clipper.cpp

/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.2.1                                                           *
* Date      :  31 October 2014                                                 *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2014                                         *
*                                                                              *
* License:                                                                     *
* Use, modification & distribution is subject to Boost Software License Ver 1. *
* http://www.boost.org/LICENSE_1_0.txt                                         *
*                                                                              *
* Attributions:                                                                *
* The code in this library is an extension of Bala Vatti's clipping algorithm: *
* "A generic solution to polygon clipping"                                     *
* Communications of the ACM, Vol 35, Issue 7 (July 1992) pp 56-63.             *
* http://portal.acm.org/citation.cfm?id=129906                                 *
*                                                                              *
* Computer graphics and geometric modeling: implementation and algorithms      *
* By Max K. Agoston                                                            *
* Springer; 1 edition (January 4, 2005)                                        *
* http://books.google.com/books?q=vatti+clipping+agoston                       *
*                                                                              *
* See also:                                                                    *
* "Polygon Offsetting by Computing Winding Numbers"                            *
* Paper no. DETC2005-85513 pp. 565-575                                         *
* ASME 2005 International Design Engineering Technical Conferences             *
* and Computers and Information in Engineering Conference (IDETC/CIE2005)      *
* September 24-28, 2005 , Long Beach, California, USA                          *
* http://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf              *
*                                                                              *
*******************************************************************************/

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

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

namespace ClipperLib {

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

	enum Direction { dRightToLeft, dLeftToRight };

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

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

	struct TEdge {
		IntPoint Bot;
		IntPoint Curr;
		IntPoint Top;
		IntPoint Delta;
		double Dx;
		PolyType PolyTyp;
		EdgeSide Side;
		int WindDelta; //1 or -1 depending on winding direction
		int WindCnt;
		int WindCnt2; //winding count of the opposite polytype
		int OutIdx;
		TEdge *Next;
		TEdge *Prev;
		TEdge *NextInLML;
		TEdge *NextInAEL;
		TEdge *PrevInAEL;
		TEdge *NextInSEL;
		TEdge *PrevInSEL;
	};

	struct IntersectNode {
		TEdge          *Edge1;
		TEdge          *Edge2;
		IntPoint        Pt;
	};

	struct LocalMinimum {
		cInt          Y;
		TEdge        *LeftBound;
		TEdge        *RightBound;
	};

	struct OutPt;

	struct OutRec {
		int       Idx;
		bool      IsHole;
		bool      IsOpen;
		OutRec   *FirstLeft;  //see comments in clipper.pas
		PolyNode *PolyNd;
		OutPt    *Pts;
		OutPt    *BottomPt;
	};

	struct OutPt {
		int       Idx;
		IntPoint  Pt;
		OutPt    *Next;
		OutPt    *Prev;
	};

	struct Join {
		OutPt    *OutPt1;
		OutPt    *OutPt2;
		IntPoint  OffPt;
	};

	struct LocMinSorter
	{
		inline bool operator()(const LocalMinimum& locMin1, const LocalMinimum& locMin2)
		{
			return locMin2.Y < locMin1.Y;
		}
	};

	//------------------------------------------------------------------------------
	//------------------------------------------------------------------------------

	inline cInt Round(double val)
	{
		if ((val < 0)) return static_cast<cInt>(val - 0.5);
		else return static_cast<cInt>(val + 0.5);
	}
	//------------------------------------------------------------------------------

	inline cInt Abs(cInt val)
	{
		return val < 0 ? -val : val;
	}

	//------------------------------------------------------------------------------
	// PolyTree methods ...
	//------------------------------------------------------------------------------

	void PolyTree::Clear()
	{
		for (PolyNodes::size_type i = 0; i < AllNodes.size(); ++i)
			delete AllNodes[i];
		AllNodes.resize(0);
		Childs.resize(0);
	}
	//------------------------------------------------------------------------------

	PolyNode* PolyTree::GetFirst() const
	{
		if (!Childs.empty())
			return Childs[0];
		else
			return 0;
	}
	//------------------------------------------------------------------------------

	int PolyTree::Total() const
	{
		int result = (int)AllNodes.size();
		//with negative offsets, ignore the hidden outer polygon ...
		if (result > 0 && Childs[0] != AllNodes[0]) result--;
		return result;
	}

	//------------------------------------------------------------------------------
	// PolyNode methods ...
	//------------------------------------------------------------------------------

	PolyNode::PolyNode() : Childs(), Parent(0), Index(0), m_IsOpen(false)
	{
	}
	//------------------------------------------------------------------------------

	int PolyNode::ChildCount() const
	{
		return (int)Childs.size();
	}
	//------------------------------------------------------------------------------

	void PolyNode::AddChild(PolyNode& child)
	{
		unsigned cnt = (unsigned)Childs.size();
		Childs.push_back(&child);
		child.Parent = this;
		child.Index = cnt;
	}
	//------------------------------------------------------------------------------

	PolyNode* PolyNode::GetNext() const
	{
		if (!Childs.empty())
			return Childs[0];
		else
			return GetNextSiblingUp();
	}
	//------------------------------------------------------------------------------

	PolyNode* PolyNode::GetNextSiblingUp() const
	{
		if (!Parent) //protects against PolyTree.GetNextSiblingUp()
			return 0;
		else if (Index == Parent->Childs.size() - 1)
			return Parent->GetNextSiblingUp();
		else
			return Parent->Childs[Index + 1];
	}
	//------------------------------------------------------------------------------

	bool PolyNode::IsHole() const
	{
		bool result = true;
		PolyNode* node = Parent;
		while (node)
		{
			result = !result;
			node = node->Parent;
		}
		return result;
	}
	//------------------------------------------------------------------------------

	bool PolyNode::IsOpen() const
	{
		return m_IsOpen;
	}
	//------------------------------------------------------------------------------

#ifndef use_int32

	//------------------------------------------------------------------------------
	// Int128 class (enables safe math on signed 64bit integers)
	// eg Int128 val1((long64)9223372036854775807); //ie 2^63 -1
	//    Int128 val2((long64)9223372036854775807);
	//    Int128 val3 = val1 * val2;
	//    val3.AsString => "85070591730234615847396907784232501249" (8.5e+37)
	//------------------------------------------------------------------------------

	class Int128
	{
	public:
		ulong64 lo;
		long64 hi;

		Int128(long64 _lo = 0)
		{
			lo = (ulong64)_lo;
			if (_lo < 0)  hi = -1; else hi = 0;
		}


		Int128(const Int128 &val) : lo(val.lo), hi(val.hi){}

		Int128(const long64& _hi, const ulong64& _lo) : lo(_lo), hi(_hi){}

		Int128& operator = (const long64 &val)
		{
			lo = (ulong64)val;
			if (val < 0) hi = -1; else hi = 0;
			return *this;
		}

		bool operator == (const Int128 &val) const
		{
			return (hi == val.hi && lo == val.lo);
		}

		bool operator != (const Int128 &val) const
		{
			return !(*this == val);
		}

		bool operator > (const Int128 &val) const
		{
			if (hi != val.hi)
				return hi > val.hi;
			else
				return lo > val.lo;
		}

		bool operator < (const Int128 &val) const
		{
			if (hi != val.hi)
				return hi < val.hi;
			else
				return lo < val.lo;
		}

		bool operator >= (const Int128 &val) const
		{
			return !(*this < val);
		}

		bool operator <= (const Int128 &val) const
		{
			return !(*this > val);
		}

		Int128& operator += (const Int128 &rhs)
		{
			hi += rhs.hi;
			lo += rhs.lo;
			if (lo < rhs.lo) hi++;
			return *this;
		}

		Int128 operator + (const Int128 &rhs) const
		{
			Int128 result(*this);
			result += rhs;
			return result;
		}

		Int128& operator -= (const Int128 &rhs)
		{
			*this += -rhs;
			return *this;
		}

		Int128 operator - (const Int128 &rhs) const
		{
			Int128 result(*this);
			result -= rhs;
			return result;
		}

		Int128 operator-() const //unary negation
		{
			if (lo == 0)
				return Int128(-hi, 0);
			else
				return Int128(~hi, ~lo + 1);
		}

		operator double() const
		{
			const double shift64 = 18446744073709551616.0; //2^64
			if (hi < 0)
			{
				if (lo == 0) return (double)hi * shift64;
				else return -(double)(~lo + ~hi * shift64);
			}
			else
				return (double)(lo + hi * shift64);
		}

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

	Int128 Int128Mul(long64 lhs, long64 rhs)
	{
		bool negate = (lhs < 0) != (rhs < 0);

		if (lhs < 0) lhs = -lhs;
		ulong64 int1Hi = ulong64(lhs) >> 32;
		ulong64 int1Lo = ulong64(lhs & 0xFFFFFFFF);

		if (rhs < 0) rhs = -rhs;
		ulong64 int2Hi = ulong64(rhs) >> 32;
		ulong64 int2Lo = ulong64(rhs & 0xFFFFFFFF);

		//nb: see comments in clipper.pas
		ulong64 a = int1Hi * int2Hi;
		ulong64 b = int1Lo * int2Lo;
		ulong64 c = int1Hi * int2Lo + int1Lo * int2Hi;

		Int128 tmp;
		tmp.hi = long64(a + (c >> 32));
		tmp.lo = long64(c << 32);
		tmp.lo += long64(b);
		if (tmp.lo < b) tmp.hi++;
		if (negate) tmp = -tmp;
		return tmp;
	}
#endif

	//------------------------------------------------------------------------------
	// Miscellaneous global functions
	//------------------------------------------------------------------------------

	void Swap(cInt& val1, cInt& val2)
	{
		cInt tmp = val1;
		val1 = val2;
		val2 = tmp;
	}
	//------------------------------------------------------------------------------
	bool Orientation(const Path &poly)
	{
		return Area(poly) >= 0;
	}
	//------------------------------------------------------------------------------

	double Area(const Path &poly)
	{
		int size = (int)poly.size();
		if (size < 3) return 0;

		double a = 0;
		for (int i = 0, j = size - 1; i < size; ++i)
		{
			a += ((double)poly[j].X + poly[i].X) * ((double)poly[j].Y - poly[i].Y);
			j = i;
		}
		return -a * 0.5;
	}
	//------------------------------------------------------------------------------

	double Area(const OutRec &outRec)
	{
		OutPt *op = outRec.Pts;
		if (!op) return 0;
		double a = 0;
		do {
			a += (double)(op->Prev->Pt.X + op->Pt.X) * (double)(op->Prev->Pt.Y - op->Pt.Y);
			op = op->Next;
		} while (op != outRec.Pts);
		return a * 0.5;
	}
	//------------------------------------------------------------------------------

	bool PointIsVertex(const IntPoint &Pt, OutPt *pp)
	{
		OutPt *pp2 = pp;
		do
		{
			if (pp2->Pt == Pt) return true;
			pp2 = pp2->Next;
		} while (pp2 != pp);
		return false;
	}
	//------------------------------------------------------------------------------

	int PointInPolygon(const IntPoint &pt, const Path &path)
	{
		//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
		//See "The Point in Polygon Problem for Arbitrary Polygons" by Hormann & Agathos
		//http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.5498&rep=rep1&type=pdf
		int result = 0;
		size_t cnt = path.size();
		if (cnt < 3) return 0;
		IntPoint ip = path[0];
		for (size_t i = 1; i <= cnt; ++i)
		{
			IntPoint ipNext = (i == cnt ? path[0] : path[i]);
			if (ipNext.Y == pt.Y)
			{
				if ((ipNext.X == pt.X) || (ip.Y == pt.Y &&
					((ipNext.X > pt.X) == (ip.X < pt.X)))) return -1;
			}
			if ((ip.Y < pt.Y) != (ipNext.Y < pt.Y))
			{
				if (ip.X >= pt.X)
				{
					if (ipNext.X > pt.X) result = 1 - result;
					else
					{
						double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
							(double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
						if (!d) return -1;
						if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
					}
				}
				else
				{
					if (ipNext.X > pt.X)
					{
						double d = (double)(ip.X - pt.X) * (ipNext.Y - pt.Y) -
							(double)(ipNext.X - pt.X) * (ip.Y - pt.Y);
						if (!d) return -1;
						if ((d > 0) == (ipNext.Y > ip.Y)) result = 1 - result;
					}
				}
			}
			ip = ipNext;
		}
		return result;
	}
	//------------------------------------------------------------------------------

	int PointInPolygon(const IntPoint &pt, OutPt *op)
	{
		//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
		int result = 0;
		OutPt* startOp = op;
		for (;;)
		{
			if (op->Next->Pt.Y == pt.Y)
			{
				if ((op->Next->Pt.X == pt.X) || (op->Pt.Y == pt.Y &&
					((op->Next->Pt.X > pt.X) == (op->Pt.X < pt.X)))) return -1;
			}
			if ((op->Pt.Y < pt.Y) != (op->Next->Pt.Y < pt.Y))
			{
				if (op->Pt.X >= pt.X)
				{
					if (op->Next->Pt.X > pt.X) result = 1 - result;
					else
					{
						double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
							(double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
						if (!d) return -1;
						if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
					}
				}
				else
				{
					if (op->Next->Pt.X > pt.X)
					{
						double d = (double)(op->Pt.X - pt.X) * (op->Next->Pt.Y - pt.Y) -
							(double)(op->Next->Pt.X - pt.X) * (op->Pt.Y - pt.Y);
						if (!d) return -1;
						if ((d > 0) == (op->Next->Pt.Y > op->Pt.Y)) result = 1 - result;
					}
				}
			}
			op = op->Next;
			if (startOp == op) break;
		}
		return result;
	}
	//------------------------------------------------------------------------------

