, const Paths &p);
+
+struct DoublePoint {
+    double X;
+    double Y;
+
+    DoublePoint(double x = 0, double y = 0) : X(x), Y(y) {}
+
+    DoublePoint(IntPoint ip) : X((double) ip.X), Y((double) ip.Y) {}
+};
+//------------------------------------------------------------------------------
+
+#ifdef use_xyz
+typedef void (*ZFillCallback)(IntPoint& e1bot, IntPoint& e1top, IntPoint& e2bot, IntPoint& e2top, IntPoint& pt);
+#endif
+
+enum InitOptions {
+    ioReverseSolution = 1, ioStrictlySimple = 2, ioPreserveCollinear = 4
+};
+enum JoinType {
+    jtSquare, jtRound, jtMiter
+};
+enum EndType {
+    etClosedPolygon, etClosedLine, etOpenButt, etOpenSquare, etOpenRound
+};
+
+class PolyNode;
+
+typedef std::vector<PolyNode *> PolyNodes;
+
+class PolyNode {
+public:
+    PolyNode();
+
+    virtual ~PolyNode() {};
+    Path Contour;
+    PolyNodes Childs;
+    PolyNode *Parent;
+
+    PolyNode *GetNext() const;
+
+    bool IsHole() const;
+
+    bool IsOpen() const;
+
+    int ChildCount() const;
+
+private:
+    //PolyNode& operator =(PolyNode& other); 
+    unsigned Index; //node index in Parent.Childs
+    bool m_IsOpen;
+    JoinType m_jointype;
+    EndType m_endtype;
+
+    PolyNode *GetNextSiblingUp() const;
+
+    void AddChild(PolyNode &child);
+
+    friend class Clipper; //to access Index
+    friend class ClipperOffset;
+};
+
+class PolyTree : public PolyNode {
+public:
+    ~PolyTree() { Clear(); };
+
+    PolyNode *GetFirst() const;
+
+    void Clear();
+
+    int Total() const;
+
+private:
+    //PolyTree& operator =(PolyTree& other);
+    PolyNodes AllNodes;
+
+    friend class Clipper; //to access AllNodes
+};
+
+bool Orientation(const Path &poly);
+
+double Area(const Path &poly);
+
+int PointInPolygon(const IntPoint &pt, const Path &path);
+
+void SimplifyPolygon(const Path &in_poly, Paths &out_polys, PolyFillType fillType = pftEvenOdd);
+
+void SimplifyPolygons(const Paths &in_polys, Paths &out_polys, PolyFillType fillType = pftEvenOdd);
+
+void SimplifyPolygons(Paths &polys, PolyFillType fillType = pftEvenOdd);
+
+void CleanPolygon(const Path &in_poly, Path &out_poly, double distance = 1.415);
+
+void CleanPolygon(Path &poly, double distance = 1.415);
+
+void CleanPolygons(const Paths &in_polys, Paths &out_polys, double distance = 1.415);
+
+void CleanPolygons(Paths &polys, double distance = 1.415);
+
+void MinkowskiSum(const Path &pattern, const Path &path, Paths &solution, bool pathIsClosed);
+
+void MinkowskiSum(const Path &pattern, const Paths &paths, Paths &solution, bool pathIsClosed);
+
+void MinkowskiDiff(const Path &poly1, const Path &poly2, Paths &solution);
+
+void PolyTreeToPaths(const PolyTree &polytree, Paths &paths);
+
+void ClosedPathsFromPolyTree(const PolyTree &polytree, Paths &paths);
+
+void OpenPathsFromPolyTree(PolyTree &polytree, Paths &paths);
+
+void ReversePath(Path &p);
+
+void ReversePaths(Paths &p);
+
+struct IntRect {
+    cInt left;
+    cInt top;
+    cInt right;
+    cInt bottom;
+};
+
+//enums that are used internally ...
+enum EdgeSide {
+    esLeft = 1, esRight = 2
+};
+
+//forward declarations (for stuff used internally) ...
+struct TEdge;
+struct IntersectNode;
+struct LocalMinimum;
+struct OutPt;
+struct OutRec;
+struct Join;
+
+typedef std::vector<OutRec *> PolyOutList;
+typedef std::vector<TEdge *> EdgeList;
+typedef std::vector<Join *> JoinList;
+typedef std::vector<IntersectNode *> IntersectList;
+
+//------------------------------------------------------------------------------
+
+//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();
+
+    virtual bool AddPath(const Path &pg, PolyType PolyTyp, bool Closed);
+
+    bool AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed);
+
+    virtual void Clear();
+
+    IntRect GetBounds();
+
+    bool PreserveCollinear() { return m_PreserveCollinear; };
+
+    void PreserveCollinear(bool value) { m_PreserveCollinear = value; };
+protected:
+    void DisposeLocalMinimaList();
+
+    TEdge *AddBoundsToLML(TEdge *e, bool IsClosed);
+
+    virtual void Reset();
+
+    TEdge *ProcessBound(TEdge *E, bool IsClockwise);
+
+    void InsertScanbeam(const cInt Y);
+
+    bool PopScanbeam(cInt &Y);
+
+    bool LocalMinimaPending();
+
+    bool PopLocalMinima(cInt Y, const LocalMinimum *&locMin);
+
+    OutRec *CreateOutRec();
+
+    void DisposeAllOutRecs();
+
+    void DisposeOutRec(PolyOutList::size_type index);
+
+    void SwapPositionsInAEL(TEdge *edge1, TEdge *edge2);
+
+    void DeleteFromAEL(TEdge *e);
+
+    void UpdateEdgeIntoAEL(TEdge *&e);
+
+    typedef std::vector <LocalMinimum> MinimaList;
+    MinimaList::iterator m_CurrentLM;
+    MinimaList m_MinimaList;
+
+    bool m_UseFullRange;
+    EdgeList m_edges;
+    bool m_PreserveCollinear;
+    bool m_HasOpenPaths;
+    PolyOutList m_PolyOuts;
+    TEdge *m_ActiveEdges;
+
+    typedef std::priority_queue <cInt> ScanbeamList;
+    ScanbeamList m_Scanbeam;
+};
+//------------------------------------------------------------------------------
+
+class Clipper : public virtual ClipperBase {
+public:
+    Clipper(int initOptions = 0);
+
+    bool Execute(ClipType clipType,
+                 Paths &solution,
+                 PolyFillType fillType = pftEvenOdd);
+
+    bool Execute(ClipType clipType,
+                 Paths &solution,
+                 PolyFillType subjFillType,
+                 PolyFillType clipFillType);
+
+    bool Execute(ClipType clipType,
+                 PolyTree &polytree,
+                 PolyFillType fillType = pftEvenOdd);
+
+    bool Execute(ClipType clipType,
+                 PolyTree &polytree,
+                 PolyFillType subjFillType,
+                 PolyFillType clipFillType);
+
+    bool ReverseSolution() { return m_ReverseOutput; };
+
+    void ReverseSolution(bool value) { m_ReverseOutput = value; };
+
+    bool StrictlySimple() { return m_StrictSimple; };
+
+    void StrictlySimple(bool value) { m_StrictSimple = value; };
+    //set the callback function for z value filling on intersections (otherwise Z is 0)
+#ifdef use_xyz
+    void ZFillFunction(ZFillCallback zFillFunc);
+#endif
+protected:
+    virtual bool ExecuteInternal();
+
+private:
+    JoinList m_Joins;
+    JoinList m_GhostJoins;
+    IntersectList m_IntersectList;
+    ClipType m_ClipType;
+    typedef std::list <cInt> MaximaList;
+    MaximaList m_Maxima;
+    TEdge *m_SortedEdges;
+    bool m_ExecuteLocked;
+    PolyFillType m_ClipFillType;
+    PolyFillType m_SubjFillType;
+    bool m_ReverseOutput;
+    bool m_UsingPolyTree;
+    bool m_StrictSimple;
+#ifdef use_xyz
+    ZFillCallback   m_ZFill; //custom callback
+#endif
+
+    void SetWindingCount(TEdge &edge);
+
+    bool IsEvenOddFillType(const TEdge &edge) const;
+
+    bool IsEvenOddAltFillType(const TEdge &edge) const;
+
+    void InsertLocalMinimaIntoAEL(const cInt botY);
+
+    void InsertEdgeIntoAEL(TEdge *edge, TEdge *startEdge);
+
+    void AddEdgeToSEL(TEdge *edge);
+
+    bool PopEdgeFromSEL(TEdge *&edge);
+
+    void CopyAELToSEL();
+
+    void DeleteFromSEL(TEdge *e);
+
+    void SwapPositionsInSEL(TEdge *edge1, TEdge *edge2);
+
+    bool IsContributing(const TEdge &edge) const;
+
+    bool IsTopHorz(const cInt XPos);
+
+    void DoMaxima(TEdge *e);
+
+    void ProcessHorizontals();
+
+    void ProcessHorizontal(TEdge *horzEdge);
+
+    void AddLocalMaxPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
+
+    OutPt *AddLocalMinPoly(TEdge *e1, TEdge *e2, const IntPoint &pt);
+
+    OutRec *GetOutRec(int idx);
+
+    void AppendPolygon(TEdge *e1, TEdge *e2);
+
+    void IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &pt);
+
+    OutPt *AddOutPt(TEdge *e, const IntPoint &pt);
+
+    OutPt *GetLastOutPt(TEdge *e);
+
+    bool ProcessIntersections(const cInt topY);
+
+    void BuildIntersectList(const cInt topY);
+
+    void ProcessIntersectList();
+
+    void ProcessEdgesAtTopOfScanbeam(const cInt topY);
+
+    void BuildResult(Paths &polys);
+
+    void BuildResult2(PolyTree &polytree);
+
+    void SetHoleState(TEdge *e, OutRec *outrec);
+
+    void DisposeIntersectNodes();
+
+    bool FixupIntersectionOrder();
+
+    void FixupOutPolygon(OutRec &outrec);
+
+    void FixupOutPolyline(OutRec &outrec);
+
+    bool IsHole(TEdge *e);
+
+    bool FindOwnerFromSplitRecs(OutRec &outRec, OutRec *&currOrfl);
+
+    void FixHoleLinkage(OutRec &outrec);
+
+    void AddJoin(OutPt *op1, OutPt *op2, const IntPoint offPt);
+
+    void ClearJoins();
+
+    void ClearGhostJoins();
+
+    void AddGhostJoin(OutPt *op, const IntPoint offPt);
+
+    bool JoinPoints(Join *j, OutRec *outRec1, OutRec *outRec2);
+
+    void JoinCommonEdges();
+
+    void DoSimplePolygons();
+
+    void FixupFirstLefts1(OutRec *OldOutRec, OutRec *NewOutRec);
+
+    void FixupFirstLefts2(OutRec *InnerOutRec, OutRec *OuterOutRec);
+
+    void FixupFirstLefts3(OutRec *OldOutRec, OutRec *NewOutRec);
+
+#ifdef use_xyz
+    void SetZ(IntPoint& pt, TEdge& e1, TEdge& e2);
+#endif
+};
+//------------------------------------------------------------------------------
+
+class ClipperOffset {
+public:
+    ClipperOffset(double miterLimit = 2.0, double roundPrecision = 0.25);
+
+    ~ClipperOffset();
+
+    void AddPath(const Path &path, JoinType joinType, EndType endType);
+
+    void AddPaths(const Paths &paths, JoinType joinType, EndType endType);
+
+    void Execute(Paths &solution, double delta);
+
+    void Execute(PolyTree &solution, double delta);
+
+    void Clear();
+
+    double MiterLimit;
+    double ArcTolerance;
+private:
+    Paths m_destPolys;
+    Path m_srcPoly;
+    Path m_destPoly;
+    std::vector <DoublePoint> m_normals;
+    double m_delta, m_sinA, m_sin, m_cos;
+    double m_miterLim, m_StepsPerRad;
+    IntPoint m_lowest;
+    PolyNode m_polyNodes;
+
+    void FixOrientations();
+
+    void DoOffset(double delta);
+
+    void OffsetPoint(int j, int &k, JoinType jointype);
+
+    void DoSquare(int j, int k);
+
+    void DoMiter(int j, int k, double r);
+
+    void DoRound(int j, int k);
+};
+//------------------------------------------------------------------------------
+
+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
+
+

