/*******************************************************************************
*                                                                              *
* Author    :  Angus Johnson                                                   *
* Version   :  6.4.0                                                           *
* Date      :  2 July 2015                                                     *
* Website   :  http://www.angusj.com                                           *
* Copyright :  Angus Johnson 2010-2015                                         *
*                                                                              *
* 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.                                          *
*                                                                              *
*******************************************************************************/

//use_int32: When enabled 32bit ints are used instead of 64bit ints. This
//improve performance but coordinate values are limited to the range +/- 46340
//#define use_int32

//use_xyz: adds a Z member to IntPoint. Adds a minor cost to performance.
//#define use_xyz

//use_lines: Enables open path clipping. Adds a very minor cost to performance.
#define use_lines


using System;
using System.Collections.Generic;

//using System.Text;          //for Int128.AsString() & StringBuilder
//using System.IO;            //debugging with streamReader & StreamWriter
//using System.Windows.Forms; //debugging to clipboard

namespace Mapbox.VectorTile.Geometry
{

	namespace InteralClipperLib
	{

#if use_int32
  using cInt = Int32;
#else
		using cInt = Int64;
#endif

		using Path = List<InternalClipper.IntPoint>;
		using Paths = List<List<InternalClipper.IntPoint>>;

		//only available with .Net >= 4
		//[System.Diagnostics.CodeAnalysis.ExcludeFromCodeCoverage]
		internal class InternalClipper
		{

			public struct DoublePoint
			{
				public double X;
				public double Y;

				public DoublePoint(double x = 0, double y = 0)
				{
					this.X = x;
					this.Y = y;
				}
				public DoublePoint(DoublePoint dp)
				{
					this.X = dp.X;
					this.Y = dp.Y;
				}
				public DoublePoint(IntPoint ip)
				{
					this.X = ip.X;
					this.Y = ip.Y;
				}
			};


			//------------------------------------------------------------------------------
			// PolyTree & PolyNode classes
			//------------------------------------------------------------------------------

			public class PolyTree : PolyNode
			{
				internal List<PolyNode> m_AllPolys = new List<PolyNode>();

				//The GC probably handles this cleanup more efficiently ...
				//~PolyTree(){Clear();}

				public void Clear()
				{
					int polyCnt = m_AllPolys.Count;
					for (int i = 0; i < polyCnt; i++)
					{
						m_AllPolys[i] = null;
					}
					m_AllPolys.Clear();
					m_Childs.Clear();
				}

				public PolyNode GetFirst()
				{
					if (m_Childs.Count > 0)
						return m_Childs[0];
					else
						return null;
				}

				public int Total
				{
					get
					{
						int result = m_AllPolys.Count;
						//with negative offsets, ignore the hidden outer polygon ...
						if (result > 0 && m_Childs[0] != m_AllPolys[0])
							result--;
						return result;
					}
				}

			}

			public class PolyNode
			{
				internal PolyNode m_Parent;
				internal Path m_polygon = new Path();
				internal int m_Index;
				internal JoinType m_jointype;
				internal EndType m_endtype;
				internal List<PolyNode> m_Childs = new List<PolyNode>();

				private bool IsHoleNode()
				{
					bool result = true;
					PolyNode node = m_Parent;
					while (node != null)
					{
						result = !result;
						node = node.m_Parent;
					}
					return result;
				}

				public int ChildCount
				{
					get { return m_Childs.Count; }
				}

				public Path Contour
				{
					get { return m_polygon; }
				}

				internal void AddChild(PolyNode Child)
				{
					int cnt = m_Childs.Count;
					m_Childs.Add(Child);
					Child.m_Parent = this;
					Child.m_Index = cnt;
				}

				public PolyNode GetNext()
				{
					if (m_Childs.Count > 0)
						return m_Childs[0];
					else
						return GetNextSiblingUp();
				}

				internal PolyNode GetNextSiblingUp()
				{
					if (m_Parent == null)
						return null;
					else if (m_Index == m_Parent.m_Childs.Count - 1)
						return m_Parent.GetNextSiblingUp();
					else
						return m_Parent.m_Childs[m_Index + 1];
				}

				public List<PolyNode> Childs
				{
					get { return m_Childs; }
				}

				public PolyNode Parent
				{
					get { return m_Parent; }
				}

				public bool IsHole
				{
					get { return IsHoleNode(); }
				}

				public bool IsOpen { get; set; }
			}


			//------------------------------------------------------------------------------
			// Int128 struct (enables safe math on signed 64bit integers)
			// eg Int128 val1((Int64)9223372036854775807); //ie 2^63 -1
			//    Int128 val2((Int64)9223372036854775807);
			//    Int128 val3 = val1 * val2;
			//    val3.ToString => "85070591730234615847396907784232501249" (8.5e+37)
			//------------------------------------------------------------------------------