	bool Poly2ContainsPoly1(OutPt *OutPt1, OutPt *OutPt2)
	{
		OutPt* op = OutPt1;
		do
		{
			//nb: PointInPolygon returns 0 if false, +1 if true, -1 if pt on polygon
			int res = PointInPolygon(op->Pt, OutPt2);
			if (res >= 0) return res > 0;
			op = op->Next;
		} while (op != OutPt1);
		return true;
	}
	//----------------------------------------------------------------------

	bool SlopesEqual(const TEdge &e1, const TEdge &e2, bool UseFullInt64Range)
	{
#ifndef use_int32
		if (UseFullInt64Range)
			return Int128Mul(e1.Delta.Y, e2.Delta.X) == Int128Mul(e1.Delta.X, e2.Delta.Y);
		else
#endif
			return e1.Delta.Y * e2.Delta.X == e1.Delta.X * e2.Delta.Y;
	}
	//------------------------------------------------------------------------------

	bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
		const IntPoint pt3, bool UseFullInt64Range)
	{
#ifndef use_int32
		if (UseFullInt64Range)
			return Int128Mul(pt1.Y - pt2.Y, pt2.X - pt3.X) == Int128Mul(pt1.X - pt2.X, pt2.Y - pt3.Y);
		else
#endif
			return (pt1.Y - pt2.Y)*(pt2.X - pt3.X) == (pt1.X - pt2.X)*(pt2.Y - pt3.Y);
	}
	//------------------------------------------------------------------------------

	bool SlopesEqual(const IntPoint pt1, const IntPoint pt2,
		const IntPoint pt3, const IntPoint pt4, bool UseFullInt64Range)
	{
#ifndef use_int32
		if (UseFullInt64Range)
			return Int128Mul(pt1.Y - pt2.Y, pt3.X - pt4.X) == Int128Mul(pt1.X - pt2.X, pt3.Y - pt4.Y);
		else
#endif
			return (pt1.Y - pt2.Y)*(pt3.X - pt4.X) == (pt1.X - pt2.X)*(pt3.Y - pt4.Y);
	}
	//------------------------------------------------------------------------------

	inline bool IsHorizontal(TEdge &e)
	{
		return e.Delta.Y == 0;
	}
	//------------------------------------------------------------------------------

	inline double GetDx(const IntPoint pt1, const IntPoint pt2)
	{
		return (pt1.Y == pt2.Y) ?
		HORIZONTAL : (double)(pt2.X - pt1.X) / (pt2.Y - pt1.Y);
	}
	//---------------------------------------------------------------------------

	inline void SetDx(TEdge &e)
	{
		e.Delta.X = (e.Top.X - e.Bot.X);
		e.Delta.Y = (e.Top.Y - e.Bot.Y);

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

	inline void SwapSides(TEdge &Edge1, TEdge &Edge2)
	{
		EdgeSide Side = Edge1.Side;
		Edge1.Side = Edge2.Side;
		Edge2.Side = Side;
	}
	//------------------------------------------------------------------------------

	inline void SwapPolyIndexes(TEdge &Edge1, TEdge &Edge2)
	{
		int OutIdx = Edge1.OutIdx;
		Edge1.OutIdx = Edge2.OutIdx;
		Edge2.OutIdx = OutIdx;
	}
	//------------------------------------------------------------------------------

	inline cInt TopX(TEdge &edge, const cInt currentY)
	{
		return (currentY == edge.Top.Y) ?
			edge.Top.X : edge.Bot.X + Round(edge.Dx *(currentY - edge.Bot.Y));
	}
	//------------------------------------------------------------------------------

	void IntersectPoint(TEdge &Edge1, TEdge &Edge2, IntPoint &ip)
	{
#ifdef use_xyz  
		ip.Z = 0;
#endif

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

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

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

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

	inline void InitEdge(TEdge* e, TEdge* eNext, TEdge* ePrev, const IntPoint& Pt)
	{
		std::memset(e, 0, sizeof(TEdge));
		e->Next = eNext;
		e->Prev = ePrev;
		e->Curr = Pt;
		e->OutIdx = Unassigned;
	}
	//------------------------------------------------------------------------------

	void InitEdge2(TEdge& e, PolyType Pt)
	{
		if (e.Curr.Y >= e.Next->Curr.Y)
		{
			e.Bot = e.Curr;
			e.Top = e.Next->Curr;
		}
		else
		{
			e.Top = e.Curr;
			e.Bot = e.Next->Curr;
		}
		SetDx(e);
		e.PolyTyp = Pt;
	}
	//------------------------------------------------------------------------------

	TEdge* RemoveEdge(TEdge* e)
	{
		//removes e from double_linked_list (but without removing from memory)
		e->Prev->Next = e->Next;
		e->Next->Prev = e->Prev;
		TEdge* result = e->Next;
		e->Prev = 0; //flag as removed (see ClipperBase.Clear)
		return result;
	}
	//------------------------------------------------------------------------------

	inline void ReverseHorizontal(TEdge &e)
	{
		//swap horizontal edges' Top and Bottom x's so they follow the natural
		//progression of the bounds - ie so their xbots will align with the
		//adjoining lower edge. [Helpful in the ProcessHorizontal() method.]
		Swap(e.Top.X, e.Bot.X);
#ifdef use_xyz  
		Swap(e.Top.Z, e.Bot.Z);
#endif
	}
	//------------------------------------------------------------------------------

	void SwapPoints(IntPoint &pt1, IntPoint &pt2)
	{
		IntPoint tmp = pt1;
		pt1 = pt2;
		pt2 = tmp;
	}
	//------------------------------------------------------------------------------

	bool GetOverlapSegment(IntPoint pt1a, IntPoint pt1b, IntPoint pt2a,
		IntPoint pt2b, IntPoint &pt1, IntPoint &pt2)
	{
		//precondition: segments are Collinear.
		if (Abs(pt1a.X - pt1b.X) > Abs(pt1a.Y - pt1b.Y))
		{
			if (pt1a.X > pt1b.X) SwapPoints(pt1a, pt1b);
			if (pt2a.X > pt2b.X) SwapPoints(pt2a, pt2b);
			if (pt1a.X > pt2a.X) pt1 = pt1a; else pt1 = pt2a;
			if (pt1b.X < pt2b.X) pt2 = pt1b; else pt2 = pt2b;
			return pt1.X < pt2.X;
		}
		else
		{
			if (pt1a.Y < pt1b.Y) SwapPoints(pt1a, pt1b);
			if (pt2a.Y < pt2b.Y) SwapPoints(pt2a, pt2b);
			if (pt1a.Y < pt2a.Y) pt1 = pt1a; else pt1 = pt2a;
			if (pt1b.Y > pt2b.Y) pt2 = pt1b; else pt2 = pt2b;
			return pt1.Y > pt2.Y;
		}
	}
	//------------------------------------------------------------------------------

	bool FirstIsBottomPt(const OutPt* btmPt1, const OutPt* btmPt2)
	{
		OutPt *p = btmPt1->Prev;
		while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Prev;
		double dx1p = std::fabs(GetDx(btmPt1->Pt, p->Pt));
		p = btmPt1->Next;
		while ((p->Pt == btmPt1->Pt) && (p != btmPt1)) p = p->Next;
		double dx1n = std::fabs(GetDx(btmPt1->Pt, p->Pt));

		p = btmPt2->Prev;
		while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Prev;
		double dx2p = std::fabs(GetDx(btmPt2->Pt, p->Pt));
		p = btmPt2->Next;
		while ((p->Pt == btmPt2->Pt) && (p != btmPt2)) p = p->Next;
		double dx2n = std::fabs(GetDx(btmPt2->Pt, p->Pt));
		return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
	}
	//------------------------------------------------------------------------------

	OutPt* GetBottomPt(OutPt *pp)
	{
		OutPt* dups = 0;
		OutPt* p = pp->Next;
		while (p != pp)
		{
			if (p->Pt.Y > pp->Pt.Y)
			{
				pp = p;
				dups = 0;
			}
			else if (p->Pt.Y == pp->Pt.Y && p->Pt.X <= pp->Pt.X)
			{
				if (p->Pt.X < pp->Pt.X)
				{
					dups = 0;
					pp = p;
				}
				else
				{
					if (p->Next != pp && p->Prev != pp) dups = p;
				}
			}
			p = p->Next;
		}
		if (dups)
		{
			//there appears to be at least 2 vertices at BottomPt so ...
			while (dups != p)
			{
				if (!FirstIsBottomPt(p, dups)) pp = dups;
				dups = dups->Next;
				while (dups->Pt != pp->Pt) dups = dups->Next;
			}
		}
		return pp;
	}
	//------------------------------------------------------------------------------

	bool Pt2IsBetweenPt1AndPt3(const IntPoint pt1,
		const IntPoint pt2, const IntPoint pt3)
	{
		if ((pt1 == pt3) || (pt1 == pt2) || (pt3 == pt2))
			return false;
		else if (pt1.X != pt3.X)
			return (pt2.X > pt1.X) == (pt2.X < pt3.X);
		else
			return (pt2.Y > pt1.Y) == (pt2.Y < pt3.Y);
	}
	//------------------------------------------------------------------------------

	bool HorzSegmentsOverlap(cInt seg1a, cInt seg1b, cInt seg2a, cInt seg2b)
	{
		if (seg1a > seg1b) Swap(seg1a, seg1b);
		if (seg2a > seg2b) Swap(seg2a, seg2b);
		return (seg1a < seg2b) && (seg2a < seg1b);
	}

	//------------------------------------------------------------------------------
	// ClipperBase class methods ...
	//------------------------------------------------------------------------------

	ClipperBase::ClipperBase() //constructor
	{
		m_CurrentLM = m_MinimaList.begin(); //begin() == end() here
		m_UseFullRange = false;
	}
	//------------------------------------------------------------------------------

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

	void RangeTest(const IntPoint& Pt, bool& useFullRange)
	{
		if (useFullRange)
		{
			if (Pt.X > hiRange || Pt.Y > hiRange || -Pt.X > hiRange || -Pt.Y > hiRange)
				throw "Coordinate outside allowed range";
		}
		else if (Pt.X > loRange || Pt.Y > loRange || -Pt.X > loRange || -Pt.Y > loRange)
		{
			useFullRange = true;
			RangeTest(Pt, useFullRange);
		}
	}
	//------------------------------------------------------------------------------

	TEdge* FindNextLocMin(TEdge* E)
	{
		for (;;)
		{
			while (E->Bot != E->Prev->Bot || E->Curr == E->Top) E = E->Next;
			if (!IsHorizontal(*E) && !IsHorizontal(*E->Prev)) break;
			while (IsHorizontal(*E->Prev)) E = E->Prev;
			TEdge* E2 = E;
			while (IsHorizontal(*E)) E = E->Next;
			if (E->Top.Y == E->Prev->Bot.Y) continue; //ie just an intermediate horz.
			if (E2->Prev->Bot.X < E->Bot.X) E = E2;
			break;
		}
		return E;
	}
	//------------------------------------------------------------------------------

	TEdge* ClipperBase::ProcessBound(TEdge* E, bool NextIsForward)
	{
		TEdge *Result = E;
		TEdge *Horz = 0;

		if (E->OutIdx == Skip)
		{
			//if edges still remain in the current bound beyond the skip edge then
			//create another LocMin and call ProcessBound once more
			if (NextIsForward)
			{
				while (E->Top.Y == E->Next->Bot.Y) E = E->Next;
				//don't include top horizontals when parsing a bound a second time,
				//they will be contained in the opposite bound ...
				while (E != Result && IsHorizontal(*E)) E = E->Prev;
			}
			else
			{
				while (E->Top.Y == E->Prev->Bot.Y) E = E->Prev;
				while (E != Result && IsHorizontal(*E)) E = E->Next;
			}

			if (E == Result)
			{
				if (NextIsForward) Result = E->Next;
				else Result = E->Prev;
			}
			else
			{
				//there are more edges in the bound beyond result starting with E
				if (NextIsForward)
					E = Result->Next;
				else
					E = Result->Prev;
				MinimaList::value_type locMin;
				locMin.Y = E->Bot.Y;
				locMin.LeftBound = 0;
				locMin.RightBound = E;
				E->WindDelta = 0;
				Result = ProcessBound(E, NextIsForward);
				m_MinimaList.push_back(locMin);
			}
			return Result;
		}