deploy/ios_demo/ocr_demo/pdocr/ocr_crnn_process.cpp

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "ocr_crnn_process.h"
+#include <iostream>
+#include <vector>
+#include <iostream>
+#include <cstring>
+#include <fstream>
+#include <cmath>
+
+const std::string CHARACTER_TYPE = "ch";
+const int MAX_DICT_LENGTH = 6624;
+const std::vector<int> REC_IMAGE_SHAPE = {3, 32, 320};
+
+static cv::Mat crnn_resize_norm_img(cv::Mat img, float wh_ratio) {
+    int imgC, imgH, imgW;
+    imgC = REC_IMAGE_SHAPE[0];
+    imgW = REC_IMAGE_SHAPE[2];
+    imgH = REC_IMAGE_SHAPE[1];
+
+    if (CHARACTER_TYPE == "ch")
+        imgW = int(32 * wh_ratio);
+
+    float ratio = float(img.cols) / float(img.rows);
+    int resize_w, resize_h;
+    if (ceilf(imgH * ratio) > imgW)
+        resize_w = imgW;
+    else
+        resize_w = int(ceilf(imgH * ratio));
+    cv::Mat resize_img;
+    cv::resize(img, resize_img, cv::Size(resize_w, imgH), 0.f, 0.f, cv::INTER_CUBIC);
+
+    resize_img.convertTo(resize_img, CV_32FC3, 1 / 255.f);
+
+    for (int h = 0; h < resize_img.rows; h++) {
+        for (int w = 0; w < resize_img.cols; w++) {
+            resize_img.at<cv::Vec3f>(h, w)[0] = (resize_img.at<cv::Vec3f>(h, w)[0] - 0.5) * 2;
+            resize_img.at<cv::Vec3f>(h, w)[1] = (resize_img.at<cv::Vec3f>(h, w)[1] - 0.5) * 2;
+            resize_img.at<cv::Vec3f>(h, w)[2] = (resize_img.at<cv::Vec3f>(h, w)[2] - 0.5) * 2;
+        }
+    }
+
+    cv::Mat dist;
+    cv::copyMakeBorder(resize_img, dist, 0, 0, 0, int(imgW - resize_w), cv::BORDER_CONSTANT,
+                       {0, 0, 0});
+
+    return dist;
+
+}
+
+cv::Mat crnn_resize_img(const cv::Mat &img, float wh_ratio) {
+    int imgC = REC_IMAGE_SHAPE[0];
+    int imgW = REC_IMAGE_SHAPE[2];
+    int imgH = REC_IMAGE_SHAPE[1];
+
+    if (CHARACTER_TYPE == "ch") {
+        imgW = int(32 * wh_ratio);
+    }
+
+    float ratio = float(img.cols) / float(img.rows);
+    int resize_w;
+    if (ceilf(imgH * ratio) > imgW)
+        resize_w = imgW;
+    else
+        resize_w = int(ceilf(imgH * ratio));
+    cv::Mat resize_img;
+    cv::resize(img, resize_img, cv::Size(resize_w, imgH));
+    return resize_img;
+}
+
+
+cv::Mat get_rotate_crop_image(const cv::Mat &srcimage, const std::vector<std::vector<int>> &box) {
+
+    std::vector<std::vector<int>> points = box;
+
+    int x_collect[4] = {box[0][0], box[1][0], box[2][0], box[3][0]};
+    int y_collect[4] = {box[0][1], box[1][1], box[2][1], box[3][1]};
+    int left = int(*std::min_element(x_collect, x_collect + 4));
+    int right = int(*std::max_element(x_collect, x_collect + 4));
+    int top = int(*std::min_element(y_collect, y_collect + 4));
+    int bottom = int(*std::max_element(y_collect, y_collect + 4));
+
+    cv::Mat img_crop;
+    srcimage(cv::Rect(left, top, right - left, bottom - top)).copyTo(img_crop);
+
+    for (int i = 0; i < points.size(); i++) {
+        points[i][0] -= left;
+        points[i][1] -= top;
+    }
+
+    int img_crop_width = int(sqrt(pow(points[0][0] - points[1][0], 2) +
+                                  pow(points[0][1] - points[1][1], 2)));
+    int img_crop_height = int(sqrt(pow(points[0][0] - points[3][0], 2) +
+                                   pow(points[0][1] - points[3][1], 2)));
+
+    cv::Point2f pts_std[4];
+    pts_std[0] = cv::Point2f(0., 0.);
+    pts_std[1] = cv::Point2f(img_crop_width, 0.);
+    pts_std[2] = cv::Point2f(img_crop_width, img_crop_height);
+    pts_std[3] = cv::Point2f(0.f, img_crop_height);
+
+    cv::Point2f pointsf[4];
+    pointsf[0] = cv::Point2f(points[0][0], points[0][1]);
+    pointsf[1] = cv::Point2f(points[1][0], points[1][1]);
+    pointsf[2] = cv::Point2f(points[2][0], points[2][1]);
+    pointsf[3] = cv::Point2f(points[3][0], points[3][1]);
+
+    cv::Mat M = cv::getPerspectiveTransform(pointsf, pts_std);
+
+    cv::Mat dst_img;
+    cv::warpPerspective(img_crop, dst_img, M, cv::Size(img_crop_width, img_crop_height),
+                        cv::BORDER_REPLICATE);
+
+    if (float(dst_img.rows) >= float(dst_img.cols) * 1.5) {
+        /*
+        cv::Mat srcCopy = cv::Mat(dst_img.rows, dst_img.cols, dst_img.depth());
+        cv::transpose(dst_img, srcCopy);
+        cv::flip(srcCopy, srcCopy, 0);
+        return srcCopy;
+        */
+        cv::transpose(dst_img, dst_img);
+        cv::flip(dst_img, dst_img, 0);
+        return dst_img;
+    } else {
+        return dst_img;
+    }
+
+}
+

deploy/ios_demo/ocr_demo/pdocr/ocr_crnn_process.h

+//
+// Created by fujiayi on 2020/7/3.
+//
+#pragma once
+
+#include <vector>
+#include <opencv2/opencv.hpp>
+
+
+extern const std::vector<int> REC_IMAGE_SHAPE;
+
+cv::Mat get_rotate_crop_image(const cv::Mat &srcimage, const std::vector<std::vector<int>>& box);
+
+cv::Mat crnn_resize_img(const cv::Mat& img, float wh_ratio);
+
+template<class ForwardIterator>
+inline size_t argmax(ForwardIterator first, ForwardIterator last) {
+    return std::distance(first, std::max_element(first, last));
+}
\ No newline at end of file