			internal struct Int128
			{
				private Int64 hi;
				private UInt64 lo;

				public Int128(Int64 _lo)
				{
					lo = (UInt64)_lo;
					if (_lo < 0)
						hi = -1;
					else
						hi = 0;
				}

				public Int128(Int64 _hi, UInt64 _lo)
				{
					lo = _lo;
					hi = _hi;
				}

				public Int128(Int128 val)
				{
					hi = val.hi;
					lo = val.lo;
				}

				public bool IsNegative()
				{
					return hi < 0;
				}

				public static bool operator ==(Int128 val1, Int128 val2)
				{
					if ((object)val1 == (object)val2)
						return true;
					else if ((object)val1 == null || (object)val2 == null)
						return false;
					return (val1.hi == val2.hi && val1.lo == val2.lo);
				}

				public static bool operator !=(Int128 val1, Int128 val2)
				{
					return !(val1 == val2);
				}

				public override bool Equals(System.Object obj)
				{
					if (obj == null || !(obj is Int128))
						return false;
					Int128 i128 = (Int128)obj;
					return (i128.hi == hi && i128.lo == lo);
				}

				public override int GetHashCode()
				{
					return hi.GetHashCode() ^ lo.GetHashCode();
				}

				public static bool operator >(Int128 val1, Int128 val2)
				{
					if (val1.hi != val2.hi)
						return val1.hi > val2.hi;
					else
						return val1.lo > val2.lo;
				}

				public static bool operator <(Int128 val1, Int128 val2)
				{
					if (val1.hi != val2.hi)
						return val1.hi < val2.hi;
					else
						return val1.lo < val2.lo;
				}

				public static Int128 operator +(Int128 lhs, Int128 rhs)
				{
					lhs.hi += rhs.hi;
					lhs.lo += rhs.lo;
					if (lhs.lo < rhs.lo)
						lhs.hi++;
					return lhs;
				}

				public static Int128 operator -(Int128 lhs, Int128 rhs)
				{
					return lhs + -rhs;
				}

				public static Int128 operator -(Int128 val)
				{
					if (val.lo == 0)
						return new Int128(-val.hi, 0);
					else
						return new Int128(~val.hi, ~val.lo + 1);
				}

				public static explicit operator double(Int128 val)
				{
					const double shift64 = 18446744073709551616.0; //2^64
					if (val.hi < 0)
					{
						if (val.lo == 0)
							return (double)val.hi * shift64;
						else
							return -(double)(~val.lo + ~val.hi * shift64);
					}
					else
						return (double)(val.lo + val.hi * shift64);
				}

				//nb: Constructing two new Int128 objects every time we want to multiply longs  
				//is slow. So, although calling the Int128Mul method doesn't look as clean, the 
				//code runs significantly faster than if we'd used the * operator.

				public static Int128 Int128Mul(Int64 lhs, Int64 rhs)
				{
					bool negate = (lhs < 0) != (rhs < 0);
					if (lhs < 0)
						lhs = -lhs;
					if (rhs < 0)
						rhs = -rhs;
					UInt64 int1Hi = (UInt64)lhs >> 32;
					UInt64 int1Lo = (UInt64)lhs & 0xFFFFFFFF;
					UInt64 int2Hi = (UInt64)rhs >> 32;
					UInt64 int2Lo = (UInt64)rhs & 0xFFFFFFFF;

					//nb: see comments in clipper.pas
					UInt64 a = int1Hi * int2Hi;
					UInt64 b = int1Lo * int2Lo;
					UInt64 c = int1Hi * int2Lo + int1Lo * int2Hi;

					UInt64 lo;
					Int64 hi;
					hi = (Int64)(a + (c >> 32));

					unchecked { lo = (c << 32) + b; }
					if (lo < b)
						hi++;
					Int128 result = new Int128(hi, lo);
					return negate ? -result : result;
				}

			};

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

			public struct IntPoint
			{
				public cInt X;
				public cInt Y;
#if use_xyz
    public cInt Z;
    
    public IntPoint(cInt x, cInt y, cInt z = 0)
    {
      this.X = x; this.Y = y; this.Z = z;
    }
    
    public IntPoint(double x, double y, double z = 0)
    {
      this.X = (cInt)x; this.Y = (cInt)y; this.Z = (cInt)z;
    }
    
    public IntPoint(DoublePoint dp)
    {
      this.X = (cInt)dp.X; this.Y = (cInt)dp.Y; this.Z = 0;
    }

    public IntPoint(IntPoint pt)
    {
      this.X = pt.X; this.Y = pt.Y; this.Z = pt.Z;
    }
#else
				public IntPoint(cInt X, cInt Y)
				{
					this.X = X;
					this.Y = Y;
				}
				public IntPoint(double x, double y)
				{
					this.X = (cInt)x;
					this.Y = (cInt)y;
				}