		TEdge *EStart;

		if (IsHorizontal(*E))
		{
			//We need to be careful with open paths because this may not be a
			//true local minima (ie E may be following a skip edge).
			//Also, consecutive horz. edges may start heading left before going right.
			if (NextIsForward)
				EStart = E->Prev;
			else
				EStart = E->Next;
			if (EStart->OutIdx != Skip)
			{
				if (IsHorizontal(*EStart)) //ie an adjoining horizontal skip edge
				{
					if (EStart->Bot.X != E->Bot.X && EStart->Top.X != E->Bot.X)
						ReverseHorizontal(*E);
				}
				else if (EStart->Bot.X != E->Bot.X)
					ReverseHorizontal(*E);
			}
		}

		EStart = E;
		if (NextIsForward)
		{
			while (Result->Top.Y == Result->Next->Bot.Y && Result->Next->OutIdx != Skip)
				Result = Result->Next;
			if (IsHorizontal(*Result) && Result->Next->OutIdx != Skip)
			{
				//nb: at the top of a bound, horizontals are added to the bound
				//only when the preceding edge attaches to the horizontal's left vertex
				//unless a Skip edge is encountered when that becomes the top divide
				Horz = Result;
				while (IsHorizontal(*Horz->Prev)) Horz = Horz->Prev;
				if (Horz->Prev->Top.X == Result->Next->Top.X)
				{
					if (!NextIsForward) Result = Horz->Prev;
				}
				else if (Horz->Prev->Top.X > Result->Next->Top.X) Result = Horz->Prev;
			}
			while (E != Result)
			{
				E->NextInLML = E->Next;
				if (IsHorizontal(*E) && E != EStart &&
					E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
				E = E->Next;
			}
			if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Prev->Top.X)
				ReverseHorizontal(*E);
			Result = Result->Next; //move to the edge just beyond current bound
		}
		else
		{
			while (Result->Top.Y == Result->Prev->Bot.Y && Result->Prev->OutIdx != Skip)
				Result = Result->Prev;
			if (IsHorizontal(*Result) && Result->Prev->OutIdx != Skip)
			{
				Horz = Result;
				while (IsHorizontal(*Horz->Next)) Horz = Horz->Next;
				if (Horz->Next->Top.X == Result->Prev->Top.X)
				{
					if (!NextIsForward) Result = Horz->Next;
				}
				else if (Horz->Next->Top.X > Result->Prev->Top.X) Result = Horz->Next;
			}

			while (E != Result)
			{
				E->NextInLML = E->Prev;
				if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
					ReverseHorizontal(*E);
				E = E->Prev;
			}
			if (IsHorizontal(*E) && E != EStart && E->Bot.X != E->Next->Top.X)
				ReverseHorizontal(*E);
			Result = Result->Prev; //move to the edge just beyond current bound
		}

		return Result;
	}
	//------------------------------------------------------------------------------

	bool ClipperBase::AddPath(const Path &pg, PolyType PolyTyp, bool Closed)
	{
#ifdef use_lines
		if (!Closed && PolyTyp == ptClip)
			throw clipperException("AddPath: Open paths must be subject.");
#else
		if (!Closed)
			throw clipperException("AddPath: Open paths have been disabled.");
#endif

		int highI = (int)pg.size() - 1;
		if (Closed) while (highI > 0 && (pg[highI] == pg[0])) --highI;
		while (highI > 0 && (pg[highI] == pg[highI - 1])) --highI;
		if ((Closed && highI < 2) || (!Closed && highI < 1)) return false;

		//create a new edge array ...
		TEdge *edges = new TEdge[highI + 1];

		bool IsFlat = true;
		//1. Basic (first) edge initialization ...
		try
		{
			edges[1].Curr = pg[1];
			RangeTest(pg[0], m_UseFullRange);
			RangeTest(pg[highI], m_UseFullRange);
			InitEdge(&edges[0], &edges[1], &edges[highI], pg[0]);
			InitEdge(&edges[highI], &edges[0], &edges[highI - 1], pg[highI]);
			for (int i = highI - 1; i >= 1; --i)
			{
				RangeTest(pg[i], m_UseFullRange);
				InitEdge(&edges[i], &edges[i + 1], &edges[i - 1], pg[i]);
			}
		}
		catch (...)
		{
			delete[] edges;
			throw; //range test fails
		}
		TEdge *eStart = &edges[0];

		//2. Remove duplicate vertices, and (when closed) collinear edges ...
		TEdge *E = eStart, *eLoopStop = eStart;
		for (;;)
		{
			//nb: allows matching start and end points when not Closed ...
			if (E->Curr == E->Next->Curr && (Closed || E->Next != eStart))
			{
				if (E == E->Next) break;
				if (E == eStart) eStart = E->Next;
				E = RemoveEdge(E);
				eLoopStop = E;
				continue;
			}
			if (E->Prev == E->Next)
				break; //only two vertices
			else if (Closed &&
				SlopesEqual(E->Prev->Curr, E->Curr, E->Next->Curr, m_UseFullRange) &&
				(!m_PreserveCollinear ||
				!Pt2IsBetweenPt1AndPt3(E->Prev->Curr, E->Curr, E->Next->Curr)))
			{
				//Collinear edges are allowed for open paths but in closed paths
				//the default is to merge adjacent collinear edges into a single edge.
				//However, if the PreserveCollinear property is enabled, only overlapping
				//collinear edges (ie spikes) will be removed from closed paths.
				if (E == eStart) eStart = E->Next;
				E = RemoveEdge(E);
				E = E->Prev;
				eLoopStop = E;
				continue;
			}
			E = E->Next;
			if ((E == eLoopStop) || (!Closed && E->Next == eStart)) break;
		}

		if ((!Closed && (E == E->Next)) || (Closed && (E->Prev == E->Next)))
		{
			delete[] edges;
			return false;
		}

		if (!Closed)
		{
			m_HasOpenPaths = true;
			eStart->Prev->OutIdx = Skip;
		}

		//3. Do second stage of edge initialization ...
		E = eStart;
		do
		{
			InitEdge2(*E, PolyTyp);
			E = E->Next;
			if (IsFlat && E->Curr.Y != eStart->Curr.Y) IsFlat = false;
		} while (E != eStart);

		//4. Finally, add edge bounds to LocalMinima list ...

		//Totally flat paths must be handled differently when adding them
		//to LocalMinima list to avoid endless loops etc ...
		if (IsFlat)
		{
			if (Closed)
			{
				delete[] edges;
				return false;
			}
			E->Prev->OutIdx = Skip;
			if (E->Prev->Bot.X < E->Prev->Top.X) ReverseHorizontal(*E->Prev);
			MinimaList::value_type locMin;
			locMin.Y = E->Bot.Y;
			locMin.LeftBound = 0;
			locMin.RightBound = E;
			locMin.RightBound->Side = esRight;
			locMin.RightBound->WindDelta = 0;
			while (E->Next->OutIdx != Skip)
			{
				E->NextInLML = E->Next;
				if (E->Bot.X != E->Prev->Top.X) ReverseHorizontal(*E);
				E = E->Next;
			}
			m_MinimaList.push_back(locMin);
			m_edges.push_back(edges);
			return true;
		}

		m_edges.push_back(edges);
		bool leftBoundIsForward;
		TEdge* EMin = 0;

		//workaround to avoid an endless loop in the while loop below when
		//open paths have matching start and end points ...
		if (E->Prev->Bot == E->Prev->Top) E = E->Next;

		for (;;)
		{
			E = FindNextLocMin(E);
			if (E == EMin) break;
			else if (!EMin) EMin = E;

			//E and E.Prev now share a local minima (left aligned if horizontal).
			//Compare their slopes to find which starts which bound ...
			MinimaList::value_type locMin;
			locMin.Y = E->Bot.Y;
			if (E->Dx < E->Prev->Dx)
			{
				locMin.LeftBound = E->Prev;
				locMin.RightBound = E;
				leftBoundIsForward = false; //Q.nextInLML = Q.prev
			}
			else
			{
				locMin.LeftBound = E;
				locMin.RightBound = E->Prev;
				leftBoundIsForward = true; //Q.nextInLML = Q.next
			}
			locMin.LeftBound->Side = esLeft;
			locMin.RightBound->Side = esRight;

			if (!Closed) locMin.LeftBound->WindDelta = 0;
			else if (locMin.LeftBound->Next == locMin.RightBound)
				locMin.LeftBound->WindDelta = -1;
			else locMin.LeftBound->WindDelta = 1;
			locMin.RightBound->WindDelta = -locMin.LeftBound->WindDelta;

			E = ProcessBound(locMin.LeftBound, leftBoundIsForward);
			if (E->OutIdx == Skip) E = ProcessBound(E, leftBoundIsForward);

			TEdge* E2 = ProcessBound(locMin.RightBound, !leftBoundIsForward);
			if (E2->OutIdx == Skip) E2 = ProcessBound(E2, !leftBoundIsForward);

			if (locMin.LeftBound->OutIdx == Skip)
				locMin.LeftBound = 0;
			else if (locMin.RightBound->OutIdx == Skip)
				locMin.RightBound = 0;
			m_MinimaList.push_back(locMin);
			if (!leftBoundIsForward) E = E2;
		}
		return true;
	}
	//------------------------------------------------------------------------------

	bool ClipperBase::AddPaths(const Paths &ppg, PolyType PolyTyp, bool Closed)
	{
		bool result = false;
		for (Paths::size_type i = 0; i < ppg.size(); ++i)
			if (AddPath(ppg[i], PolyTyp, Closed)) result = true;
		return result;
	}
	//------------------------------------------------------------------------------

	void ClipperBase::Clear()
	{
		DisposeLocalMinimaList();
		for (EdgeList::size_type i = 0; i < m_edges.size(); ++i)
		{
			//for each edge array in turn, find the first used edge and 
			//check for and remove any hiddenPts in each edge in the array.
			TEdge* edges = m_edges[i];
			delete[] edges;
		}
		m_edges.clear();
		m_UseFullRange = false;
		m_HasOpenPaths = false;
	}
	//------------------------------------------------------------------------------

	void ClipperBase::Reset()
	{
		m_CurrentLM = m_MinimaList.begin();
		if (m_CurrentLM == m_MinimaList.end()) return; //ie nothing to process
		std::sort(m_MinimaList.begin(), m_MinimaList.end(), LocMinSorter());

		//reset all edges ...
		for (MinimaList::iterator lm = m_MinimaList.begin(); lm != m_MinimaList.end(); ++lm)
		{
			TEdge* e = lm->LeftBound;
			if (e)
			{
				e->Curr = e->Bot;
				e->Side = esLeft;
				e->OutIdx = Unassigned;
			}

			e = lm->RightBound;
			if (e)
			{
				e->Curr = e->Bot;
				e->Side = esRight;
				e->OutIdx = Unassigned;
			}
		}
	}
	//------------------------------------------------------------------------------

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

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

	IntRect ClipperBase::GetBounds()
	{
		IntRect result;
		MinimaList::iterator lm = m_MinimaList.begin();
		if (lm == m_MinimaList.end())
		{
			result.left = result.top = result.right = result.bottom = 0;
			return result;
		}
		result.left = lm->LeftBound->Bot.X;
		result.top = lm->LeftBound->Bot.Y;
		result.right = lm->LeftBound->Bot.X;
		result.bottom = lm->LeftBound->Bot.Y;
		while (lm != m_MinimaList.end())
		{
			result.bottom = std::max(result.bottom, lm->LeftBound->Bot.Y);
			TEdge* e = lm->LeftBound;
			for (;;) {
				TEdge* bottomE = e;
				while (e->NextInLML)
				{
					if (e->Bot.X < result.left) result.left = e->Bot.X;
					if (e->Bot.X > result.right) result.right = e->Bot.X;
					e = e->NextInLML;
				}
				result.left = std::min(result.left, e->Bot.X);
				result.right = std::max(result.right, e->Bot.X);
				result.left = std::min(result.left, e->Top.X);
				result.right = std::max(result.right, e->Top.X);
				result.top = std::min(result.top, e->Top.Y);
				if (bottomE == lm->LeftBound) e = lm->RightBound;
				else break;
			}
			++lm;
		}
		return result;
	}

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

	Clipper::Clipper(int initOptions) : ClipperBase() //constructor
	{
		m_ActiveEdges = 0;
		m_SortedEdges = 0;
		m_ExecuteLocked = false;
		m_UseFullRange = false;
		m_ReverseOutput = ((initOptions & ioReverseSolution) != 0);
		m_StrictSimple = ((initOptions & ioStrictlySimple) != 0);
		m_PreserveCollinear = ((initOptions & ioPreserveCollinear) != 0);
		m_HasOpenPaths = false;
#ifdef use_xyz  
		m_ZFill = 0;
#endif
	}
	//------------------------------------------------------------------------------