deploy/ios_demo/ocr_demo/pdocr/ocr_db_post_process.cpp

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include <iostream>
+#include <vector>
+#include <math.h>
+#include "opencv2/core.hpp"
+#include "opencv2/imgcodecs.hpp"
+#include "opencv2/imgproc.hpp"
+#include "ocr_clipper.hpp"
+
+
+static void getcontourarea(float **box, float unclip_ratio, float &distance) {
+    int pts_num = 4;
+    float area = 0.0f;
+    float dist = 0.0f;
+    for (int i = 0; i < pts_num; i++) {
+        area += box[i][0] * box[(i + 1) % pts_num][1] - box[i][1] * box[(i + 1) % pts_num][0];
+        dist += sqrtf(
+            (box[i][0] - box[(i + 1) % pts_num][0]) * (box[i][0] - box[(i + 1) % pts_num][0]) +
+            (box[i][1] - box[(i + 1) % pts_num][1]) * (box[i][1] - box[(i + 1) % pts_num][1]));
+    }
+    area = fabs(float(area / 2.0));
+
+    distance = area * unclip_ratio / dist;
+
+}
+
+static cv::RotatedRect unclip(float **box) {
+    float unclip_ratio = 2.0;
+    float distance = 1.0;
+
+    getcontourarea(box, unclip_ratio, distance);
+
+    ClipperLib::ClipperOffset offset;
+    ClipperLib::Path p;
+    p << ClipperLib::IntPoint(int(box[0][0]), int(box[0][1]))
+      << ClipperLib::IntPoint(int(box[1][0]), int(box[1][1])) <<
+      ClipperLib::IntPoint(int(box[2][0]), int(box[2][1]))
+      << ClipperLib::IntPoint(int(box[3][0]), int(box[3][1]));
+    offset.AddPath(p, ClipperLib::jtRound, ClipperLib::etClosedPolygon);
+
+    ClipperLib::Paths soln;
+    offset.Execute(soln, distance);
+    std::vector<cv::Point2f> points;
+
+    for (int j = 0; j < soln.size(); j++) {
+        for (int i = 0; i < soln[soln.size() - 1].size(); i++) {
+            points.emplace_back(soln[j][i].X, soln[j][i].Y);
+        }
+    }
+    cv::RotatedRect res = cv::minAreaRect(points);
+
+    return res;
+}
+
+static float **Mat2Vec(cv::Mat mat) {
+    auto **array = new float *[mat.rows];
+    for (int i = 0; i < mat.rows; ++i)
+        array[i] = new float[mat.cols];
+    for (int i = 0; i < mat.rows; ++i) {
+        for (int j = 0; j < mat.cols; ++j) {
+            array[i][j] = mat.at<float>(i, j);
+        }
+    }
+
+    return array;
+}
+
+static void quickSort(float **s, int l, int r) {
+    if (l < r) {
+        int i = l, j = r;
+        float x = s[l][0];
+        float *xp = s[l];
+        while (i < j) {
+            while (i < j && s[j][0] >= x)
+                j--;
+            if (i < j)
+                std::swap(s[i++], s[j]);
+            while (i < j && s[i][0] < x)
+                i++;
+            if (i < j)
+                std::swap(s[j--], s[i]);
+        }
+        s[i] = xp;
+        quickSort(s, l, i - 1);
+        quickSort(s, i + 1, r);
+    }
+}
+
+static void quickSort_vector(std::vector<std::vector<int>> &box, int l, int r, int axis) {
+    if (l < r) {
+        int i = l, j = r;
+        int x = box[l][axis];
+        std::vector<int> xp(box[l]);
+        while (i < j) {
+            while (i < j && box[j][axis] >= x)
+                j--;
+            if (i < j)
+                std::swap(box[i++], box[j]);
+            while (i < j && box[i][axis] < x)
+                i++;
+            if (i < j)
+                std::swap(box[j--], box[i]);
+        }
+        box[i] = xp;
+        quickSort_vector(box, l, i - 1, axis);
+        quickSort_vector(box, i + 1, r, axis);
+    }
+}
+
+static std::vector<std::vector<int>> order_points_clockwise(std::vector<std::vector<int>> pts) {
+    std::vector<std::vector<int>> box = pts;
+    quickSort_vector(box, 0, int(box.size() - 1), 0);
+    std::vector<std::vector<int>> leftmost = {box[0], box[1]};
+    std::vector<std::vector<int>> rightmost = {box[2], box[3]};
+
+    if (leftmost[0][1] > leftmost[1][1])
+        std::swap(leftmost[0], leftmost[1]);
+
+    if (rightmost[0][1] > rightmost[1][1])
+        std::swap(rightmost[0], rightmost[1]);
+
+    std::vector<std::vector<int>> rect = {leftmost[0], rightmost[0], rightmost[1], leftmost[1]};
+    return rect;
+}
+
+static float **get_mini_boxes(cv::RotatedRect box, float &ssid) {
+    ssid = box.size.width >= box.size.height ? box.size.height : box.size.width;
+
+    cv::Mat points;
+    cv::boxPoints(box, points);
+    // sorted box points
+    auto array = Mat2Vec(points);
+    quickSort(array, 0, 3);
+
+    float *idx1 = array[0], *idx2 = array[1], *idx3 = array[2], *idx4 = array[3];
+    if (array[3][1] <= array[2][1]) {
+        idx2 = array[3];
+        idx3 = array[2];
+    } else {
+        idx2 = array[2];
+        idx3 = array[3];
+    }
+    if (array[1][1] <= array[0][1]) {
+        idx1 = array[1];
+        idx4 = array[0];
+    } else {
+        idx1 = array[0];
+        idx4 = array[1];
+    }
+
+    array[0] = idx1;
+    array[1] = idx2;
+    array[2] = idx3;
+    array[3] = idx4;
+
+    return array;
+}
+
+template <class T> T clamp(T x,   T min, T   max) {
+    if (x > max){
+        return  max;
+    }
+    if (x < min){
+        return min;
+    }
+    return x;
+}
+
+static float clampf(float x, float min, float max) {
+    if (x > max)
+        return max;
+    if (x < min)
+        return min;
+    return x;
+}
+
+
+float box_score_fast(float **box_array, cv::Mat pred) {
+    auto array = box_array;
+    int width = pred.cols;
+    int height = pred.rows;
+
+    float box_x[4] = {array[0][0], array[1][0], array[2][0], array[3][0]};
+    float box_y[4] = {array[0][1], array[1][1], array[2][1], array[3][1]};
+
+    int xmin = clamp(int(std::floorf(*(std::min_element(box_x, box_x + 4)))), 0, width - 1);
+    int xmax = clamp(int(std::ceilf(*(std::max_element(box_x, box_x + 4)))), 0, width - 1);
+    int ymin = clamp(int(std::floorf(*(std::min_element(box_y, box_y + 4)))), 0, height - 1);
+    int ymax = clamp(int(std::ceilf(*(std::max_element(box_y, box_y + 4)))), 0, height - 1);
+
+    cv::Mat mask;
+    mask = cv::Mat::zeros(ymax - ymin + 1, xmax - xmin + 1, CV_8UC1);
+
+    cv::Point root_point[4];
+    root_point[0] = cv::Point(int(array[0][0]) - xmin, int(array[0][1]) - ymin);
+    root_point[1] = cv::Point(int(array[1][0]) - xmin, int(array[1][1]) - ymin);
+    root_point[2] = cv::Point(int(array[2][0]) - xmin, int(array[2][1]) - ymin);
+    root_point[3] = cv::Point(int(array[3][0]) - xmin, int(array[3][1]) - ymin);
+    const cv::Point *ppt[1] = {root_point};
+    int npt[] = {4};
+    cv::fillPoly(mask, ppt, npt, 1, cv::Scalar(1));
+
+    cv::Mat croppedImg;
+    pred(cv::Rect(xmin, ymin, xmax - xmin + 1, ymax - ymin + 1)).copyTo(croppedImg);
+
+    auto score = cv::mean(croppedImg, mask)[0];
+    return score;
+}
+
+
+std::vector<std::vector<std::vector<int>>>
+boxes_from_bitmap(const cv::Mat& pred, const cv::Mat& bitmap) {
+    const int min_size = 3;
+    const int max_candidates = 1000;
+    const float box_thresh = 0.5;
+
+    int width = bitmap.cols;
+    int height = bitmap.rows;
+
+    std::vector<std::vector<cv::Point>> contours;
+    std::vector<cv::Vec4i> hierarchy;
+
+    cv::findContours(bitmap, contours, hierarchy, cv::RETR_LIST, cv::CHAIN_APPROX_SIMPLE);
+
+    int num_contours = contours.size() >= max_candidates ? max_candidates : contours.size();
+
+    std::vector<std::vector<std::vector<int>>> boxes;
+
+    for (int _i = 0; _i < num_contours; _i++) {
+        float ssid;
+        cv::RotatedRect box = cv::minAreaRect(contours[_i]);
+        auto array = get_mini_boxes(box, ssid);
+
+        auto box_for_unclip = array;
+        //end get_mini_box
+
+        if (ssid < min_size) {
+            continue;
+        }
+
+        float score;
+        score = box_score_fast(array, pred);
+        //end box_score_fast
+        if (score < box_thresh)
+            continue;
+
+
+        // start for unclip
+        cv::RotatedRect points = unclip(box_for_unclip);
+        // end for unclip
+
+        cv::RotatedRect clipbox = points;
+        auto cliparray = get_mini_boxes(clipbox, ssid);
+
+        if (ssid < min_size + 2) continue;
+
+        int dest_width = pred.cols;
+        int dest_height = pred.rows;
+        std::vector<std::vector<int>> intcliparray;
+
+        for (int num_pt = 0; num_pt < 4; num_pt++) {
+            std::vector<int> a{
+                int(clampf(roundf(cliparray[num_pt][0] / float(width) * float(dest_width)), 0,
+                           float(dest_width))),
+                int(clampf(roundf(cliparray[num_pt][1] / float(height) * float(dest_height)), 0,
+                           float(dest_height)))};
+            intcliparray.push_back(a);
+        }
+        boxes.push_back(intcliparray);
+
+    }//end for
+    return boxes;
+}
+
+int _max(int a, int b) {
+    return a >= b ? a : b;
+}
+
+int _min(int a, int b) {
+    return a >= b ? b : a;
+}
+
+std::vector<std::vector<std::vector<int>>>
+filter_tag_det_res(const std::vector<std::vector<std::vector<int>>>& o_boxes,
+                   float ratio_h, float ratio_w,const cv::Mat& srcimg) {
+    int oriimg_h = srcimg.rows;
+    int oriimg_w = srcimg.cols;
+    std::vector<std::vector<std::vector<int>>> boxes{o_boxes};
+    std::vector<std::vector<std::vector<int>>> root_points;
+    for (int n = 0; n < boxes.size(); n++) {
+        boxes[n] = order_points_clockwise(boxes[n]);
+        for (int m = 0; m < boxes[0].size(); m++) {
+            boxes[n][m][0] /= ratio_w;
+            boxes[n][m][1] /= ratio_h;
+
+            boxes[n][m][0] = int(_min(_max(boxes[n][m][0], 0), oriimg_w - 1));
+            boxes[n][m][1] = int(_min(_max(boxes[n][m][1], 0), oriimg_h - 1));
+        }
+    }
+
+    for (int n = 0; n < boxes.size(); n++) {
+        int rect_width, rect_height;
+        rect_width = int(sqrt(
+            pow(boxes[n][0][0] - boxes[n][1][0], 2) + pow(boxes[n][0][1] - boxes[n][1][1], 2)));
+        rect_height = int(sqrt(
+            pow(boxes[n][0][0] - boxes[n][3][0], 2) + pow(boxes[n][0][1] - boxes[n][3][1], 2)));
+        if (rect_width <= 10 || rect_height <= 10)
+            continue;
+        root_points.push_back(boxes[n]);
+    }
+    return root_points;
+}
+
+/*
+using namespace std;
+// read data from txt file
+cv::Mat readtxt2(std::string path, int imgw, int imgh, int imgc) {
+  std::cout << "read data file from txt file! " << std::endl;
+  ifstream in(path);
+  string line;
+  int count = 0;
+  int i = 0, j = 0;
+  std::vector<float> img_mean = {0.485, 0.456, 0.406};
+  std::vector<float> img_std = {0.229, 0.224, 0.225};
+
+  float trainData[imgh][imgw*imgc];
+
+  while (getline(in, line)) {
+    stringstream ss(line);
+    double x;
+    while (ss >> x) {
+//      trainData[i][j] = float(x) * img_std[j % 3] + img_mean[j % 3];
+      trainData[i][j] = float(x);
+      j++;
+    }
+    i++;
+    j = 0;
+  }
+
+  cv::Mat pred_map(imgh, imgw*imgc, CV_32FC1, (float *) trainData);
+  cv::Mat reshape_img = pred_map.reshape(imgc, imgh);
+  return reshape_img;
+}
+ */
+//using namespace std;
+//
+//void writetxt(vector<vector<float>> data, std::string save_path){
+//
+//  ofstream fout(save_path);
+//
+//  for (int i = 0; i < data.size(); i++) {
+//    for (int j=0; j< data[0].size(); j++){
+//      fout << data[i][j] << " ";
+//    }
+//    fout << endl;
+//  }
+//  fout << endl;
+//  fout.close();
+//}