				public IntPoint(IntPoint pt)
				{
					this.X = pt.X;
					this.Y = pt.Y;
				}
#endif

				public static bool operator ==(IntPoint a, IntPoint b)
				{
					return a.X == b.X && a.Y == b.Y;
				}

				public static bool operator !=(IntPoint a, IntPoint b)
				{
					return a.X != b.X || a.Y != b.Y;
				}

				public override bool Equals(object obj)
				{
					if (obj == null)
						return false;
					if (obj is IntPoint)
					{
						IntPoint a = (IntPoint)obj;
						return (X == a.X) && (Y == a.Y);
					}
					else
						return false;
				}

				public override int GetHashCode()
				{
					//simply prevents a compiler warning
					return base.GetHashCode();
				}

			}// end struct IntPoint

			public struct IntRect
			{
				public cInt left;
				public cInt top;
				public cInt right;
				public cInt bottom;

				public IntRect(cInt l, cInt t, cInt r, cInt b)
				{
					this.left = l;
					this.top = t;
					this.right = r;
					this.bottom = b;
				}
				public IntRect(IntRect ir)
				{
					this.left = ir.left;
					this.top = ir.top;
					this.right = ir.right;
					this.bottom = ir.bottom;
				}
			}

			public enum ClipType { ctIntersection, ctUnion, ctDifference, ctXor };
			public enum PolyType { ptSubject, ptClip };

			//By far the most widely used winding rules for polygon filling are
			//EvenOdd & NonZero (GDI, GDI+, XLib, OpenGL, Cairo, AGG, Quartz, SVG, Gr32)
			//Others rules include Positive, Negative and ABS_GTR_EQ_TWO (only in OpenGL)
			//see http://glprogramming.com/red/chapter11.html
			public enum PolyFillType { pftEvenOdd, pftNonZero, pftPositive, pftNegative };

			public enum JoinType { jtSquare, jtRound, jtMiter };
			public enum EndType { etClosedPolygon, etClosedLine, etOpenButt, etOpenSquare, etOpenRound };

			internal enum EdgeSide { esLeft, esRight };
			internal enum Direction { dRightToLeft, dLeftToRight };

			internal class TEdge
			{
				internal IntPoint Bot;
				internal IntPoint Curr; //current (updated for every new scanbeam)
				internal IntPoint Top;
				internal IntPoint Delta;
				internal double Dx;
				internal PolyType PolyTyp;
				internal EdgeSide Side; //side only refers to current side of solution poly
				internal int WindDelta; //1 or -1 depending on winding direction
				internal int WindCnt;
				internal int WindCnt2; //winding count of the opposite polytype
				internal int OutIdx;
				internal TEdge Next;
				internal TEdge Prev;
				internal TEdge NextInLML;
				internal TEdge NextInAEL;
				internal TEdge PrevInAEL;
				internal TEdge NextInSEL;
				internal TEdge PrevInSEL;
			};

			public class IntersectNode
			{
				internal TEdge Edge1;
				internal TEdge Edge2;
				internal IntPoint Pt;
			};

			public class MyIntersectNodeSort : IComparer<IntersectNode>
			{
				public int Compare(IntersectNode node1, IntersectNode node2)
				{
					cInt i = node2.Pt.Y - node1.Pt.Y;
					if (i > 0)
						return 1;
					else if (i < 0)
						return -1;
					else
						return 0;
				}
			}

			internal class LocalMinima
			{
				internal cInt Y;
				internal TEdge LeftBound;
				internal TEdge RightBound;
				internal LocalMinima Next;
			};

			internal class Scanbeam
			{
				internal cInt Y;
				internal Scanbeam Next;
			};

			internal class Maxima
			{
				internal cInt X;
				internal Maxima Next;
				internal Maxima Prev;
			};

			//OutRec: contains a path in the clipping solution. Edges in the AEL will
			//carry a pointer to an OutRec when they are part of the clipping solution.
			internal class OutRec
			{
				internal int Idx;
				internal bool IsHole;
				internal bool IsOpen;
				internal OutRec FirstLeft; //see comments in clipper.pas
				internal OutPt Pts;
				internal OutPt BottomPt;
				internal PolyNode PolyNode;
			};

			internal class OutPt
			{
				internal int Idx;
				internal IntPoint Pt;
				internal OutPt Next;
				internal OutPt Prev;
			};

			internal class Join
			{
				internal OutPt OutPt1;
				internal OutPt OutPt2;
				internal IntPoint OffPt;
			};

			public class ClipperBase
			{
				internal const double horizontal = -3.4E+38;
				internal const int Skip = -2;
				internal const int Unassigned = -1;
				internal const double tolerance = 1.0E-20;
				internal static bool near_zero(double val) { return (val > -tolerance) && (val < tolerance); }