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

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

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

	bool Clipper::Execute(ClipType clipType, Paths &solution,
		PolyFillType subjFillType, PolyFillType clipFillType)
	{
		if (m_ExecuteLocked) return false;
		if (m_HasOpenPaths)
			throw clipperException("Error: PolyTree struct is need for open path clipping.");
		m_ExecuteLocked = true;
		solution.resize(0);
		m_SubjFillType = subjFillType;
		m_ClipFillType = clipFillType;
		m_ClipType = clipType;
		m_UsingPolyTree = false;
		bool succeeded = ExecuteInternal();
		if (succeeded) BuildResult(solution);
		DisposeAllOutRecs();
		m_ExecuteLocked = false;
		return succeeded;
	}
	//------------------------------------------------------------------------------

	bool Clipper::Execute(ClipType clipType, PolyTree& polytree,
		PolyFillType subjFillType, PolyFillType clipFillType)
	{
		if (m_ExecuteLocked) return false;
		m_ExecuteLocked = true;
		m_SubjFillType = subjFillType;
		m_ClipFillType = clipFillType;
		m_ClipType = clipType;
		m_UsingPolyTree = true;
		bool succeeded = ExecuteInternal();
		if (succeeded) BuildResult2(polytree);
		DisposeAllOutRecs();
		m_ExecuteLocked = false;
		return succeeded;
	}
	//------------------------------------------------------------------------------

	void Clipper::FixHoleLinkage(OutRec &outrec)
	{
		//skip OutRecs that (a) contain outermost polygons or
		//(b) already have the correct owner/child linkage ...
		if (!outrec.FirstLeft ||
			(outrec.IsHole != outrec.FirstLeft->IsHole &&
			outrec.FirstLeft->Pts)) return;

		OutRec* orfl = outrec.FirstLeft;
		while (orfl && ((orfl->IsHole == outrec.IsHole) || !orfl->Pts))
			orfl = orfl->FirstLeft;
		outrec.FirstLeft = orfl;
	}
	//------------------------------------------------------------------------------

	bool Clipper::ExecuteInternal()
	{
		bool succeeded = true;
		try {
			Reset();
			if (m_CurrentLM == m_MinimaList.end()) return true;
			cInt botY = PopScanbeam();
			do {
				InsertLocalMinimaIntoAEL(botY);
				ClearGhostJoins();
				ProcessHorizontals(false);
				if (m_Scanbeam.empty()) break;
				cInt topY = PopScanbeam();
				succeeded = ProcessIntersections(topY);
				if (!succeeded) break;
				ProcessEdgesAtTopOfScanbeam(topY);
				botY = topY;
			} while (!m_Scanbeam.empty() || m_CurrentLM != m_MinimaList.end());
		}
		catch (...)
		{
			succeeded = false;
		}

		if (succeeded)
		{
			//fix orientations ...
			for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
			{
				OutRec *outRec = m_PolyOuts[i];
				if (!outRec->Pts || outRec->IsOpen) continue;
				if ((outRec->IsHole ^ m_ReverseOutput) == (Area(*outRec) > 0))
					ReversePolyPtLinks(outRec->Pts);
			}

			if (!m_Joins.empty()) JoinCommonEdges();

			//unfortunately FixupOutPolygon() must be done after JoinCommonEdges()
			for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
			{
				OutRec *outRec = m_PolyOuts[i];
				if (outRec->Pts && !outRec->IsOpen)
					FixupOutPolygon(*outRec);
			}

			if (m_StrictSimple) DoSimplePolygons();
		}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

			if (rb)
			{
				if (IsHorizontal(*rb)) AddEdgeToSEL(rb);
				else InsertScanbeam(rb->Top.Y);
			}

			if (!lb || !rb) continue;

			//if any output polygons share an edge, they'll need joining later ...
			if (Op1 && IsHorizontal(*rb) &&
				m_GhostJoins.size() > 0 && (rb->WindDelta != 0))
			{
				for (JoinList::size_type i = 0; i < m_GhostJoins.size(); ++i)
				{
					Join* jr = m_GhostJoins[i];
					//if the horizontal Rb and a 'ghost' horizontal overlap, then convert
					//the 'ghost' join to a real join ready for later ...
					if (HorzSegmentsOverlap(jr->OutPt1->Pt.X, jr->OffPt.X, rb->Bot.X, rb->Top.X))
						AddJoin(jr->OutPt1, Op1, jr->OffPt);
				}
			}

			if (lb->OutIdx >= 0 && lb->PrevInAEL &&
				lb->PrevInAEL->Curr.X == lb->Bot.X &&
				lb->PrevInAEL->OutIdx >= 0 &&
				SlopesEqual(*lb->PrevInAEL, *lb, m_UseFullRange) &&
				(lb->WindDelta != 0) && (lb->PrevInAEL->WindDelta != 0))
			{
				OutPt *Op2 = AddOutPt(lb->PrevInAEL, lb->Bot);
				AddJoin(Op1, Op2, lb->Top);
			}

			if (lb->NextInAEL != rb)
			{

				if (rb->OutIdx >= 0 && rb->PrevInAEL->OutIdx >= 0 &&
					SlopesEqual(*rb->PrevInAEL, *rb, m_UseFullRange) &&
					(rb->WindDelta != 0) && (rb->PrevInAEL->WindDelta != 0))
				{
					OutPt *Op2 = AddOutPt(rb->PrevInAEL, rb->Bot);
					AddJoin(Op1, Op2, rb->Top);
				}

				TEdge* e = lb->NextInAEL;
				if (e)
				{
					while (e != rb)
					{
						//nb: For calculating winding counts etc, IntersectEdges() assumes
						//that param1 will be to the Right of param2 ABOVE the intersection ...
						IntersectEdges(rb, e, lb->Curr); //order important here
						e = e->NextInAEL;
					}
				}
			}

		}
	}
	//------------------------------------------------------------------------------

	void Clipper::DeleteFromAEL(TEdge *e)
	{
		TEdge* AelPrev = e->PrevInAEL;
		TEdge* AelNext = e->NextInAEL;
		if (!AelPrev &&  !AelNext && (e != m_ActiveEdges)) return; //already deleted
		if (AelPrev) AelPrev->NextInAEL = AelNext;
		else m_ActiveEdges = AelNext;
		if (AelNext) AelNext->PrevInAEL = AelPrev;
		e->NextInAEL = 0;
		e->PrevInAEL = 0;
	}
	//------------------------------------------------------------------------------

	void Clipper::DeleteFromSEL(TEdge *e)
	{
		TEdge* SelPrev = e->PrevInSEL;
		TEdge* SelNext = e->NextInSEL;
		if (!SelPrev &&  !SelNext && (e != m_SortedEdges)) return; //already deleted
		if (SelPrev) SelPrev->NextInSEL = SelNext;
		else m_SortedEdges = SelNext;
		if (SelNext) SelNext->PrevInSEL = SelPrev;
		e->NextInSEL = 0;
		e->PrevInSEL = 0;
	}
	//------------------------------------------------------------------------------

#ifdef use_xyz
	void Clipper::SetZ(IntPoint& pt, TEdge& e1, TEdge& e2)
	{
		if (pt.Z != 0 || !m_ZFill) return;
		else if (pt == e1.Bot) pt.Z = e1.Bot.Z;
		else if (pt == e1.Top) pt.Z = e1.Top.Z;
		else if (pt == e2.Bot) pt.Z = e2.Bot.Z;
		else if (pt == e2.Top) pt.Z = e2.Top.Z;
		else (*m_ZFill)(e1.Bot, e1.Top, e2.Bot, e2.Top, pt); 
	}
	//------------------------------------------------------------------------------
#endif

	void Clipper::IntersectEdges(TEdge *e1, TEdge *e2, IntPoint &Pt)
	{
		bool e1Contributing = (e1->OutIdx >= 0);
		bool e2Contributing = (e2->OutIdx >= 0);

#ifdef use_xyz
		SetZ(Pt, *e1, *e2);
#endif

#ifdef use_lines
		//if either edge is on an OPEN path ...
		if (e1->WindDelta == 0 || e2->WindDelta == 0)
		{
			//ignore subject-subject open path intersections UNLESS they
			//are both open paths, AND they are both 'contributing maximas' ...
			if (e1->WindDelta == 0 && e2->WindDelta == 0) return;

			//if intersecting a subj line with a subj poly ...
			else if (e1->PolyTyp == e2->PolyTyp && 
				e1->WindDelta != e2->WindDelta && m_ClipType == ctUnion)
			{
				if (e1->WindDelta == 0)
				{
					if (e2Contributing)
					{
						AddOutPt(e1, Pt);
						if (e1Contributing) e1->OutIdx = Unassigned;
					}
				}
				else
				{
					if (e1Contributing)
					{
						AddOutPt(e2, Pt);
						if (e2Contributing) e2->OutIdx = Unassigned;
					}
				}
			}
			else if (e1->PolyTyp != e2->PolyTyp)
			{
				//toggle subj open path OutIdx on/off when Abs(clip.WndCnt) == 1 ...
				if ((e1->WindDelta == 0) && abs(e2->WindCnt) == 1 && 
					(m_ClipType != ctUnion || e2->WindCnt2 == 0))
				{
					AddOutPt(e1, Pt);
					if (e1Contributing) e1->OutIdx = Unassigned;
				}
				else if ((e2->WindDelta == 0) && (abs(e1->WindCnt) == 1) && 
					(m_ClipType != ctUnion || e1->WindCnt2 == 0))
				{
					AddOutPt(e2, Pt);
					if (e2Contributing) e2->OutIdx = Unassigned;
				}
			}
			return;
		}
#endif

		//update winding counts...
		//assumes that e1 will be to the Right of e2 ABOVE the intersection
		if (e1->PolyTyp == e2->PolyTyp)
		{
			if (IsEvenOddFillType(*e1))
			{
				int oldE1WindCnt = e1->WindCnt;
				e1->WindCnt = e2->WindCnt;
				e2->WindCnt = oldE1WindCnt;
			}
			else
			{
				if (e1->WindCnt + e2->WindDelta == 0) e1->WindCnt = -e1->WindCnt;
				else e1->WindCnt += e2->WindDelta;
				if (e2->WindCnt - e1->WindDelta == 0) e2->WindCnt = -e2->WindCnt;
				else e2->WindCnt -= e1->WindDelta;
			}
		}
		else
		{
			if (!IsEvenOddFillType(*e2)) e1->WindCnt2 += e2->WindDelta;
			else e1->WindCnt2 = (e1->WindCnt2 == 0) ? 1 : 0;
			if (!IsEvenOddFillType(*e1)) e2->WindCnt2 -= e1->WindDelta;
			else e2->WindCnt2 = (e2->WindCnt2 == 0) ? 1 : 0;
		}

		PolyFillType e1FillType, e2FillType, e1FillType2, e2FillType2;
		if (e1->PolyTyp == ptSubject)
		{
			e1FillType = m_SubjFillType;
			e1FillType2 = m_ClipFillType;
		}
		else
		{
			e1FillType = m_ClipFillType;
			e1FillType2 = m_SubjFillType;
		}
		if (e2->PolyTyp == ptSubject)
		{
			e2FillType = m_SubjFillType;
			e2FillType2 = m_ClipFillType;
		}
		else
		{
			e2FillType = m_ClipFillType;
			e2FillType2 = m_SubjFillType;
		}

		cInt e1Wc, e2Wc;
		switch (e1FillType)
		{
		case pftPositive: e1Wc = e1->WindCnt; break;
		case pftNegative: e1Wc = -e1->WindCnt; break;
		default: e1Wc = Abs(e1->WindCnt);
		}
		switch (e2FillType)
		{
		case pftPositive: e2Wc = e2->WindCnt; break;
		case pftNegative: e2Wc = -e2->WindCnt; break;
		default: e2Wc = Abs(e2->WindCnt);
		}

		if (e1Contributing && e2Contributing)
		{
			if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
				(e1->PolyTyp != e2->PolyTyp && m_ClipType != ctXor))
			{
				AddLocalMaxPoly(e1, e2, Pt);
			}
			else
			{
				AddOutPt(e1, Pt);
				AddOutPt(e2, Pt);
				SwapSides(*e1, *e2);
				SwapPolyIndexes(*e1, *e2);
			}
		}
		else if (e1Contributing)
		{
			if (e2Wc == 0 || e2Wc == 1)
			{
				AddOutPt(e1, Pt);
				SwapSides(*e1, *e2);
				SwapPolyIndexes(*e1, *e2);
			}
		}
		else if (e2Contributing)
		{
			if (e1Wc == 0 || e1Wc == 1)
			{
				AddOutPt(e2, Pt);
				SwapSides(*e1, *e2);
				SwapPolyIndexes(*e1, *e2);
			}
		}
		else if ((e1Wc == 0 || e1Wc == 1) && (e2Wc == 0 || e2Wc == 1))
		{
			//neither edge is currently contributing ...