deploy/ios_demo/ocr_demo/pdocr/ocr_db_post_process.h

+//
+// Created by fujiayi on 2020/7/2.
+//
+#pragma once
+
+std::vector<std::vector<std::vector<int>>> boxes_from_bitmap(const cv::Mat& pred, const cv::Mat& bitmap);
+
+std::vector<std::vector<std::vector<int>>>
+filter_tag_det_res(const std::vector<std::vector<std::vector<int>>>& o_boxes,
+                   float ratio_h, float ratio_w, const cv::Mat& srcimg);
\ No newline at end of file

deploy/ios_demo/ocr_demo/timer.h

+//
+//  timer.h
+//  face_demo
+//
+//  Created by Li,Xiaoyang(SYS) on 2019/8/20.
+//  Copyright © 2019年 Li,Xiaoyang(SYS). All rights reserved.
+//
+
+#ifndef timer_h
+#define timer_h
+#include <chrono>
+#include <list>
+class Timer final {
+    
+public:
+    Timer() {}
+    
+    ~Timer() {}
+    
+    void clear() {
+        ms_time.clear();
+    }
+    
+    void start() {
+        tstart = std::chrono::system_clock::now();
+    }
+    
+    void end() {
+        tend = std::chrono::system_clock::now();
+        auto ts = std::chrono::duration_cast<std::chrono::microseconds>(tend - tstart);
+        float elapse_ms = 1000.f * float(ts.count()) * std::chrono::microseconds::period::num / \
+        std::chrono::microseconds::period::den;
+        ms_time.push_back(elapse_ms);
+    }
+    
+    float get_average_ms() {
+        if (ms_time.size() == 0) {
+            return 0.f;
+        }
+        float sum = 0.f;
+        for (auto i : ms_time){
+            sum += i;
+        }
+        return sum / ms_time.size();
+    }
+    
+    float get_sum_ms(){
+        if (ms_time.size() == 0) {
+            return 0.f;
+        }
+        float sum = 0.f;
+        for (auto i : ms_time){
+            sum += i;
+        }
+        return sum;
+    }
+    
+    // return tile (0-99) time.
+    float get_tile_time(float tile) {
+        
+        if (tile <0 || tile > 100) {
+            return -1.f;
+        }
+        int total_items = (int)ms_time.size();
+        if (total_items <= 0) {
+            return -2.f;
+        }
+        ms_time.sort();
+        int pos = (int)(tile * total_items / 100);
+        auto it = ms_time.begin();
+        for (int i = 0; i < pos; ++i) {
+            ++it;
+        }
+        return *it;
+    }
+    
+    const std::list<float> get_time_stat() {
+        return ms_time;
+    }
+    
+private:
+    std::chrono::time_point<std::chrono::system_clock> tstart;
+    std::chrono::time_point<std::chrono::system_clock> tend;
+    std::list<float> ms_time;
+};
+
+#endif /* timer_h */

deploy/lite/Makefile

+ARM_ABI = arm8
+export ARM_ABI
+
+include ../Makefile.def
+
+LITE_ROOT=../../../
+
+THIRD_PARTY_DIR=${LITE_ROOT}/third_party
+
+OPENCV_VERSION=opencv4.1.0
+
+OPENCV_LIBS = ../../../third_party/${OPENCV_VERSION}/arm64-v8a/libs/libopencv_imgcodecs.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/libs/libopencv_imgproc.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/libs/libopencv_core.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/libtegra_hal.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/liblibjpeg-turbo.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/liblibwebp.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/liblibpng.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/liblibjasper.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/liblibtiff.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/libIlmImf.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/libtbb.a \
+              ../../../third_party/${OPENCV_VERSION}/arm64-v8a/3rdparty/libs/libcpufeatures.a
+
+OPENCV_INCLUDE = -I../../../third_party/${OPENCV_VERSION}/arm64-v8a/include
+
+CXX_INCLUDES = $(INCLUDES) ${OPENCV_INCLUDE} -I$(LITE_ROOT)/cxx/include
+
+CXX_LIBS = ${OPENCV_LIBS} -L$(LITE_ROOT)/cxx/lib/ -lpaddle_light_api_shared $(SYSTEM_LIBS)
+
+###############################################################
+# How to use one of static libaray:                           #
+#  `libpaddle_api_full_bundled.a`                             #
+#  `libpaddle_api_light_bundled.a`                            #
+###############################################################
+# Note: default use lite's shared library.                    #
+###############################################################
+# 1. Comment above line using `libpaddle_light_api_shared.so`
+# 2. Undo comment below line using `libpaddle_api_light_bundled.a`
+
+#CXX_LIBS = $(LITE_ROOT)/cxx/lib/libpaddle_api_light_bundled.a $(SYSTEM_LIBS)
+
+ocr_db_crnn: fetch_opencv ocr_db_crnn.o crnn_process.o db_post_process.o clipper.o
+	$(CC) $(SYSROOT_LINK) $(CXXFLAGS_LINK) ocr_db_crnn.o crnn_process.o db_post_process.o clipper.o  -o ocr_db_crnn  $(CXX_LIBS) $(LDFLAGS)
+
+ocr_db_crnn.o: ocr_db_crnn.cc
+	$(CC) $(SYSROOT_COMPLILE) $(CXX_DEFINES) $(CXX_INCLUDES) $(CXX_FLAGS) -o ocr_db_crnn.o -c ocr_db_crnn.cc
+
+crnn_process.o: fetch_opencv crnn_process.cc
+	$(CC) $(SYSROOT_COMPLILE) $(CXX_DEFINES) $(CXX_INCLUDES) $(CXX_FLAGS) -o crnn_process.o -c crnn_process.cc
+
+db_post_process.o: fetch_clipper fetch_opencv db_post_process.cc
+	$(CC) $(SYSROOT_COMPLILE) $(CXX_DEFINES) $(CXX_INCLUDES) $(CXX_FLAGS) -o db_post_process.o -c db_post_process.cc
+
+clipper.o: fetch_clipper
+	$(CC) $(SYSROOT_COMPLILE) $(CXX_DEFINES) $(CXX_INCLUDES) $(CXX_FLAGS) -o clipper.o -c clipper.cpp
+
+fetch_clipper:
+	@test -e clipper.hpp || \
+        ( echo "Fetch clipper " && \
+        wget -c https://paddle-inference-dist.cdn.bcebos.com/PaddleLite/Clipper/clipper.hpp)
+	@ test -e clipper.cpp || \
+        wget -c https://paddle-inference-dist.cdn.bcebos.com/PaddleLite/Clipper/clipper.cpp
+
+fetch_opencv:
+	@ test -d ${THIRD_PARTY_DIR} ||  mkdir ${THIRD_PARTY_DIR}
+	@ test -e ${THIRD_PARTY_DIR}/${OPENCV_VERSION}.tar.gz || \
+      (echo "fetch opencv libs" && \
+      wget -P ${THIRD_PARTY_DIR} https://paddle-inference-dist.bj.bcebos.com/${OPENCV_VERSION}.tar.gz)
+	@ test -d ${THIRD_PARTY_DIR}/${OPENCV_VERSION} || \
+      tar -zxvf ${THIRD_PARTY_DIR}/${OPENCV_VERSION}.tar.gz -C ${THIRD_PARTY_DIR}
+
+
+.PHONY: clean
+clean:
+	rm -f ocr_db_crnn.o clipper.o db_post_process.o crnn_process.o
+	rm -f ocr_db_crnn

deploy/lite/config.txt

+max_side_len  960
+det_db_thresh  0.3
+det_db_box_thresh  0.5
+det_db_unclip_ratio  2.0
\ No newline at end of file

deploy/lite/crnn_process.cc

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "crnn_process.h" //NOLINT
+#include <algorithm>
+#include <memory>
+#include <string>
+
+const std::vector<int> rec_image_shape{3, 32, 320};
+
+cv::Mat CrnnResizeImg(cv::Mat img, float wh_ratio) {
+  int imgC, imgH, imgW;
+  imgC = rec_image_shape[0];
+  imgW = rec_image_shape[2];
+  imgH = rec_image_shape[1];
+
+  imgW = int(32 * wh_ratio);
+
+  float ratio = static_cast<float>(img.cols) / static_cast<float>(img.rows);
+  int resize_w, resize_h;
+  if (ceilf(imgH * ratio) > imgW)
+    resize_w = imgW;
+  else
+    resize_w = static_cast<int>(ceilf(imgH * ratio));
+  cv::Mat resize_img;
+  cv::resize(img, resize_img, cv::Size(resize_w, imgH), 0.f, 0.f,
+             cv::INTER_LINEAR);
+
+  return resize_img;
+}
+
+std::vector<std::string> ReadDict(std::string path) {
+  std::ifstream in(path);
+  std::string filename;
+  std::string line;
+  std::vector<std::string> m_vec;
+  if (in) {
+    while (getline(in, line)) {
+      m_vec.push_back(line);
+    }
+  } else {
+    std::cout << "no such file" << std::endl;
+  }
+  return m_vec;
+}
+
+cv::Mat GetRotateCropImage(cv::Mat srcimage,
+                           std::vector<std::vector<int>> box) {
+  cv::Mat image;
+  srcimage.copyTo(image);
+  std::vector<std::vector<int>> points = box;
+
+  int x_collect[4] = {box[0][0], box[1][0], box[2][0], box[3][0]};
+  int y_collect[4] = {box[0][1], box[1][1], box[2][1], box[3][1]};
+  int left = int(*std::min_element(x_collect, x_collect + 4));
+  int right = int(*std::max_element(x_collect, x_collect + 4));
+  int top = int(*std::min_element(y_collect, y_collect + 4));
+  int bottom = int(*std::max_element(y_collect, y_collect + 4));
+
+  cv::Mat img_crop;
+  image(cv::Rect(left, top, right - left, bottom - top)).copyTo(img_crop);
+
+  for (int i = 0; i < points.size(); i++) {
+    points[i][0] -= left;
+    points[i][1] -= top;
+  }
+
+  int img_crop_width =
+      static_cast<int>(sqrt(pow(points[0][0] - points[1][0], 2) +
+                            pow(points[0][1] - points[1][1], 2)));
+  int img_crop_height =
+      static_cast<int>(sqrt(pow(points[0][0] - points[3][0], 2) +
+                            pow(points[0][1] - points[3][1], 2)));
+
+  cv::Point2f pts_std[4];
+  pts_std[0] = cv::Point2f(0., 0.);
+  pts_std[1] = cv::Point2f(img_crop_width, 0.);
+  pts_std[2] = cv::Point2f(img_crop_width, img_crop_height);
+  pts_std[3] = cv::Point2f(0.f, img_crop_height);
+
+  cv::Point2f pointsf[4];
+  pointsf[0] = cv::Point2f(points[0][0], points[0][1]);
+  pointsf[1] = cv::Point2f(points[1][0], points[1][1]);
+  pointsf[2] = cv::Point2f(points[2][0], points[2][1]);
+  pointsf[3] = cv::Point2f(points[3][0], points[3][1]);
+
+  cv::Mat M = cv::getPerspectiveTransform(pointsf, pts_std);
+
+  cv::Mat dst_img;
+  cv::warpPerspective(img_crop, dst_img, M,
+                      cv::Size(img_crop_width, img_crop_height),
+                      cv::BORDER_REPLICATE);
+
+  const float ratio = 1.5;
+  if (static_cast<float>(dst_img.rows) >=
+      static_cast<float>(dst_img.cols) * ratio) {
+    cv::Mat srcCopy = cv::Mat(dst_img.rows, dst_img.cols, dst_img.depth());
+    cv::transpose(dst_img, srcCopy);
+    cv::flip(srcCopy, srcCopy, 0);
+    return srcCopy;
+  } else {
+    return dst_img;
+  }
+}

deploy/lite/crnn_process.h

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include <cstring>
+#include <fstream>
+#include <iostream>
+#include <memory>
+#include <string>
+#include <vector>
+
+#include "math.h" //NOLINT
+#include "opencv2/core.hpp"
+#include "opencv2/imgcodecs.hpp"
+#include "opencv2/imgproc.hpp"
+
+cv::Mat CrnnResizeImg(cv::Mat img, float wh_ratio);
+
+std::vector<std::string> ReadDict(std::string path);
+
+cv::Mat GetRotateCropImage(cv::Mat srcimage, std::vector<std::vector<int>> box);
+
+template <class ForwardIterator>
+inline size_t Argmax(ForwardIterator first, ForwardIterator last) {
+  return std::distance(first, std::max_element(first, last));
+}

deploy/lite/db_post_process.cc

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "db_post_process.h" // NOLINT
+#include <algorithm>
+#include <utility>
+
+void GetContourArea(std::vector<std::vector<float>> box, float unclip_ratio,
+                    float &distance) {
+  int pts_num = 4;
+  float area = 0.0f;
+  float dist = 0.0f;
+  for (int i = 0; i < pts_num; i++) {
+    area += box[i][0] * box[(i + 1) % pts_num][1] -
+            box[i][1] * box[(i + 1) % pts_num][0];
+    dist += sqrtf((box[i][0] - box[(i + 1) % pts_num][0]) *
+                      (box[i][0] - box[(i + 1) % pts_num][0]) +
+                  (box[i][1] - box[(i + 1) % pts_num][1]) *
+                      (box[i][1] - box[(i + 1) % pts_num][1]));
+  }
+  area = fabs(float(area / 2.0));
+
+  distance = area * unclip_ratio / dist;
+}
+
+cv::RotatedRect Unclip(std::vector<std::vector<float>> box,
+                       float unclip_ratio) {
+  float distance = 1.0;
+
+  GetContourArea(box, unclip_ratio, distance);
+
+  ClipperLib::ClipperOffset offset;
+  ClipperLib::Path p;
+  p << ClipperLib::IntPoint(static_cast<int>(box[0][0]),
+                            static_cast<int>(box[0][1]))
+    << ClipperLib::IntPoint(static_cast<int>(box[1][0]),
+                            static_cast<int>(box[1][1]))
+    << ClipperLib::IntPoint(static_cast<int>(box[2][0]),
+                            static_cast<int>(box[2][1]))
+    << ClipperLib::IntPoint(static_cast<int>(box[3][0]),
+                            static_cast<int>(box[3][1]));
+  offset.AddPath(p, ClipperLib::jtRound, ClipperLib::etClosedPolygon);
+
+  ClipperLib::Paths soln;
+  offset.Execute(soln, distance);
+  std::vector<cv::Point2f> points;
+
+  for (int j = 0; j < soln.size(); j++) {
+    for (int i = 0; i < soln[soln.size() - 1].size(); i++) {
+      points.emplace_back(soln[j][i].X, soln[j][i].Y);
+    }
+  }
+  cv::RotatedRect res = cv::minAreaRect(points);
+
+  return res;
+}
+
+std::vector<std::vector<float>> Mat2Vector(cv::Mat mat) {
+  std::vector<std::vector<float>> img_vec;
+  std::vector<float> tmp;
+
+  for (int i = 0; i < mat.rows; ++i) {
+    tmp.clear();
+    for (int j = 0; j < mat.cols; ++j) {
+      tmp.push_back(mat.at<float>(i, j));
+    }
+    img_vec.push_back(tmp);
+  }
+  return img_vec;
+}
+
+bool XsortFp32(std::vector<float> a, std::vector<float> b) {
+  if (a[0] != b[0])
+    return a[0] < b[0];
+  return false;
+}
+
+bool XsortInt(std::vector<int> a, std::vector<int> b) {
+  if (a[0] != b[0])
+    return a[0] < b[0];
+  return false;
+}
+
+std::vector<std::vector<int>>
+OrderPointsClockwise(std::vector<std::vector<int>> pts) {
+  std::vector<std::vector<int>> box = pts;
+  std::sort(box.begin(), box.end(), XsortInt);
+
+  std::vector<std::vector<int>> leftmost = {box[0], box[1]};
+  std::vector<std::vector<int>> rightmost = {box[2], box[3]};
+
+  if (leftmost[0][1] > leftmost[1][1])
+    std::swap(leftmost[0], leftmost[1]);
+
+  if (rightmost[0][1] > rightmost[1][1])
+    std::swap(rightmost[0], rightmost[1]);
+
+  std::vector<std::vector<int>> rect = {leftmost[0], rightmost[0], rightmost[1],
+                                        leftmost[1]};
+  return rect;
+}
+
+std::vector<std::vector<float>> GetMiniBoxes(cv::RotatedRect box, float &ssid) {
+  ssid = std::max(box.size.width, box.size.height);
+
+  cv::Mat points;
+  cv::boxPoints(box, points);
+
+  auto array = Mat2Vector(points);
+  std::sort(array.begin(), array.end(), XsortFp32);
+
+  std::vector<float> idx1 = array[0], idx2 = array[1], idx3 = array[2],
+                     idx4 = array[3];
+  if (array[3][1] <= array[2][1]) {
+    idx2 = array[3];
+    idx3 = array[2];
+  } else {
+    idx2 = array[2];
+    idx3 = array[3];
+  }
+  if (array[1][1] <= array[0][1]) {
+    idx1 = array[1];
+    idx4 = array[0];
+  } else {
+    idx1 = array[0];
+    idx4 = array[1];
+  }
+
+  array[0] = idx1;
+  array[1] = idx2;
+  array[2] = idx3;
+  array[3] = idx4;
+
+  return array;
+}
+
+float BoxScoreFast(std::vector<std::vector<float>> box_array, cv::Mat pred) {
+  auto array = box_array;
+  int width = pred.cols;
+  int height = pred.rows;
+
+  float box_x[4] = {array[0][0], array[1][0], array[2][0], array[3][0]};
+  float box_y[4] = {array[0][1], array[1][1], array[2][1], array[3][1]};
+
+  int xmin = clamp(
+      static_cast<int>(std::floorf(*(std::min_element(box_x, box_x + 4)))), 0,
+      width - 1);
+  int xmax =
+      clamp(static_cast<int>(std::ceilf(*(std::max_element(box_x, box_x + 4)))),
+            0, width - 1);
+  int ymin = clamp(
+      static_cast<int>(std::floorf(*(std::min_element(box_y, box_y + 4)))), 0,
+      height - 1);
+  int ymax =
+      clamp(static_cast<int>(std::ceilf(*(std::max_element(box_y, box_y + 4)))),
+            0, height - 1);
+
+  cv::Mat mask;
+  mask = cv::Mat::zeros(ymax - ymin + 1, xmax - xmin + 1, CV_8UC1);
+
+  cv::Point root_point[4];
+  root_point[0] = cv::Point(static_cast<int>(array[0][0]) - xmin,
+                            static_cast<int>(array[0][1]) - ymin);
+  root_point[1] = cv::Point(static_cast<int>(array[1][0]) - xmin,
+                            static_cast<int>(array[1][1]) - ymin);
+  root_point[2] = cv::Point(static_cast<int>(array[2][0]) - xmin,
+                            static_cast<int>(array[2][1]) - ymin);
+  root_point[3] = cv::Point(static_cast<int>(array[3][0]) - xmin,
+                            static_cast<int>(array[3][1]) - ymin);
+  const cv::Point *ppt[1] = {root_point};
+  int npt[] = {4};
+  cv::fillPoly(mask, ppt, npt, 1, cv::Scalar(1));
+
+  cv::Mat croppedImg;
+  pred(cv::Rect(xmin, ymin, xmax - xmin + 1, ymax - ymin + 1))
+      .copyTo(croppedImg);
+
+  auto score = cv::mean(croppedImg, mask)[0];
+  return score;
+}
+
+std::vector<std::vector<std::vector<int>>>
+BoxesFromBitmap(const cv::Mat pred, const cv::Mat bitmap,
+                std::map<std::string, double> Config) {
+  const int min_size = 3;
+  const int max_candidates = 1000;
+  const float box_thresh = static_cast<float>(Config["det_db_box_thresh"]);
+  const float unclip_ratio = static_cast<float>(Config["det_db_unclip_ratio"]);
+
+  int width = bitmap.cols;
+  int height = bitmap.rows;
+
+  std::vector<std::vector<cv::Point>> contours;
+  std::vector<cv::Vec4i> hierarchy;
+
+  cv::findContours(bitmap, contours, hierarchy, cv::RETR_LIST,
+                   cv::CHAIN_APPROX_SIMPLE);
+
+  int num_contours =
+      contours.size() >= max_candidates ? max_candidates : contours.size();
+
+  std::vector<std::vector<std::vector<int>>> boxes;
+
+  for (int i = 0; i < num_contours; i++) {
+    float ssid;
+    if (contours[i].size() <= 2)
+      continue;
+
+    cv::RotatedRect box = cv::minAreaRect(contours[i]);
+    auto array = GetMiniBoxes(box, ssid);
+
+    auto box_for_unclip = array;
+    // end get_mini_box
+
+    if (ssid < min_size) {
+      continue;
+    }
+
+    float score;
+    score = BoxScoreFast(array, pred);
+    // end box_score_fast
+    if (score < box_thresh)
+      continue;
+
+    // start for unclip
+    cv::RotatedRect points = Unclip(box_for_unclip, unclip_ratio);
+    if (points.size.height < 1.001 && points.size.width < 1.001)
+      continue;
+    // end for unclip
+
+    cv::RotatedRect clipbox = points;
+    auto cliparray = GetMiniBoxes(clipbox, ssid);
+
+    if (ssid < min_size + 2)
+      continue;
+
+    int dest_width = pred.cols;
+    int dest_height = pred.rows;
+    std::vector<std::vector<int>> intcliparray;
+
+    for (int num_pt = 0; num_pt < 4; num_pt++) {
+      std::vector<int> a{
+          static_cast<int>(clamp(
+              roundf(cliparray[num_pt][0] / float(width) * float(dest_width)),
+              float(0), float(dest_width))),
+          static_cast<int>(clamp(
+              roundf(cliparray[num_pt][1] / float(height) * float(dest_height)),
+              float(0), float(dest_height)))};
+      intcliparray.push_back(a);
+    }
+    boxes.push_back(intcliparray);
+
+  } // end for
+  return boxes;
+}
+
+std::vector<std::vector<std::vector<int>>>
+FilterTagDetRes(std::vector<std::vector<std::vector<int>>> boxes, float ratio_h,
+                float ratio_w, cv::Mat srcimg) {
+  int oriimg_h = srcimg.rows;
+  int oriimg_w = srcimg.cols;
+
+  std::vector<std::vector<std::vector<int>>> root_points;
+  for (int n = 0; n < static_cast<int>(boxes.size()); n++) {
+    boxes[n] = OrderPointsClockwise(boxes[n]);
+    for (int m = 0; m < static_cast<int>(boxes[0].size()); m++) {
+      boxes[n][m][0] /= ratio_w;
+      boxes[n][m][1] /= ratio_h;
+
+      boxes[n][m][0] =
+          static_cast<int>(std::min(std::max(boxes[n][m][0], 0), oriimg_w - 1));
+      boxes[n][m][1] =
+          static_cast<int>(std::min(std::max(boxes[n][m][1], 0), oriimg_h - 1));
+    }
+  }
+
+  for (int n = 0; n < boxes.size(); n++) {
+    int rect_width, rect_height;
+    rect_width =
+        static_cast<int>(sqrt(pow(boxes[n][0][0] - boxes[n][1][0], 2) +
+                              pow(boxes[n][0][1] - boxes[n][1][1], 2)));
+    rect_height =
+        static_cast<int>(sqrt(pow(boxes[n][0][0] - boxes[n][3][0], 2) +
+                              pow(boxes[n][0][1] - boxes[n][3][1], 2)));
+    if (rect_width <= 10 || rect_height <= 10)
+      continue;
+    root_points.push_back(boxes[n]);
+  }
+  return root_points;
+}