			cInt e1Wc2, e2Wc2;
			switch (e1FillType2)
			{
			case pftPositive: e1Wc2 = e1->WindCnt2; break;
			case pftNegative: e1Wc2 = -e1->WindCnt2; break;
			default: e1Wc2 = Abs(e1->WindCnt2);
			}
			switch (e2FillType2)
			{
			case pftPositive: e2Wc2 = e2->WindCnt2; break;
			case pftNegative: e2Wc2 = -e2->WindCnt2; break;
			default: e2Wc2 = Abs(e2->WindCnt2);
			}

			if (e1->PolyTyp != e2->PolyTyp)
			{
				AddLocalMinPoly(e1, e2, Pt);
			}
			else if (e1Wc == 1 && e2Wc == 1)
				switch (m_ClipType) {
				case ctIntersection:
					if (e1Wc2 > 0 && e2Wc2 > 0)
						AddLocalMinPoly(e1, e2, Pt);
					break;
				case ctUnion:
					if (e1Wc2 <= 0 && e2Wc2 <= 0)
						AddLocalMinPoly(e1, e2, Pt);
					break;
				case ctDifference:
					if (((e1->PolyTyp == ptClip) && (e1Wc2 > 0) && (e2Wc2 > 0)) ||
						((e1->PolyTyp == ptSubject) && (e1Wc2 <= 0) && (e2Wc2 <= 0)))
						AddLocalMinPoly(e1, e2, Pt);
					break;
				case ctXor:
					AddLocalMinPoly(e1, e2, Pt);
			}
			else
				SwapSides(*e1, *e2);
		}
	}
	//------------------------------------------------------------------------------

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

	OutRec* GetLowermostRec(OutRec *outRec1, OutRec *outRec2)
	{
		//work out which polygon fragment has the correct hole state ...
		if (!outRec1->BottomPt)
			outRec1->BottomPt = GetBottomPt(outRec1->Pts);
		if (!outRec2->BottomPt)
			outRec2->BottomPt = GetBottomPt(outRec2->Pts);
		OutPt *OutPt1 = outRec1->BottomPt;
		OutPt *OutPt2 = outRec2->BottomPt;
		if (OutPt1->Pt.Y > OutPt2->Pt.Y) return outRec1;
		else if (OutPt1->Pt.Y < OutPt2->Pt.Y) return outRec2;
		else if (OutPt1->Pt.X < OutPt2->Pt.X) return outRec1;
		else if (OutPt1->Pt.X > OutPt2->Pt.X) return outRec2;
		else if (OutPt1->Next == OutPt1) return outRec2;
		else if (OutPt2->Next == OutPt2) return outRec1;
		else if (FirstIsBottomPt(OutPt1, OutPt2)) return outRec1;
		else return outRec2;
	}
	//------------------------------------------------------------------------------

	bool Param1RightOfParam2(OutRec* outRec1, OutRec* outRec2)
	{
		do
		{
			outRec1 = outRec1->FirstLeft;
			if (outRec1 == outRec2) return true;
		} while (outRec1);
		return false;
	}
	//------------------------------------------------------------------------------

	OutRec* Clipper::GetOutRec(int Idx)
	{
		OutRec* outrec = m_PolyOuts[Idx];
		while (outrec != m_PolyOuts[outrec->Idx])
			outrec = m_PolyOuts[outrec->Idx];
		return outrec;
	}
	//------------------------------------------------------------------------------

	void Clipper::AppendPolygon(TEdge *e1, TEdge *e2)
	{
		//get the start and ends of both output polygons ...
		OutRec *outRec1 = m_PolyOuts[e1->OutIdx];
		OutRec *outRec2 = m_PolyOuts[e2->OutIdx];

		OutRec *holeStateRec;
		if (Param1RightOfParam2(outRec1, outRec2))
			holeStateRec = outRec2;
		else if (Param1RightOfParam2(outRec2, outRec1))
			holeStateRec = outRec1;
		else
			holeStateRec = GetLowermostRec(outRec1, outRec2);

		//get the start and ends of both output polygons and
		//join e2 poly onto e1 poly and delete pointers to e2 ...

		OutPt* p1_lft = outRec1->Pts;
		OutPt* p1_rt = p1_lft->Prev;
		OutPt* p2_lft = outRec2->Pts;
		OutPt* p2_rt = p2_lft->Prev;

		EdgeSide Side;
		//join e2 poly onto e1 poly and delete pointers to e2 ...
		if (e1->Side == esLeft)
		{
			if (e2->Side == esLeft)
			{
				//z y x a b c
				ReversePolyPtLinks(p2_lft);
				p2_lft->Next = p1_lft;
				p1_lft->Prev = p2_lft;
				p1_rt->Next = p2_rt;
				p2_rt->Prev = p1_rt;
				outRec1->Pts = p2_rt;
			}
			else
			{
				//x y z a b c
				p2_rt->Next = p1_lft;
				p1_lft->Prev = p2_rt;
				p2_lft->Prev = p1_rt;
				p1_rt->Next = p2_lft;
				outRec1->Pts = p2_lft;
			}
			Side = esLeft;
		}
		else
		{
			if (e2->Side == esRight)
			{
				//a b c z y x
				ReversePolyPtLinks(p2_lft);
				p1_rt->Next = p2_rt;
				p2_rt->Prev = p1_rt;
				p2_lft->Next = p1_lft;
				p1_lft->Prev = p2_lft;
			}
			else
			{
				//a b c x y z
				p1_rt->Next = p2_lft;
				p2_lft->Prev = p1_rt;
				p1_lft->Prev = p2_rt;
				p2_rt->Next = p1_lft;
			}
			Side = esRight;
		}

		outRec1->BottomPt = 0;
		if (holeStateRec == outRec2)
		{
			if (outRec2->FirstLeft != outRec1)
				outRec1->FirstLeft = outRec2->FirstLeft;
			outRec1->IsHole = outRec2->IsHole;
		}
		outRec2->Pts = 0;
		outRec2->BottomPt = 0;
		outRec2->FirstLeft = outRec1;

		int OKIdx = e1->OutIdx;
		int ObsoleteIdx = e2->OutIdx;

		e1->OutIdx = Unassigned; //nb: safe because we only get here via AddLocalMaxPoly
		e2->OutIdx = Unassigned;

		TEdge* e = m_ActiveEdges;
		while (e)
		{
			if (e->OutIdx == ObsoleteIdx)
			{
				e->OutIdx = OKIdx;
				e->Side = Side;
				break;
			}
			e = e->NextInAEL;
		}

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

	OutRec* Clipper::CreateOutRec()
	{
		OutRec* result = new OutRec;
		result->IsHole = false;
		result->IsOpen = false;
		result->FirstLeft = 0;
		result->Pts = 0;
		result->BottomPt = 0;
		result->PolyNd = 0;
		m_PolyOuts.push_back(result);
		result->Idx = (int)m_PolyOuts.size() - 1;
		return result;
	}
	//------------------------------------------------------------------------------

	OutPt* Clipper::AddOutPt(TEdge *e, const IntPoint &pt)
	{
		bool ToFront = (e->Side == esLeft);
		if (e->OutIdx < 0)
		{
			OutRec *outRec = CreateOutRec();
			outRec->IsOpen = (e->WindDelta == 0);
			OutPt* newOp = new OutPt;
			outRec->Pts = newOp;
			newOp->Idx = outRec->Idx;
			newOp->Pt = pt;
			newOp->Next = newOp;
			newOp->Prev = newOp;
			if (!outRec->IsOpen)
				SetHoleState(e, outRec);
			e->OutIdx = outRec->Idx;
			return newOp;
		}
		else
		{
			OutRec *outRec = m_PolyOuts[e->OutIdx];
			//OutRec.Pts is the 'Left-most' point & OutRec.Pts.Prev is the 'Right-most'
			OutPt* op = outRec->Pts;

			if (ToFront && (pt == op->Pt)) return op;
			else if (!ToFront && (pt == op->Prev->Pt)) return op->Prev;

			OutPt* newOp = new OutPt;
			newOp->Idx = outRec->Idx;
			newOp->Pt = pt;
			newOp->Next = op;
			newOp->Prev = op->Prev;
			newOp->Prev->Next = newOp;
			op->Prev = newOp;
			if (ToFront) outRec->Pts = newOp;
			return newOp;
		}
	}
	//------------------------------------------------------------------------------

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

	inline bool IsMinima(TEdge *e)
	{
		return e && (e->Prev->NextInLML != e) && (e->Next->NextInLML != e);
	}
	//------------------------------------------------------------------------------

	inline bool IsMaxima(TEdge *e, const cInt Y)
	{
		return e && e->Top.Y == Y && !e->NextInLML;
	}
	//------------------------------------------------------------------------------

	inline bool IsIntermediate(TEdge *e, const cInt Y)
	{
		return e->Top.Y == Y && e->NextInLML;
	}
	//------------------------------------------------------------------------------

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

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

	void Clipper::SwapPositionsInAEL(TEdge *Edge1, TEdge *Edge2)
	{
		//check that one or other edge hasn't already been removed from AEL ...
		if (Edge1->NextInAEL == Edge1->PrevInAEL ||
			Edge2->NextInAEL == Edge2->PrevInAEL) return;

		if (Edge1->NextInAEL == Edge2)
		{
			TEdge* Next = Edge2->NextInAEL;
			if (Next) Next->PrevInAEL = Edge1;
			TEdge* Prev = Edge1->PrevInAEL;
			if (Prev) Prev->NextInAEL = Edge2;
			Edge2->PrevInAEL = Prev;
			Edge2->NextInAEL = Edge1;
			Edge1->PrevInAEL = Edge2;
			Edge1->NextInAEL = Next;
		}
		else if (Edge2->NextInAEL == Edge1)
		{
			TEdge* Next = Edge1->NextInAEL;
			if (Next) Next->PrevInAEL = Edge2;
			TEdge* Prev = Edge2->PrevInAEL;
			if (Prev) Prev->NextInAEL = Edge1;
			Edge1->PrevInAEL = Prev;
			Edge1->NextInAEL = Edge2;
			Edge2->PrevInAEL = Edge1;
			Edge2->NextInAEL = Next;
		}
		else
		{
			TEdge* Next = Edge1->NextInAEL;
			TEdge* Prev = Edge1->PrevInAEL;
			Edge1->NextInAEL = Edge2->NextInAEL;
			if (Edge1->NextInAEL) Edge1->NextInAEL->PrevInAEL = Edge1;
			Edge1->PrevInAEL = Edge2->PrevInAEL;
			if (Edge1->PrevInAEL) Edge1->PrevInAEL->NextInAEL = Edge1;
			Edge2->NextInAEL = Next;
			if (Edge2->NextInAEL) Edge2->NextInAEL->PrevInAEL = Edge2;
			Edge2->PrevInAEL = Prev;
			if (Edge2->PrevInAEL) Edge2->PrevInAEL->NextInAEL = Edge2;
		}

		if (!Edge1->PrevInAEL) m_ActiveEdges = Edge1;
		else if (!Edge2->PrevInAEL) m_ActiveEdges = Edge2;
	}
	//------------------------------------------------------------------------------

	void Clipper::SwapPositionsInSEL(TEdge *Edge1, TEdge *Edge2)
	{
		if (!(Edge1->NextInSEL) && !(Edge1->PrevInSEL)) return;
		if (!(Edge2->NextInSEL) && !(Edge2->PrevInSEL)) return;

		if (Edge1->NextInSEL == Edge2)
		{
			TEdge* Next = Edge2->NextInSEL;
			if (Next) Next->PrevInSEL = Edge1;
			TEdge* Prev = Edge1->PrevInSEL;
			if (Prev) Prev->NextInSEL = Edge2;
			Edge2->PrevInSEL = Prev;
			Edge2->NextInSEL = Edge1;
			Edge1->PrevInSEL = Edge2;
			Edge1->NextInSEL = Next;
		}
		else if (Edge2->NextInSEL == Edge1)
		{
			TEdge* Next = Edge1->NextInSEL;
			if (Next) Next->PrevInSEL = Edge2;
			TEdge* Prev = Edge2->PrevInSEL;
			if (Prev) Prev->NextInSEL = Edge1;
			Edge1->PrevInSEL = Prev;
			Edge1->NextInSEL = Edge2;
			Edge2->PrevInSEL = Edge1;
			Edge2->NextInSEL = Next;
		}
		else
		{
			TEdge* Next = Edge1->NextInSEL;
			TEdge* Prev = Edge1->PrevInSEL;
			Edge1->NextInSEL = Edge2->NextInSEL;
			if (Edge1->NextInSEL) Edge1->NextInSEL->PrevInSEL = Edge1;
			Edge1->PrevInSEL = Edge2->PrevInSEL;
			if (Edge1->PrevInSEL) Edge1->PrevInSEL->NextInSEL = Edge1;
			Edge2->NextInSEL = Next;
			if (Edge2->NextInSEL) Edge2->NextInSEL->PrevInSEL = Edge2;
			Edge2->PrevInSEL = Prev;
			if (Edge2->PrevInSEL) Edge2->PrevInSEL->NextInSEL = Edge2;
		}

		if (!Edge1->PrevInSEL) m_SortedEdges = Edge1;
		else if (!Edge2->PrevInSEL) m_SortedEdges = Edge2;
	}
	//------------------------------------------------------------------------------

	TEdge* GetNextInAEL(TEdge *e, Direction dir)
	{
		return dir == dLeftToRight ? e->NextInAEL : e->PrevInAEL;
	}
	//------------------------------------------------------------------------------

	void GetHorzDirection(TEdge& HorzEdge, Direction& Dir, cInt& Left, cInt& Right)
	{
		if (HorzEdge.Bot.X < HorzEdge.Top.X)
		{
			Left = HorzEdge.Bot.X;
			Right = HorzEdge.Top.X;
			Dir = dLeftToRight;
		}
		else
		{
			Left = HorzEdge.Top.X;
			Right = HorzEdge.Bot.X;
			Dir = dRightToLeft;
		}
	}
	//------------------------------------------------------------------------

	/*******************************************************************************
	* Notes: Horizontal edges (HEs) at scanline intersections (ie at the Top or    *
	* Bottom of a scanbeam) are processed as if layered. The order in which HEs    *
	* are processed doesn't matter. HEs intersect with other HE Bot.Xs only [#]    *
	* (or they could intersect with Top.Xs only, ie EITHER Bot.Xs OR Top.Xs),      *
	* and with other non-horizontal edges [*]. Once these intersections are        *
	* processed, intermediate HEs then 'promote' the Edge above (NextInLML) into   *
	* the AEL. These 'promoted' edges may in turn intersect [%] with other HEs.    *
	*******************************************************************************/

	void Clipper::ProcessHorizontal(TEdge *horzEdge, bool isTopOfScanbeam)
	{
		Direction dir;
		cInt horzLeft, horzRight;

		GetHorzDirection(*horzEdge, dir, horzLeft, horzRight);

		TEdge* eLastHorz = horzEdge, *eMaxPair = 0;
		while (eLastHorz->NextInLML && IsHorizontal(*eLastHorz->NextInLML))
			eLastHorz = eLastHorz->NextInLML;
		if (!eLastHorz->NextInLML)
			eMaxPair = GetMaximaPair(eLastHorz);

		for (;;)
		{
			bool IsLastHorz = (horzEdge == eLastHorz);
			TEdge* e = GetNextInAEL(horzEdge, dir);
			while (e)
			{
				//Break if we've got to the end of an intermediate horizontal edge ...
				//nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
				if (e->Curr.X == horzEdge->Top.X && horzEdge->NextInLML &&
					e->Dx < horzEdge->NextInLML->Dx) break;

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

				if ((dir == dLeftToRight && e->Curr.X <= horzRight) ||
					(dir == dRightToLeft && e->Curr.X >= horzLeft))
				{
					//so far we're still in range of the horizontal Edge  but make sure
					//we're at the last of consec. horizontals when matching with eMaxPair
					if (e == eMaxPair && IsLastHorz)
					{

						if (horzEdge->OutIdx >= 0)
						{
							OutPt* op1 = AddOutPt(horzEdge, horzEdge->Top);
							TEdge* eNextHorz = m_SortedEdges;
							while (eNextHorz)
							{
								if (eNextHorz->OutIdx >= 0 &&
									HorzSegmentsOverlap(horzEdge->Bot.X,
									horzEdge->Top.X, eNextHorz->Bot.X, eNextHorz->Top.X))
								{
									OutPt* op2 = AddOutPt(eNextHorz, eNextHorz->Bot);
									AddJoin(op2, op1, eNextHorz->Top);
								}
								eNextHorz = eNextHorz->NextInSEL;
							}
							AddGhostJoin(op1, horzEdge->Bot);
							AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge->Top);
						}
						DeleteFromAEL(horzEdge);
						DeleteFromAEL(eMaxPair);
						return;
					}
					else if (dir == dLeftToRight)
					{
						IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
						IntersectEdges(horzEdge, e, Pt);
					}
					else
					{
						IntPoint Pt = IntPoint(e->Curr.X, horzEdge->Curr.Y);
						IntersectEdges(e, horzEdge, Pt);
					}
					SwapPositionsInAEL(horzEdge, e);
				}
				else if ((dir == dLeftToRight && e->Curr.X >= horzRight) ||
					(dir == dRightToLeft && e->Curr.X <= horzLeft)) break;
				e = eNext;
			} //end while

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

		if (horzEdge->NextInLML)
		{
			if (horzEdge->OutIdx >= 0)
			{
				OutPt* op1 = AddOutPt(horzEdge, horzEdge->Top);
				if (isTopOfScanbeam) AddGhostJoin(op1, horzEdge->Bot);
				UpdateEdgeIntoAEL(horzEdge);
				if (horzEdge->WindDelta == 0) return;
				//nb: HorzEdge is no longer horizontal here
				TEdge* ePrev = horzEdge->PrevInAEL;
				TEdge* eNext = horzEdge->NextInAEL;
				if (ePrev && ePrev->Curr.X == horzEdge->Bot.X &&
					ePrev->Curr.Y == horzEdge->Bot.Y && ePrev->WindDelta != 0 &&
					(ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
					SlopesEqual(*horzEdge, *ePrev, m_UseFullRange)))
				{
					OutPt* op2 = AddOutPt(ePrev, horzEdge->Bot);
					AddJoin(op1, op2, horzEdge->Top);
				}
				else if (eNext && eNext->Curr.X == horzEdge->Bot.X &&
					eNext->Curr.Y == horzEdge->Bot.Y && eNext->WindDelta != 0 &&
					eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
					SlopesEqual(*horzEdge, *eNext, m_UseFullRange))
				{
					OutPt* op2 = AddOutPt(eNext, horzEdge->Bot);
					AddJoin(op1, op2, horzEdge->Top);
				}
			}
			else
				UpdateEdgeIntoAEL(horzEdge);
		}
		else
		{
			if (horzEdge->OutIdx >= 0) AddOutPt(horzEdge, horzEdge->Top);
			DeleteFromAEL(horzEdge);
		}
	}
	//------------------------------------------------------------------------------

	void Clipper::UpdateEdgeIntoAEL(TEdge *&e)
	{
		if (!e->NextInLML) throw
			clipperException("UpdateEdgeIntoAEL: invalid call");

		e->NextInLML->OutIdx = e->OutIdx;
		TEdge* AelPrev = e->PrevInAEL;
		TEdge* AelNext = e->NextInAEL;
		if (AelPrev) AelPrev->NextInAEL = e->NextInLML;
		else m_ActiveEdges = e->NextInLML;
		if (AelNext) AelNext->PrevInAEL = e->NextInLML;
		e->NextInLML->Side = e->Side;
		e->NextInLML->WindDelta = e->WindDelta;
		e->NextInLML->WindCnt = e->WindCnt;
		e->NextInLML->WindCnt2 = e->WindCnt2;
		e = e->NextInLML;
		e->Curr = e->Bot;
		e->PrevInAEL = AelPrev;
		e->NextInAEL = AelNext;
		if (!IsHorizontal(*e)) InsertScanbeam(e->Top.Y);
	}
	//------------------------------------------------------------------------------

	bool Clipper::ProcessIntersections(const cInt topY)
	{
		if (!m_ActiveEdges) return true;
		try {
			BuildIntersectList(topY);
			size_t IlSize = m_IntersectList.size();
			if (IlSize == 0) return true;
			if (IlSize == 1 || FixupIntersectionOrder()) ProcessIntersectList();
			else return false;
		}
		catch (...)
		{
			m_SortedEdges = 0;
			DisposeIntersectNodes();
			throw clipperException("ProcessIntersections error");
		}
		m_SortedEdges = 0;
		return true;
	}
	//------------------------------------------------------------------------------

	void Clipper::DisposeIntersectNodes()
	{
		for (size_t i = 0; i < m_IntersectList.size(); ++i)
			delete m_IntersectList[i];
		m_IntersectList.clear();
	}
	//------------------------------------------------------------------------------

	void Clipper::BuildIntersectList(const cInt topY)
	{
		if (!m_ActiveEdges) return;

		//prepare for sorting ...
		TEdge* e = m_ActiveEdges;
		m_SortedEdges = e;
		while (e)
		{
			e->PrevInSEL = e->PrevInAEL;
			e->NextInSEL = e->NextInAEL;
			e->Curr.X = TopX(*e, topY);
			e = e->NextInAEL;
		}

		//bubblesort ...
		bool isModified;
		do
		{
			isModified = false;
			e = m_SortedEdges;
			while (e->NextInSEL)
			{
				TEdge *eNext = e->NextInSEL;
				IntPoint Pt;
				if (e->Curr.X > eNext->Curr.X)
				{
					IntersectPoint(*e, *eNext, Pt);
					IntersectNode * newNode = new IntersectNode;
					newNode->Edge1 = e;
					newNode->Edge2 = eNext;
					newNode->Pt = Pt;
					m_IntersectList.push_back(newNode);

					SwapPositionsInSEL(e, eNext);
					isModified = true;
				}
				else
					e = eNext;
			}
			if (e->PrevInSEL) e->PrevInSEL->NextInSEL = 0;
			else break;
		} while (isModified);
		m_SortedEdges = 0; //important
	}
	//------------------------------------------------------------------------------


	void Clipper::ProcessIntersectList()
	{
		for (size_t i = 0; i < m_IntersectList.size(); ++i)
		{
			IntersectNode* iNode = m_IntersectList[i];
			{
				IntersectEdges(iNode->Edge1, iNode->Edge2, iNode->Pt);
				SwapPositionsInAEL(iNode->Edge1, iNode->Edge2);
			}
			delete iNode;
		}
		m_IntersectList.clear();
	}
	//------------------------------------------------------------------------------

	bool IntersectListSort(IntersectNode* node1, IntersectNode* node2)
	{
		return node2->Pt.Y < node1->Pt.Y;
	}
	//------------------------------------------------------------------------------

	inline bool EdgesAdjacent(const IntersectNode &inode)
	{
		return (inode.Edge1->NextInSEL == inode.Edge2) ||
			(inode.Edge1->PrevInSEL == inode.Edge2);
	}
	//------------------------------------------------------------------------------

	bool Clipper::FixupIntersectionOrder()
	{
		//pre-condition: intersections are sorted Bottom-most first.
		//Now it's crucial that intersections are made only between adjacent edges,
		//so to ensure this the order of intersections may need adjusting ...
		CopyAELToSEL();
		std::sort(m_IntersectList.begin(), m_IntersectList.end(), IntersectListSort);
		size_t cnt = m_IntersectList.size();
		for (size_t i = 0; i < cnt; ++i)
		{
			if (!EdgesAdjacent(*m_IntersectList[i]))
			{
				size_t j = i + 1;
				while (j < cnt && !EdgesAdjacent(*m_IntersectList[j])) j++;
				if (j == cnt)  return false;
				std::swap(m_IntersectList[i], m_IntersectList[j]);
			}
			SwapPositionsInSEL(m_IntersectList[i]->Edge1, m_IntersectList[i]->Edge2);
		}
		return true;
	}
	//------------------------------------------------------------------------------

	void Clipper::DoMaxima(TEdge *e)
	{
		TEdge* eMaxPair = GetMaximaPair(e);
		if (!eMaxPair)
		{
			if (e->OutIdx >= 0)
				AddOutPt(e, e->Top);
			DeleteFromAEL(e);
			return;
		}

		TEdge* eNext = e->NextInAEL;
		while (eNext && eNext != eMaxPair)
		{
			IntersectEdges(e, eNext, e->Top);
			SwapPositionsInAEL(e, eNext);
			eNext = e->NextInAEL;
		}

		if (e->OutIdx == Unassigned && eMaxPair->OutIdx == Unassigned)
		{
			DeleteFromAEL(e);
			DeleteFromAEL(eMaxPair);
		}
		else if (e->OutIdx >= 0 && eMaxPair->OutIdx >= 0)
		{
			if (e->OutIdx >= 0) AddLocalMaxPoly(e, eMaxPair, e->Top);
			DeleteFromAEL(e);
			DeleteFromAEL(eMaxPair);
		}
#ifdef use_lines
		else if (e->WindDelta == 0)
		{
			if (e->OutIdx >= 0) 
			{
				AddOutPt(e, e->Top);
				e->OutIdx = Unassigned;
			}
			DeleteFromAEL(e);

			if (eMaxPair->OutIdx >= 0)
			{
				AddOutPt(eMaxPair, e->Top);
				eMaxPair->OutIdx = Unassigned;
			}
			DeleteFromAEL(eMaxPair);
		} 
#endif
		else throw clipperException("DoMaxima error");
	}
	//------------------------------------------------------------------------------

	void Clipper::ProcessEdgesAtTopOfScanbeam(const cInt topY)
	{
		TEdge* e = m_ActiveEdges;
		while (e)
		{
			//1. process maxima, treating them as if they're 'bent' horizontal edges,
			//   but exclude maxima with horizontal edges. nb: e can't be a horizontal.
			bool IsMaximaEdge = IsMaxima(e, topY);

			if (IsMaximaEdge)
			{
				TEdge* eMaxPair = GetMaximaPair(e);
				IsMaximaEdge = (!eMaxPair || !IsHorizontal(*eMaxPair));
			}

			if (IsMaximaEdge)
			{
				TEdge* ePrev = e->PrevInAEL;
				DoMaxima(e);
				if (!ePrev) e = m_ActiveEdges;
				else e = ePrev->NextInAEL;
			}
			else
			{
				//2. promote horizontal edges, otherwise update Curr.X and Curr.Y ...
				if (IsIntermediate(e, topY) && IsHorizontal(*e->NextInLML))
				{
					UpdateEdgeIntoAEL(e);
					if (e->OutIdx >= 0)
						AddOutPt(e, e->Bot);
					AddEdgeToSEL(e);
				}
				else
				{
					e->Curr.X = TopX(*e, topY);
					e->Curr.Y = topY;
				}

				if (m_StrictSimple)
				{
					TEdge* ePrev = e->PrevInAEL;
					if ((e->OutIdx >= 0) && (e->WindDelta != 0) && ePrev && (ePrev->OutIdx >= 0) &&
						(ePrev->Curr.X == e->Curr.X) && (ePrev->WindDelta != 0))
					{
						IntPoint pt = e->Curr;
#ifdef use_xyz
						SetZ(pt, *ePrev, *e);
#endif
						OutPt* op = AddOutPt(ePrev, pt);
						OutPt* op2 = AddOutPt(e, pt);
						AddJoin(op, op2, pt); //StrictlySimple (type-3) join
					}
				}

				e = e->NextInAEL;
			}
		}

		//3. Process horizontals at the Top of the scanbeam ...
		ProcessHorizontals(true);