deploy/lite/db_post_process.h

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#pragma once
+
+#include <math.h>
+
+#include <iostream>
+#include <map>
+#include <vector>
+
+#include "clipper.hpp"
+#include "opencv2/core.hpp"
+#include "opencv2/imgcodecs.hpp"
+#include "opencv2/imgproc.hpp"
+
+template <class T> T clamp(T x, T min, T max) {
+  if (x > max)
+    return max;
+  if (x < min)
+    return min;
+  return x;
+}
+
+std::vector<std::vector<float>> Mat2Vector(cv::Mat mat);
+
+void GetContourArea(std::vector<std::vector<float>> box, float unclip_ratio,
+                    float &distance);
+
+cv::RotatedRect Unclip(std::vector<std::vector<float>> box, float unclip_ratio);
+
+std::vector<std::vector<float>> Mat2Vector(cv::Mat mat);
+
+bool XsortFp32(std::vector<float> a, std::vector<float> b);
+
+bool XsortInt(std::vector<int> a, std::vector<int> b);
+
+std::vector<std::vector<int>>
+OrderPointsClockwise(std::vector<std::vector<int>> pts);
+
+std::vector<std::vector<float>> GetMiniBoxes(cv::RotatedRect box, float &ssid);
+
+float BoxScoreFast(std::vector<std::vector<float>> box_array, cv::Mat pred);
+
+std::vector<std::vector<std::vector<int>>>
+BoxesFromBitmap(const cv::Mat pred, const cv::Mat bitmap,
+                std::map<std::string, double> Config);
+
+std::vector<std::vector<std::vector<int>>>
+FilterTagDetRes(std::vector<std::vector<std::vector<int>>> boxes, float ratio_h,
+                float ratio_w, cv::Mat srcimg);