		//4. Promote intermediate vertices ...
		e = m_ActiveEdges;
		while (e)
		{
			if (IsIntermediate(e, topY))
			{
				OutPt* op = 0;
				if (e->OutIdx >= 0)
					op = AddOutPt(e, e->Top);
				UpdateEdgeIntoAEL(e);

				//if output polygons share an edge, they'll need joining later ...
				TEdge* ePrev = e->PrevInAEL;
				TEdge* eNext = e->NextInAEL;
				if (ePrev && ePrev->Curr.X == e->Bot.X &&
					ePrev->Curr.Y == e->Bot.Y && op &&
					ePrev->OutIdx >= 0 && ePrev->Curr.Y > ePrev->Top.Y &&
					SlopesEqual(*e, *ePrev, m_UseFullRange) &&
					(e->WindDelta != 0) && (ePrev->WindDelta != 0))
				{
					OutPt* op2 = AddOutPt(ePrev, e->Bot);
					AddJoin(op, op2, e->Top);
				}
				else if (eNext && eNext->Curr.X == e->Bot.X &&
					eNext->Curr.Y == e->Bot.Y && op &&
					eNext->OutIdx >= 0 && eNext->Curr.Y > eNext->Top.Y &&
					SlopesEqual(*e, *eNext, m_UseFullRange) &&
					(e->WindDelta != 0) && (eNext->WindDelta != 0))
				{
					OutPt* op2 = AddOutPt(eNext, e->Bot);
					AddJoin(op, op2, e->Top);
				}
			}
			e = e->NextInAEL;
		}
	}
	//------------------------------------------------------------------------------

	void Clipper::FixupOutPolygon(OutRec &outrec)
	{
		//FixupOutPolygon() - removes duplicate points and simplifies consecutive
		//parallel edges by removing the middle vertex.
		OutPt *lastOK = 0;
		outrec.BottomPt = 0;
		OutPt *pp = outrec.Pts;

		for (;;)
		{
			if (pp->Prev == pp || pp->Prev == pp->Next)
			{
				DisposeOutPts(pp);
				outrec.Pts = 0;
				return;
			}

			//test for duplicate points and collinear edges ...
			if ((pp->Pt == pp->Next->Pt) || (pp->Pt == pp->Prev->Pt) ||
				(SlopesEqual(pp->Prev->Pt, pp->Pt, pp->Next->Pt, m_UseFullRange) &&
				(!m_PreserveCollinear ||
				!Pt2IsBetweenPt1AndPt3(pp->Prev->Pt, pp->Pt, pp->Next->Pt))))
			{
				lastOK = 0;
				OutPt *tmp = pp;
				pp->Prev->Next = pp->Next;
				pp->Next->Prev = pp->Prev;
				pp = pp->Prev;
				delete tmp;
			}
			else if (pp == lastOK) break;
			else
			{
				if (!lastOK) lastOK = pp;
				pp = pp->Next;
			}
		}
		outrec.Pts = pp;
	}
	//------------------------------------------------------------------------------

	int PointCount(OutPt *Pts)
	{
		if (!Pts) return 0;
		int result = 0;
		OutPt* p = Pts;
		do
		{
			result++;
			p = p->Next;
		} while (p != Pts);
		return result;
	}
	//------------------------------------------------------------------------------

	void Clipper::BuildResult(Paths &polys)
	{
		polys.reserve(m_PolyOuts.size());
		for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
		{
			if (!m_PolyOuts[i]->Pts) continue;
			Path pg;
			OutPt* p = m_PolyOuts[i]->Pts->Prev;
			int cnt = PointCount(p);
			if (cnt < 2) continue;
			pg.reserve(cnt);
			for (int j = 0; j < cnt; ++j)
			{
				pg.push_back(p->Pt);
				p = p->Prev;
			}
			polys.push_back(pg);
		}
	}
	//------------------------------------------------------------------------------

	void Clipper::BuildResult2(PolyTree& polytree)
	{
		polytree.Clear();
		polytree.AllNodes.reserve(m_PolyOuts.size());
		//add each output polygon/contour to polytree ...
		for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
		{
			OutRec* outRec = m_PolyOuts[i];
			int cnt = PointCount(outRec->Pts);
			if ((outRec->IsOpen && cnt < 2) || (!outRec->IsOpen && cnt < 3)) continue;
			FixHoleLinkage(*outRec);
			PolyNode* pn = new PolyNode();
			//nb: polytree takes ownership of all the PolyNodes
			polytree.AllNodes.push_back(pn);
			outRec->PolyNd = pn;
			pn->Parent = 0;
			pn->Index = 0;
			pn->Contour.reserve(cnt);
			OutPt *op = outRec->Pts->Prev;
			for (int j = 0; j < cnt; j++)
			{
				pn->Contour.push_back(op->Pt);
				op = op->Prev;
			}
		}

		//fixup PolyNode links etc ...
		polytree.Childs.reserve(m_PolyOuts.size());
		for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); i++)
		{
			OutRec* outRec = m_PolyOuts[i];
			if (!outRec->PolyNd) continue;
			if (outRec->IsOpen)
			{
				outRec->PolyNd->m_IsOpen = true;
				polytree.AddChild(*outRec->PolyNd);
			}
			else if (outRec->FirstLeft && outRec->FirstLeft->PolyNd)
				outRec->FirstLeft->PolyNd->AddChild(*outRec->PolyNd);
			else
				polytree.AddChild(*outRec->PolyNd);
		}
	}
	//------------------------------------------------------------------------------

	void SwapIntersectNodes(IntersectNode &int1, IntersectNode &int2)
	{
		//just swap the contents (because fIntersectNodes is a single-linked-list)
		IntersectNode inode = int1; //gets a copy of Int1
		int1.Edge1 = int2.Edge1;
		int1.Edge2 = int2.Edge2;
		int1.Pt = int2.Pt;
		int2.Edge1 = inode.Edge1;
		int2.Edge2 = inode.Edge2;
		int2.Pt = inode.Pt;
	}
	//------------------------------------------------------------------------------

	inline bool E2InsertsBeforeE1(TEdge &e1, TEdge &e2)
	{
		if (e2.Curr.X == e1.Curr.X)
		{
			if (e2.Top.Y > e1.Top.Y)
				return e2.Top.X < TopX(e1, e2.Top.Y);
			else return e1.Top.X > TopX(e2, e1.Top.Y);
		}
		else return e2.Curr.X < e1.Curr.X;
	}
	//------------------------------------------------------------------------------

	bool GetOverlap(const cInt a1, const cInt a2, const cInt b1, const cInt b2,
		cInt& Left, cInt& Right)
	{
		if (a1 < a2)
		{
			if (b1 < b2) { Left = std::max(a1, b1); Right = std::min(a2, b2); }
			else { Left = std::max(a1, b2); Right = std::min(a2, b1); }
		}
		else
		{
			if (b1 < b2) { Left = std::max(a2, b1); Right = std::min(a1, b2); }
			else { Left = std::max(a2, b2); Right = std::min(a1, b1); }
		}
		return Left < Right;
	}
	//------------------------------------------------------------------------------

	inline void UpdateOutPtIdxs(OutRec& outrec)
	{
		OutPt* op = outrec.Pts;
		do
		{
			op->Idx = outrec.Idx;
			op = op->Prev;
		} while (op != outrec.Pts);
	}
	//------------------------------------------------------------------------------

	void Clipper::InsertEdgeIntoAEL(TEdge *edge, TEdge* startEdge)
	{
		if (!m_ActiveEdges)
		{
			edge->PrevInAEL = 0;
			edge->NextInAEL = 0;
			m_ActiveEdges = edge;
		}
		else if (!startEdge && E2InsertsBeforeE1(*m_ActiveEdges, *edge))
		{
			edge->PrevInAEL = 0;
			edge->NextInAEL = m_ActiveEdges;
			m_ActiveEdges->PrevInAEL = edge;
			m_ActiveEdges = edge;
		}
		else
		{
			if (!startEdge) startEdge = m_ActiveEdges;
			while (startEdge->NextInAEL  &&
				!E2InsertsBeforeE1(*startEdge->NextInAEL, *edge))
				startEdge = startEdge->NextInAEL;
			edge->NextInAEL = startEdge->NextInAEL;
			if (startEdge->NextInAEL) startEdge->NextInAEL->PrevInAEL = edge;
			edge->PrevInAEL = startEdge;
			startEdge->NextInAEL = edge;
		}
	}
	//----------------------------------------------------------------------

	OutPt* DupOutPt(OutPt* outPt, bool InsertAfter)
	{
		OutPt* result = new OutPt;
		result->Pt = outPt->Pt;
		result->Idx = outPt->Idx;
		if (InsertAfter)
		{
			result->Next = outPt->Next;
			result->Prev = outPt;
			outPt->Next->Prev = result;
			outPt->Next = result;
		}
		else
		{
			result->Prev = outPt->Prev;
			result->Next = outPt;
			outPt->Prev->Next = result;
			outPt->Prev = result;
		}
		return result;
	}
	//------------------------------------------------------------------------------

	bool JoinHorz(OutPt* op1, OutPt* op1b, OutPt* op2, OutPt* op2b,
		const IntPoint Pt, bool DiscardLeft)
	{
		Direction Dir1 = (op1->Pt.X > op1b->Pt.X ? dRightToLeft : dLeftToRight);
		Direction Dir2 = (op2->Pt.X > op2b->Pt.X ? dRightToLeft : dLeftToRight);
		if (Dir1 == Dir2) return false;

		//When DiscardLeft, we want Op1b to be on the Left of Op1, otherwise we
		//want Op1b to be on the Right. (And likewise with Op2 and Op2b.)
		//So, to facilitate this while inserting Op1b and Op2b ...
		//when DiscardLeft, make sure we're AT or RIGHT of Pt before adding Op1b,
		//otherwise make sure we're AT or LEFT of Pt. (Likewise with Op2b.)
		if (Dir1 == dLeftToRight)
		{
			while (op1->Next->Pt.X <= Pt.X &&
				op1->Next->Pt.X >= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
				op1 = op1->Next;
			if (DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
			op1b = DupOutPt(op1, !DiscardLeft);
			if (op1b->Pt != Pt)
			{
				op1 = op1b;
				op1->Pt = Pt;
				op1b = DupOutPt(op1, !DiscardLeft);
			}
		}
		else
		{
			while (op1->Next->Pt.X >= Pt.X &&
				op1->Next->Pt.X <= op1->Pt.X && op1->Next->Pt.Y == Pt.Y)
				op1 = op1->Next;
			if (!DiscardLeft && (op1->Pt.X != Pt.X)) op1 = op1->Next;
			op1b = DupOutPt(op1, DiscardLeft);
			if (op1b->Pt != Pt)
			{
				op1 = op1b;
				op1->Pt = Pt;
				op1b = DupOutPt(op1, DiscardLeft);
			}
		}

		if (Dir2 == dLeftToRight)
		{
			while (op2->Next->Pt.X <= Pt.X &&
				op2->Next->Pt.X >= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
				op2 = op2->Next;
			if (DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
			op2b = DupOutPt(op2, !DiscardLeft);
			if (op2b->Pt != Pt)
			{
				op2 = op2b;
				op2->Pt = Pt;
				op2b = DupOutPt(op2, !DiscardLeft);
			};
		}
		else
		{
			while (op2->Next->Pt.X >= Pt.X &&
				op2->Next->Pt.X <= op2->Pt.X && op2->Next->Pt.Y == Pt.Y)
				op2 = op2->Next;
			if (!DiscardLeft && (op2->Pt.X != Pt.X)) op2 = op2->Next;
			op2b = DupOutPt(op2, DiscardLeft);
			if (op2b->Pt != Pt)
			{
				op2 = op2b;
				op2->Pt = Pt;
				op2b = DupOutPt(op2, DiscardLeft);
			};
		};

		if ((Dir1 == dLeftToRight) == DiscardLeft)
		{
			op1->Prev = op2;
			op2->Next = op1;
			op1b->Next = op2b;
			op2b->Prev = op1b;
		}
		else
		{
			op1->Next = op2;
			op2->Prev = op1;
			op1b->Prev = op2b;
			op2b->Next = op1b;
		}
		return true;
	}
	//------------------------------------------------------------------------------

	bool Clipper::JoinPoints(Join *j, OutRec* outRec1, OutRec* outRec2)
	{
		OutPt *op1 = j->OutPt1, *op1b;
		OutPt *op2 = j->OutPt2, *op2b;

		//There are 3 kinds of joins for output polygons ...
		//1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are a vertices anywhere
		//along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
		//2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
		//location at the Bottom of the overlapping segment (& Join.OffPt is above).
		//3. StrictSimple joins where edges touch but are not collinear and where
		//Join.OutPt1, Join.OutPt2 & Join.OffPt all share the same point.
		bool isHorizontal = (j->OutPt1->Pt.Y == j->OffPt.Y);

		if (isHorizontal && (j->OffPt == j->OutPt1->Pt) &&
			(j->OffPt == j->OutPt2->Pt))
		{
			//Strictly Simple join ...
			if (outRec1 != outRec2) return false;
			op1b = j->OutPt1->Next;
			while (op1b != op1 && (op1b->Pt == j->OffPt))
				op1b = op1b->Next;
			bool reverse1 = (op1b->Pt.Y > j->OffPt.Y);
			op2b = j->OutPt2->Next;
			while (op2b != op2 && (op2b->Pt == j->OffPt))
				op2b = op2b->Next;
			bool reverse2 = (op2b->Pt.Y > j->OffPt.Y);
			if (reverse1 == reverse2) return false;
			if (reverse1)
			{
				op1b = DupOutPt(op1, false);
				op2b = DupOutPt(op2, true);
				op1->Prev = op2;
				op2->Next = op1;
				op1b->Next = op2b;
				op2b->Prev = op1b;
				j->OutPt1 = op1;
				j->OutPt2 = op1b;
				return true;
			}
			else
			{
				op1b = DupOutPt(op1, true);
				op2b = DupOutPt(op2, false);
				op1->Next = op2;
				op2->Prev = op1;
				op1b->Prev = op2b;
				op2b->Next = op1b;
				j->OutPt1 = op1;
				j->OutPt2 = op1b;
				return true;
			}
		}
		else if (isHorizontal)
		{
			//treat horizontal joins differently to non-horizontal joins since with
			//them we're not yet sure where the overlapping is. OutPt1.Pt & OutPt2.Pt
			//may be anywhere along the horizontal edge.
			op1b = op1;
			while (op1->Prev->Pt.Y == op1->Pt.Y && op1->Prev != op1b && op1->Prev != op2)
				op1 = op1->Prev;
			while (op1b->Next->Pt.Y == op1b->Pt.Y && op1b->Next != op1 && op1b->Next != op2)
				op1b = op1b->Next;
			if (op1b->Next == op1 || op1b->Next == op2) return false; //a flat 'polygon'

			op2b = op2;
			while (op2->Prev->Pt.Y == op2->Pt.Y && op2->Prev != op2b && op2->Prev != op1b)
				op2 = op2->Prev;
			while (op2b->Next->Pt.Y == op2b->Pt.Y && op2b->Next != op2 && op2b->Next != op1)
				op2b = op2b->Next;
			if (op2b->Next == op2 || op2b->Next == op1) return false; //a flat 'polygon'

			cInt Left, Right;
			//Op1 --> Op1b & Op2 --> Op2b are the extremites of the horizontal edges
			if (!GetOverlap(op1->Pt.X, op1b->Pt.X, op2->Pt.X, op2b->Pt.X, Left, Right))
				return false;

			//DiscardLeftSide: when overlapping edges are joined, a spike will created
			//which needs to be cleaned up. However, we don't want Op1 or Op2 caught up
			//on the discard Side as either may still be needed for other joins ...
			IntPoint Pt;
			bool DiscardLeftSide;
			if (op1->Pt.X >= Left && op1->Pt.X <= Right)
			{
				Pt = op1->Pt; DiscardLeftSide = (op1->Pt.X > op1b->Pt.X);
			}
			else if (op2->Pt.X >= Left&& op2->Pt.X <= Right)
			{
				Pt = op2->Pt; DiscardLeftSide = (op2->Pt.X > op2b->Pt.X);
			}
			else if (op1b->Pt.X >= Left && op1b->Pt.X <= Right)
			{
				Pt = op1b->Pt; DiscardLeftSide = op1b->Pt.X > op1->Pt.X;
			}
			else
			{
				Pt = op2b->Pt; DiscardLeftSide = (op2b->Pt.X > op2->Pt.X);
			}
			j->OutPt1 = op1; j->OutPt2 = op2;
			return JoinHorz(op1, op1b, op2, op2b, Pt, DiscardLeftSide);
		}
		else
		{
			//nb: For non-horizontal joins ...
			//    1. Jr.OutPt1.Pt.Y == Jr.OutPt2.Pt.Y
			//    2. Jr.OutPt1.Pt > Jr.OffPt.Y

			//make sure the polygons are correctly oriented ...
			op1b = op1->Next;
			while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Next;
			bool Reverse1 = ((op1b->Pt.Y > op1->Pt.Y) ||
				!SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange));
			if (Reverse1)
			{
				op1b = op1->Prev;
				while ((op1b->Pt == op1->Pt) && (op1b != op1)) op1b = op1b->Prev;
				if ((op1b->Pt.Y > op1->Pt.Y) ||
					!SlopesEqual(op1->Pt, op1b->Pt, j->OffPt, m_UseFullRange)) return false;
			};
			op2b = op2->Next;
			while ((op2b->Pt == op2->Pt) && (op2b != op2))op2b = op2b->Next;
			bool Reverse2 = ((op2b->Pt.Y > op2->Pt.Y) ||
				!SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange));
			if (Reverse2)
			{
				op2b = op2->Prev;
				while ((op2b->Pt == op2->Pt) && (op2b != op2)) op2b = op2b->Prev;
				if ((op2b->Pt.Y > op2->Pt.Y) ||
					!SlopesEqual(op2->Pt, op2b->Pt, j->OffPt, m_UseFullRange)) return false;
			}

			if ((op1b == op1) || (op2b == op2) || (op1b == op2b) ||
				((outRec1 == outRec2) && (Reverse1 == Reverse2))) return false;

			if (Reverse1)
			{
				op1b = DupOutPt(op1, false);
				op2b = DupOutPt(op2, true);
				op1->Prev = op2;
				op2->Next = op1;
				op1b->Next = op2b;
				op2b->Prev = op1b;
				j->OutPt1 = op1;
				j->OutPt2 = op1b;
				return true;
			}
			else
			{
				op1b = DupOutPt(op1, true);
				op2b = DupOutPt(op2, false);
				op1->Next = op2;
				op2->Prev = op1;
				op1b->Prev = op2b;
				op2b->Next = op1b;
				j->OutPt1 = op1;
				j->OutPt2 = op1b;
				return true;
			}
		}
	}
	//----------------------------------------------------------------------

	static OutRec* ParseFirstLeft(OutRec* FirstLeft)
	{
		while (FirstLeft && !FirstLeft->Pts)
			FirstLeft = FirstLeft->FirstLeft;
		return FirstLeft;
	}
	//------------------------------------------------------------------------------

	void Clipper::FixupFirstLefts1(OutRec* OldOutRec, OutRec* NewOutRec)
	{
		//tests if NewOutRec contains the polygon before reassigning FirstLeft
		for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
		{
			OutRec* outRec = m_PolyOuts[i];
			if (!outRec->Pts || !outRec->FirstLeft) continue;
			OutRec* firstLeft = ParseFirstLeft(outRec->FirstLeft);
			if (firstLeft == OldOutRec)
			{
				if (Poly2ContainsPoly1(outRec->Pts, NewOutRec->Pts))
					outRec->FirstLeft = NewOutRec;
			}
		}
	}
	//----------------------------------------------------------------------

	void Clipper::FixupFirstLefts2(OutRec* OldOutRec, OutRec* NewOutRec)
	{
		//reassigns FirstLeft WITHOUT testing if NewOutRec contains the polygon
		for (PolyOutList::size_type i = 0; i < m_PolyOuts.size(); ++i)
		{
			OutRec* outRec = m_PolyOuts[i];
			if (outRec->FirstLeft == OldOutRec) outRec->FirstLeft = NewOutRec;
		}
	}
	//----------------------------------------------------------------------

	void Clipper::JoinCommonEdges()
	{
		for (JoinList::size_type i = 0; i < m_Joins.size(); i++)
		{
			Join* join = m_Joins[i];

			OutRec *outRec1 = GetOutRec(join->OutPt1->Idx);
			OutRec *outRec2 = GetOutRec(join->OutPt2->Idx);

			if (!outRec1->Pts || !outRec2->Pts) continue;

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

			if (!JoinPoints(join, outRec1, outRec2)) continue;

			if (outRec1 == outRec2)
			{
				//instead of joining two polygons, we've just created a new one by
				//splitting one polygon into two.
				outRec1->Pts = join->OutPt1;
				outRec1->BottomPt = 0;
				outRec2 = CreateOutRec();
				outRec2->Pts = join->OutPt2;

				//update all OutRec2.Pts Idx's ...
				UpdateOutPtIdxs(*outRec2);

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

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

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

					if ((outRec2->IsHole ^ m_ReverseOutput) == (Area(*outRec2) > 0))
						ReversePolyPtLinks(outRec2->Pts);

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

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

					if ((outRec1->IsHole ^ m_ReverseOutput) == (Area(*outRec1) > 0))
						ReversePolyPtLinks(outRec1->Pts);
				}
				else
				{
					//the 2 polygons are completely separate ...
					outRec2->IsHole = outRec1->IsHole;
					outRec2->FirstLeft = outRec1->FirstLeft;

					//fixup FirstLeft pointers that may need reassigning to OutRec2
					if (m_UsingPolyTree) FixupFirstLefts1(outRec1, outRec2);
				}

			}
			else
			{
				//joined 2 polygons together ...

				outRec2->Pts = 0;
				outRec2->BottomPt = 0;
				outRec2->Idx = outRec1->Idx;

				outRec1->IsHole = holeStateRec->IsHole;
				if (holeStateRec == outRec2)
					outRec1->FirstLeft = outRec2->FirstLeft;
				outRec2->FirstLeft = outRec1;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

	void CleanPolygon(const Path& in_poly, Path& out_poly, double distance)
	{
		//distance = proximity in units/pixels below which vertices
		//will be stripped. Default ~= sqrt(2).

		size_t size = in_poly.size();

		if (size == 0)
		{
			out_poly.clear();
			return;
		}

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

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

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

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

	void CleanPolygons(const Paths& in_polys, Paths& out_polys, double distance)
	{
		for (Paths::size_type i = 0; i < in_polys.size(); ++i)
			CleanPolygon(in_polys[i], out_polys[i], distance);
	}
	//------------------------------------------------------------------------------

	void CleanPolygons(Paths& polys, double distance)
	{
		CleanPolygons(polys, polys, distance);
	}
	//------------------------------------------------------------------------------

	void Minkowski(const Path& poly, const Path& path,
		Paths& solution, bool isSum, bool isClosed)
	{
		int delta = (isClosed ? 1 : 0);
		size_t polyCnt = poly.size();
		size_t pathCnt = path.size();
		Paths pp;
		pp.reserve(pathCnt);
		if (isSum)
			for (size_t i = 0; i < pathCnt; ++i)
			{
				Path p;
				p.reserve(polyCnt);
				for (size_t j = 0; j < poly.size(); ++j)
					p.push_back(IntPoint(path[i].X + poly[j].X, path[i].Y + poly[j].Y));
				pp.push_back(p);
			}
		else
			for (size_t i = 0; i < pathCnt; ++i)
			{
				Path p;
				p.reserve(polyCnt);
				for (size_t j = 0; j < poly.size(); ++j)
					p.push_back(IntPoint(path[i].X - poly[j].X, path[i].Y - poly[j].Y));
				pp.push_back(p);
			}

		solution.clear();
		solution.reserve((pathCnt + delta) * (polyCnt + 1));
		for (size_t i = 0; i < pathCnt - 1 + delta; ++i)
			for (size_t j = 0; j < polyCnt; ++j)
			{
				Path quad;
				quad.reserve(4);
				quad.push_back(pp[i % pathCnt][j % polyCnt]);
				quad.push_back(pp[(i + 1) % pathCnt][j % polyCnt]);
				quad.push_back(pp[(i + 1) % pathCnt][(j + 1) % polyCnt]);
				quad.push_back(pp[i % pathCnt][(j + 1) % polyCnt]);
				if (!Orientation(quad)) ReversePath(quad);
				solution.push_back(quad);
			}
	}
	//------------------------------------------------------------------------------

	void MinkowskiSum(const Path& pattern, const Path& path, Paths& solution, bool pathIsClosed)
	{
		Minkowski(pattern, path, solution, true, pathIsClosed);
		Clipper c;
		c.AddPaths(solution, ptSubject, true);
		c.Execute(ctUnion, solution, pftNonZero, pftNonZero);
	}
	//------------------------------------------------------------------------------

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

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

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

	enum NodeType { ntAny, ntOpen, ntClosed };

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

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

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

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

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

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

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

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

} //ClipperLib namespace