deploy/lite/ocr_db_crnn.cc

+// Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "paddle_api.h" // NOLINT
+#include <chrono>
+
+#include "crnn_process.h"
+#include "db_post_process.h"
+
+using namespace paddle::lite_api; // NOLINT
+using namespace std;
+
+// fill tensor with mean and scale and trans layout: nhwc -> nchw, neon speed up
+void NeonMeanScale(const float *din, float *dout, int size,
+                   const std::vector<float> mean,
+                   const std::vector<float> scale) {
+  if (mean.size() != 3 || scale.size() != 3) {
+    std::cerr << "[ERROR] mean or scale size must equal to 3\n";
+    exit(1);
+  }
+  float32x4_t vmean0 = vdupq_n_f32(mean[0]);
+  float32x4_t vmean1 = vdupq_n_f32(mean[1]);
+  float32x4_t vmean2 = vdupq_n_f32(mean[2]);
+  float32x4_t vscale0 = vdupq_n_f32(scale[0]);
+  float32x4_t vscale1 = vdupq_n_f32(scale[1]);
+  float32x4_t vscale2 = vdupq_n_f32(scale[2]);
+
+  float *dout_c0 = dout;
+  float *dout_c1 = dout + size;
+  float *dout_c2 = dout + size * 2;
+
+  int i = 0;
+  for (; i < size - 3; i += 4) {
+    float32x4x3_t vin3 = vld3q_f32(din);
+    float32x4_t vsub0 = vsubq_f32(vin3.val[0], vmean0);
+    float32x4_t vsub1 = vsubq_f32(vin3.val[1], vmean1);
+    float32x4_t vsub2 = vsubq_f32(vin3.val[2], vmean2);
+    float32x4_t vs0 = vmulq_f32(vsub0, vscale0);
+    float32x4_t vs1 = vmulq_f32(vsub1, vscale1);
+    float32x4_t vs2 = vmulq_f32(vsub2, vscale2);
+    vst1q_f32(dout_c0, vs0);
+    vst1q_f32(dout_c1, vs1);
+    vst1q_f32(dout_c2, vs2);
+
+    din += 12;
+    dout_c0 += 4;
+    dout_c1 += 4;
+    dout_c2 += 4;
+  }
+  for (; i < size; i++) {
+    *(dout_c0++) = (*(din++) - mean[0]) * scale[0];
+    *(dout_c1++) = (*(din++) - mean[1]) * scale[1];
+    *(dout_c2++) = (*(din++) - mean[2]) * scale[2];
+  }
+}
+
+// resize image to a size multiple of 32 which is required by the network
+cv::Mat DetResizeImg(const cv::Mat img, int max_size_len,
+                     std::vector<float> &ratio_hw) {
+  int w = img.cols;
+  int h = img.rows;
+
+  float ratio = 1.f;
+  int max_wh = w >= h ? w : h;
+  if (max_wh > max_size_len) {
+    if (h > w) {
+      ratio = static_cast<float>(max_size_len) / static_cast<float>(h);
+    } else {
+      ratio = static_cast<float>(max_size_len) / static_cast<float>(w);
+    }
+  }
+
+  int resize_h = static_cast<int>(float(h) * ratio);
+  int resize_w = static_cast<int>(float(w) * ratio);
+  if (resize_h % 32 == 0)
+    resize_h = resize_h;
+  else if (resize_h / 32 < 1 + 1e-5)
+    resize_h = 32;
+  else
+    resize_h = (resize_h / 32 - 1) * 32;
+
+  if (resize_w % 32 == 0)
+    resize_w = resize_w;
+  else if (resize_w / 32 < 1 + 1e-5)
+    resize_w = 32;
+  else
+    resize_w = (resize_w / 32 - 1) * 32;
+
+  cv::Mat resize_img;
+  cv::resize(img, resize_img, cv::Size(resize_w, resize_h));
+
+  ratio_hw.push_back(static_cast<float>(resize_h) / static_cast<float>(h));
+  ratio_hw.push_back(static_cast<float>(resize_w) / static_cast<float>(w));
+  return resize_img;
+}
+
+void RunRecModel(std::vector<std::vector<std::vector<int>>> boxes, cv::Mat img,
+                 std::shared_ptr<PaddlePredictor> predictor_crnn,
+                 std::vector<std::string> &rec_text,
+                 std::vector<float> &rec_text_score,
+                 std::vector<std::string> charactor_dict) {
+  std::vector<float> mean = {0.5f, 0.5f, 0.5f};
+  std::vector<float> scale = {1 / 0.5f, 1 / 0.5f, 1 / 0.5f};
+
+  cv::Mat srcimg;
+  img.copyTo(srcimg);
+  cv::Mat crop_img;
+  cv::Mat resize_img;
+
+  int index = 0;
+  for (int i = boxes.size() - 1; i >= 0; i--) {
+    crop_img = GetRotateCropImage(srcimg, boxes[i]);
+    float wh_ratio =
+        static_cast<float>(crop_img.cols) / static_cast<float>(crop_img.rows);
+
+    resize_img = CrnnResizeImg(crop_img, wh_ratio);
+    resize_img.convertTo(resize_img, CV_32FC3, 1 / 255.f);
+
+    const float *dimg = reinterpret_cast<const float *>(resize_img.data);
+
+    std::unique_ptr<Tensor> input_tensor0(
+        std::move(predictor_crnn->GetInput(0)));
+    input_tensor0->Resize({1, 3, resize_img.rows, resize_img.cols});
+    auto *data0 = input_tensor0->mutable_data<float>();
+
+    NeonMeanScale(dimg, data0, resize_img.rows * resize_img.cols, mean, scale);
+    //// Run CRNN predictor
+    predictor_crnn->Run();
+
+    // Get output and run postprocess
+    std::unique_ptr<const Tensor> output_tensor0(
+        std::move(predictor_crnn->GetOutput(0)));
+    auto *rec_idx = output_tensor0->data<int64>();
+
+    auto rec_idx_lod = output_tensor0->lod();
+    auto shape_out = output_tensor0->shape();
+
+    std::vector<int> pred_idx;
+    for (int n = static_cast<int>(rec_idx_lod[0][0]);
+         n < static_cast<int>(rec_idx_lod[0][1]); n += 1) {
+      pred_idx.push_back(static_cast<int>(rec_idx[n]));
+    }
+
+    if (pred_idx.size() < 1e-3)
+      continue;
+
+    index += 1;
+    std::string pred_txt = "";
+    for (int n = 0; n < pred_idx.size(); n++) {
+      pred_txt += charactor_dict[pred_idx[n]];
+    }
+    rec_text.push_back(pred_txt);
+
+    ////get score
+    std::unique_ptr<const Tensor> output_tensor1(
+        std::move(predictor_crnn->GetOutput(1)));
+    auto *predict_batch = output_tensor1->data<float>();
+    auto predict_shape = output_tensor1->shape();
+
+    auto predict_lod = output_tensor1->lod();
+
+    int blank = predict_shape[1];
+    float score = 0.f;
+    int count = 0;
+
+    for (int n = predict_lod[0][0]; n < predict_lod[0][1] - 1; n++) {
+      int argmax_idx =
+          static_cast<int>(Argmax(&predict_batch[n * predict_shape[1]],
+                                  &predict_batch[(n + 1) * predict_shape[1]]));
+      float max_value =
+          float(*std::max_element(&predict_batch[n * predict_shape[1]],
+                                  &predict_batch[(n + 1) * predict_shape[1]]));
+
+      if (blank - 1 - argmax_idx > 1e-5) {
+        score += max_value;
+        count += 1;
+      }
+    }
+    score /= count;
+    rec_text_score.push_back(score);
+  }
+}
+
+std::vector<std::vector<std::vector<int>>>
+RunDetModel(std::shared_ptr<PaddlePredictor> predictor, cv::Mat img,
+            std::map<std::string, double> Config) {
+  // Read img
+  int max_side_len = int(Config["max_side_len"]);
+
+  cv::Mat srcimg;
+  img.copyTo(srcimg);
+
+  std::vector<float> ratio_hw;
+  img = DetResizeImg(img, max_side_len, ratio_hw);
+  cv::Mat img_fp;
+  img.convertTo(img_fp, CV_32FC3, 1.0 / 255.f);
+
+  // Prepare input data from image
+  std::unique_ptr<Tensor> input_tensor0(std::move(predictor->GetInput(0)));
+  input_tensor0->Resize({1, 3, img_fp.rows, img_fp.cols});
+  auto *data0 = input_tensor0->mutable_data<float>();
+
+  std::vector<float> mean = {0.485f, 0.456f, 0.406f};
+  std::vector<float> scale = {1 / 0.229f, 1 / 0.224f, 1 / 0.225f};
+  const float *dimg = reinterpret_cast<const float *>(img_fp.data);
+  NeonMeanScale(dimg, data0, img_fp.rows * img_fp.cols, mean, scale);
+
+  // Run predictor
+  predictor->Run();
+
+  // Get output and post process
+  std::unique_ptr<const Tensor> output_tensor(
+      std::move(predictor->GetOutput(0)));
+  auto *outptr = output_tensor->data<float>();
+  auto shape_out = output_tensor->shape();
+
+  // Save output
+  float pred[shape_out[2] * shape_out[3]];
+  unsigned char cbuf[shape_out[2] * shape_out[3]];
+
+  for (int i = 0; i < int(shape_out[2] * shape_out[3]); i++) {
+    pred[i] = static_cast<float>(outptr[i]);
+    cbuf[i] = static_cast<unsigned char>((outptr[i]) * 255);
+  }
+
+  cv::Mat cbuf_map(shape_out[2], shape_out[3], CV_8UC1,
+                   reinterpret_cast<unsigned char *>(cbuf));
+  cv::Mat pred_map(shape_out[2], shape_out[3], CV_32F,
+                   reinterpret_cast<float *>(pred));
+
+  const double threshold = double(Config["det_db_thresh"]) * 255;
+  const double maxvalue = 255;
+  cv::Mat bit_map;
+  cv::threshold(cbuf_map, bit_map, threshold, maxvalue, cv::THRESH_BINARY);
+
+  auto boxes = BoxesFromBitmap(pred_map, bit_map, Config);
+
+  std::vector<std::vector<std::vector<int>>> filter_boxes =
+      FilterTagDetRes(boxes, ratio_hw[0], ratio_hw[1], srcimg);
+
+  return filter_boxes;
+}
+
+std::shared_ptr<PaddlePredictor> loadModel(std::string model_file) {
+  MobileConfig config;
+  config.set_model_from_file(model_file);
+
+  std::shared_ptr<PaddlePredictor> predictor =
+      CreatePaddlePredictor<MobileConfig>(config);
+  return predictor;
+}
+
+cv::Mat Visualization(cv::Mat srcimg,
+                      std::vector<std::vector<std::vector<int>>> boxes) {
+  cv::Point rook_points[boxes.size()][4];
+  for (int n = 0; n < boxes.size(); n++) {
+    for (int m = 0; m < boxes[0].size(); m++) {
+      rook_points[n][m] = cv::Point(static_cast<int>(boxes[n][m][0]),
+                                    static_cast<int>(boxes[n][m][1]));
+    }
+  }
+  cv::Mat img_vis;
+  srcimg.copyTo(img_vis);
+  for (int n = 0; n < boxes.size(); n++) {
+    const cv::Point *ppt[1] = {rook_points[n]};
+    int npt[] = {4};
+    cv::polylines(img_vis, ppt, npt, 1, 1, CV_RGB(0, 255, 0), 2, 8, 0);
+  }
+
+  cv::imwrite("./vis.jpg", img_vis);
+  std::cout << "The detection visualized image saved in ./vis.jpg" << std::endl;
+  return img_vis;
+}
+
+std::vector<std::string> split(const std::string &str,
+                               const std::string &delim) {
+  std::vector<std::string> res;
+  if ("" == str)
+    return res;
+  char *strs = new char[str.length() + 1];
+  std::strcpy(strs, str.c_str());
+
+  char *d = new char[delim.length() + 1];
+  std::strcpy(d, delim.c_str());
+
+  char *p = std::strtok(strs, d);
+  while (p) {
+    string s = p;
+    res.push_back(s);
+    p = std::strtok(NULL, d);
+  }
+
+  return res;
+}
+
+std::map<std::string, double> LoadConfigTxt(std::string config_path) {
+  auto config = ReadDict(config_path);
+
+  std::map<std::string, double> dict;
+  for (int i = 0; i < config.size(); i++) {
+    std::vector<std::string> res = split(config[i], " ");
+    dict[res[0]] = stod(res[1]);
+  }
+  return dict;
+}
+
+int main(int argc, char **argv) {
+  if (argc < 5) {
+    std::cerr << "[ERROR] usage: " << argv[0]
+              << " det_model_file rec_model_file image_path\n";
+    exit(1);
+  }
+  std::string det_model_file = argv[1];
+  std::string rec_model_file = argv[2];
+  std::string img_path = argv[3];
+  std::string dict_path = argv[4];
+
+  //// load config from txt file
+  auto Config = LoadConfigTxt("./config.txt");
+
+  auto start = std::chrono::system_clock::now();
+
+  auto det_predictor = loadModel(det_model_file);
+  auto rec_predictor = loadModel(rec_model_file);
+
+  auto charactor_dict = ReadDict(dict_path);
+  charactor_dict.push_back(" ");
+
+  cv::Mat srcimg = cv::imread(img_path, cv::IMREAD_COLOR);
+  auto boxes = RunDetModel(det_predictor, srcimg, Config);
+
+  std::vector<std::string> rec_text;
+  std::vector<float> rec_text_score;
+  RunRecModel(boxes, srcimg, rec_predictor, rec_text, rec_text_score,
+              charactor_dict);
+
+  auto end = std::chrono::system_clock::now();
+  auto duration =
+      std::chrono::duration_cast<std::chrono::microseconds>(end - start);
+
+  //// visualization
+  auto img_vis = Visualization(srcimg, boxes);
+
+  //// print recognized text
+  for (int i = 0; i < rec_text.size(); i++) {
+    std::cout << i << "\t" << rec_text[i] << "\t" << rec_text_score[i]
+              << std::endl;
+  }
+
+  std::cout << "花费了"
+            << double(duration.count()) *
+                   std::chrono::microseconds::period::num /
+                   std::chrono::microseconds::period::den
+            << "秒" << std::endl;
+
+  return 0;
+}

deploy/lite/readme.md

+# 端侧部署
+
+本教程将介绍基于[Paddle Lite](https://github.com/PaddlePaddle/Paddle-Lite) 在移动端部署PaddleOCR超轻量中文检测、识别模型的详细步骤。
+
+Paddle Lite是飞桨轻量化推理引擎，为手机、IOT端提供高效推理能力，并广泛整合跨平台硬件，为端侧部署及应用落地问题提供轻量化的部署方案。
+
+
+## 1. 准备环境
+
+### 运行准备
+- 电脑（编译Paddle Lite）
+- 安卓手机（armv7或armv8）
+
+### 1.1 准备交叉编译环境
+交叉编译环境用于编译 Paddle Lite 和 PaddleOCR 的C++ demo。
+支持多种开发环境，不同开发环境的编译流程请参考对应文档。
+
+1. [Docker](https://paddle-lite.readthedocs.io/zh/latest/user_guides/source_compile.html#docker)
+2. [Linux](https://paddle-lite.readthedocs.io/zh/latest/user_guides/source_compile.html#android)
+3. [MAC OS](https://paddle-lite.readthedocs.io/zh/latest/user_guides/source_compile.html#id13)
+4. [Windows](https://paddle-lite.readthedocs.io/zh/latest/demo_guides/x86.html#windows)
+
+### 1.2 准备预测库
+
+预测库有两种获取方式：
+- 1. 直接下载，预测库下载链接如下：
+      |平台|预测库下载链接|
+      |-|-|
+      |Android|[arm7](https://paddlelite-data.bj.bcebos.com/Release/2.6.1/Android/inference_lite_lib.android.armv7.gcc.c++_static.with_extra.CV_ON.tar.gz) / [arm8](https://paddlelite-data.bj.bcebos.com/Release/2.6.1/Android/inference_lite_lib.android.armv8.gcc.c++_static.with_extra.CV_ON.tar.gz)|
+      |IOS|[arm7](https://paddlelite-data.bj.bcebos.com/Release/2.6.1/iOS/inference_lite_lib.ios.armv7.with_extra.CV_ON.tar.gz) / [arm8](https://paddlelite-data.bj.bcebos.com/Release/2.6.1/iOS/inference_lite_lib.ios64.armv8.with_extra.CV_ON.tar.gz)|
+      |x86(Linux)|[预测库](https://paddlelite-data.bj.bcebos.com/Release/2.6.1/X86/Linux/inference_lite_lib.x86.linux.tar.gz)|
+
+      注：如果是从下Paddle-Lite[官网文档](https://paddle-lite.readthedocs.io/zh/latest/user_guides/release_lib.html#android-toolchain-gcc)下载的预测库，
+      注意选择`with_extra=ON，with_cv=ON`的下载链接。
+
+- 2. 编译Paddle-Lite得到预测库，Paddle-Lite的编译方式如下：
+```
+git clone https://github.com/PaddlePaddle/Paddle-Lite.git
+cd Paddle-Lite
+git checkout develop
+./lite/tools/build_android.sh  --arch=armv8  --with_cv=ON --with_extra=ON
+```
+
+注意：编译Paddle-Lite获得预测库时，需要打开`--with_cv=ON --with_extra=ON`两个选项，`--arch`表示`arm`版本，这里指定为armv8，
+更多编译命令
+介绍请参考[链接](https://paddle-lite.readthedocs.io/zh/latest/user_guides/Compile/Android.html#id2)。
+
+直接下载预测库并解压后，可以得到`inference_lite_lib.android.armv8/`文件夹，通过编译Paddle-Lite得到的预测库位于
+`Paddle-Lite/build.lite.android.armv8.gcc/inference_lite_lib.android.armv8/`文件夹下。
+预测库的文件目录如下：
+```
+inference_lite_lib.android.armv8/
+|-- cxx                                        C++ 预测库和头文件
+|   |-- include                                C++ 头文件
+|   |   |-- paddle_api.h
+|   |   |-- paddle_image_preprocess.h
+|   |   |-- paddle_lite_factory_helper.h
+|   |   |-- paddle_place.h
+|   |   |-- paddle_use_kernels.h
+|   |   |-- paddle_use_ops.h
+|   |   `-- paddle_use_passes.h
+|   `-- lib                                           C++预测库
+|       |-- libpaddle_api_light_bundled.a             C++静态库
+|       `-- libpaddle_light_api_shared.so             C++动态库
+|-- java                                     Java预测库
+|   |-- jar
+|   |   `-- PaddlePredictor.jar
+|   |-- so
+|   |   `-- libpaddle_lite_jni.so
+|   `-- src
+|-- demo                                     C++和Java示例代码
+|   |-- cxx                                  C++  预测库demo
+|   `-- java                                 Java 预测库demo
+```
+
+## 2 开始运行
+
+### 2.1 模型优化
+
+Paddle-Lite 提供了多种策略来自动优化原始的模型，其中包括量化、子图融合、混合调度、Kernel优选等方法，使用Paddle-lite的opt工具可以自动
+对inference模型进行优化，优化后的模型更轻量，模型运行速度更快。
+
+下述表格中提供了优化好的超轻量中文模型：
+
+|模型简介|检测模型|识别模型|Paddle-Lite版本|
+|-|-|-|-|
+|超轻量级中文OCR opt优化模型|[下载地址](https://paddleocr.bj.bcebos.com/deploy/lite/ch_det_mv3_db_opt.nb)|[下载地址](https://paddleocr.bj.bcebos.com/deploy/lite/ch_rec_mv3_crnn_opt.nb)|2.6.1|
+
+如果直接使用上述表格中的模型进行部署，可略过下述步骤，直接阅读 [2.2节](#2.2与手机联调)。
+
+如果要部署的模型不在上述表格中，则需要按照如下步骤获得优化后的模型。
+
+模型优化需要Paddle-Lite的opt可执行文件，可以通过编译Paddle-Lite源码获得，编译步骤如下：
+```
+# 如果准备环境时已经clone了Paddle-Lite，则不用重新clone Paddle-Lite
+git clone https://github.com/PaddlePaddle/Paddle-Lite.git
+cd Paddle-Lite
+git checkout develop
+# 启动编译
+./lite/tools/build.sh build_optimize_tool
+```
+
+编译完成后，opt文件位于`build.opt/lite/api/`下，可通过如下方式查看opt的运行选项和使用方式；
+```
+cd build.opt/lite/api/
+./opt
+```
+
+|选项|说明|
+|-|-|
+|--model_dir|待优化的PaddlePaddle模型（非combined形式）的路径|
+|--model_file|待优化的PaddlePaddle模型（combined形式）的网络结构文件路径|
+|--param_file|待优化的PaddlePaddle模型（combined形式）的权重文件路径|
+|--optimize_out_type|输出模型类型，目前支持两种类型：protobuf和naive_buffer，其中naive_buffer是一种更轻量级的序列化/反序列化实现。若您需要在mobile端执行模型预测，请将此选项设置为naive_buffer。默认为protobuf|
+|--optimize_out|优化模型的输出路径|
+|--valid_targets|指定模型可执行的backend，默认为arm。目前可支持x86、arm、opencl、npu、xpu，可以同时指定多个backend(以空格分隔)，Model Optimize Tool将会自动选择最佳方式。如果需要支持华为NPU（Kirin 810/990 Soc搭载的达芬奇架构NPU），应当设置为npu, arm|
+|--record_tailoring_info|当使用 根据模型裁剪库文件 功能时，则设置该选项为true，以记录优化后模型含有的kernel和OP信息，默认为false|
+
+`--model_dir`适用于待优化的模型是非combined方式，PaddleOCR的inference模型是combined方式，即模型结构和模型参数使用单独一个文件存储。
+
+下面以PaddleOCR的超轻量中文模型为例，介绍使用编译好的opt文件完成inference模型到Paddle-Lite优化模型的转换。
+
+```
+# 下载PaddleOCR的超轻量文inference模型，并解压
+wget  https://paddleocr.bj.bcebos.com/ch_models/ch_det_mv3_db_infer.tar && tar xf ch_det_mv3_db_infer.tar
+wget  https://paddleocr.bj.bcebos.com/ch_models/ch_rec_mv3_crnn_infer.tar && tar xf ch_rec_mv3_crnn_infer.tar
+
+# 转换检测模型
+./opt --model_file=./ch_det_mv3_db/model --param_file=./ch_det_mv3_db/params --optimize_out_type=naive_buffer --optimize_out=./ch_det_mv3_db_opt --valid_targets=arm
+
+# 转换识别模型
+./opt --model_file=./ch_rec_mv3_crnn/model --param_file=./ch_rec_mv3_crnn/params --optimize_out_type=naive_buffer --optimize_out=./ch_rec_mv3_crnn_opt --valid_targets=arm
+```
+
+转换成功后，当前目录下会多出`ch_det_mv3_db_opt.nb`, `ch_rec_mv3_crnn_opt.nb`结尾的文件，即是转换成功的模型文件。
+
+注意：使用paddle-lite部署时，需要使用opt工具优化后的模型。 opt 转换的输入模型是paddle保存的inference模型
+
+<a name="2.2与手机联调"></a>
+### 2.2 与手机联调
+
+首先需要进行一些准备工作。
+ 1. 准备一台arm8的安卓手机，如果编译的预测库和opt文件是armv7，则需要arm7的手机，并修改Makefile中`ARM_ABI = arm7`。
+ 2. 打开手机的USB调试选项，选择文件传输模式，连接电脑。
+ 3. 电脑上安装adb工具，用于调试。 adb安装方式如下：
+
+    3.1. MAC电脑安装ADB:
+    ```
+    brew cask install android-platform-tools
+    ```
+    3.2. Linux安装ADB
+    ```
+    sudo apt update
+    sudo apt install -y wget adb
+    ```
+    3.3. Window安装ADB
+
+    win上安装需要去谷歌的安卓平台下载adb软件包进行安装：[链接](https://developer.android.com/studio)
+
+    打开终端，手机连接电脑，在终端中输入
+    ```
+    adb devices
+    ```
+    如果有device输出，则表示安装成功。
+    ```
+       List of devices attached
+       744be294    device
+    ```
+
+ 4. 准备优化后的模型、预测库文件、测试图像和使用的字典文件。
+ 在预测库`inference_lite_lib.android.armv8/demo/cxx/`下新建一个`ocr/`文件夹，
+ 将PaddleOCR repo中`PaddleOCR/deploy/lite/` 下的除`readme.md`所有文件放在新建的ocr文件夹下。在`ocr`文件夹下新建一个`debug`文件夹，
+ 将C++预测库so文件复制到debug文件夹下。
+  ```
+ # 进入OCR demo的工作目录
+ cd demo/cxx/ocr/
+ # 将C++预测动态库so文件复制到debug文件夹中
+ cp ../../../cxx/lib/libpaddle_light_api_shared.so ./debug/
+  ```
+ 准备测试图像，以`PaddleOCR/doc/imgs/11.jpg`为例，将测试的图像复制到`demo/cxx/ocr/debug/`文件夹下。
+ 准备字典文件，中文超轻量模型的字典文件是`PaddleOCR/ppocr/utils/ppocr_keys_v1.txt`，将其复制到`demo/cxx/ocr/debug/`文件夹下。
+
+ 执行完成后，ocr文件夹下将有如下文件格式：
+
+```
+demo/cxx/ocr/
+|-- debug/  
+|   |--ch_det_mv3_db_opt.nb             优化后的检测模型文件
+|   |--ch_rec_mv3_crnn_opt.nb           优化后的识别模型文件
+|   |--11.jpg                           待测试图像
+|   |--ppocr_keys_v1.txt                字典文件
+|   |--libpaddle_light_api_shared.so    C++预测库文件
+|   |--config.txt                       DB-CRNN超参数配置
+|-- config.txt                  DB-CRNN超参数配置
+|-- crnn_process.cc             识别模型CRNN的预处理和后处理文件
+|-- crnn_process.h
+|-- db_post_process.cc          检测模型DB的后处理文件
+|-- db_post_process.h
+|-- Makefile                    编译文件
+|-- ocr_db_crnn.cc              C++预测源文件
+
+```
+
+ 5. 启动调试
+
+ 上述步骤完成后就可以使用adb将文件push到手机上运行，步骤如下：
+
+ ```
+ # 执行编译，得到可执行文件ocr_db_crnn
+ # ocr_db_crnn可执行文件的使用方式为:
+ # ./ocr_db_crnn  检测模型文件  识别模型文件  测试图像路径
+ make -j
+ # 将编译的可执行文件移动到debug文件夹中
+ mv ocr_db_crnn ./debug/
+ # 将debug文件夹push到手机上
+ adb push debug /data/local/tmp/
+ adb shell
+ cd /data/local/tmp/debug
+ export LD_LIBRARY_PATH=/data/local/tmp/debug:$LD_LIBRARY_PATH
+ ./ocr_db_crnn ch_det_mv3_db_opt.nb  ch_rec_mv3_crnn_opt.nb ./11.jpg  ppocr_keys_v1.txt
+ ```
+
+ 如果对代码做了修改，则需要重新编译并push到手机上。
+
+ 运行效果如下：
+
+<div align="center">
+    <img src="../imgs/demo.png" width="600">
+</div>