#if use_int32
    public const cInt loRange = 0x7FFF;
    public const cInt hiRange = 0x7FFF;
#else
				public const cInt loRange = 0x3FFFFFFF;
				public const cInt hiRange = 0x3FFFFFFFFFFFFFFFL;
#endif

				internal LocalMinima m_MinimaList;
				internal LocalMinima m_CurrentLM;
				internal List<List<TEdge>> m_edges = new List<List<TEdge>>();
				internal Scanbeam m_Scanbeam;
				internal List<OutRec> m_PolyOuts;
				internal TEdge m_ActiveEdges;
				internal bool m_UseFullRange;
				internal bool m_HasOpenPaths;

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

				public bool PreserveCollinear
				{
					get;
					set;
				}
				//------------------------------------------------------------------------------

				public void Swap(ref cInt val1, ref cInt val2)
				{
					cInt tmp = val1;
					val1 = val2;
					val2 = tmp;
				}
				//------------------------------------------------------------------------------

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

				internal bool PointIsVertex(IntPoint pt, OutPt pp)
				{
					OutPt pp2 = pp;
					do
					{
						if (pp2.Pt == pt)
							return true;
						pp2 = pp2.Next;
					}
					while (pp2 != pp);
					return false;
				}
				//------------------------------------------------------------------------------

				internal bool PointOnLineSegment(IntPoint pt,
					IntPoint linePt1, IntPoint linePt2, bool UseFullRange)
				{
					if (UseFullRange)
						return ((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
						  ((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
						  (((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
						  ((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
						  ((Int128.Int128Mul((pt.X - linePt1.X), (linePt2.Y - linePt1.Y)) ==
						  Int128.Int128Mul((linePt2.X - linePt1.X), (pt.Y - linePt1.Y)))));
					else
						return ((pt.X == linePt1.X) && (pt.Y == linePt1.Y)) ||
						  ((pt.X == linePt2.X) && (pt.Y == linePt2.Y)) ||
						  (((pt.X > linePt1.X) == (pt.X < linePt2.X)) &&
						  ((pt.Y > linePt1.Y) == (pt.Y < linePt2.Y)) &&
						  ((pt.X - linePt1.X) * (linePt2.Y - linePt1.Y) ==
							(linePt2.X - linePt1.X) * (pt.Y - linePt1.Y)));
				}
				//------------------------------------------------------------------------------

				internal bool PointOnPolygon(IntPoint pt, OutPt pp, bool UseFullRange)
				{
					OutPt pp2 = pp;
					while (true)
					{
						if (PointOnLineSegment(pt, pp2.Pt, pp2.Next.Pt, UseFullRange))
							return true;
						pp2 = pp2.Next;
						if (pp2 == pp)
							break;
					}
					return false;
				}
				//------------------------------------------------------------------------------

				internal static bool SlopesEqual(TEdge e1, TEdge e2, bool UseFullRange)
				{
					if (UseFullRange)
						return Int128.Int128Mul(e1.Delta.Y, e2.Delta.X) ==
							Int128.Int128Mul(e1.Delta.X, e2.Delta.Y);
					else
						return (cInt)(e1.Delta.Y) * (e2.Delta.X) ==
					 (cInt)(e1.Delta.X) * (e2.Delta.Y);
				}
				//------------------------------------------------------------------------------

				internal static bool SlopesEqual(IntPoint pt1, IntPoint pt2,
					IntPoint pt3, bool UseFullRange)
				{
					if (UseFullRange)
						return Int128.Int128Mul(pt1.Y - pt2.Y, pt2.X - pt3.X) ==
						  Int128.Int128Mul(pt1.X - pt2.X, pt2.Y - pt3.Y);
					else
						return
					 (cInt)(pt1.Y - pt2.Y) * (pt2.X - pt3.X) - (cInt)(pt1.X - pt2.X) * (pt2.Y - pt3.Y) == 0;
				}
				//------------------------------------------------------------------------------

				internal static bool SlopesEqual(IntPoint pt1, IntPoint pt2,
					IntPoint pt3, IntPoint pt4, bool UseFullRange)
				{
					if (UseFullRange)
						return Int128.Int128Mul(pt1.Y - pt2.Y, pt3.X - pt4.X) ==
						  Int128.Int128Mul(pt1.X - pt2.X, pt3.Y - pt4.Y);
					else
						return
					 (cInt)(pt1.Y - pt2.Y) * (pt3.X - pt4.X) - (cInt)(pt1.X - pt2.X) * (pt3.Y - pt4.Y) == 0;
				}
				//------------------------------------------------------------------------------

				internal ClipperBase() //constructor (nb: no external instantiation)
				{
					m_MinimaList = null;
					m_CurrentLM = null;
					m_UseFullRange = false;
					m_HasOpenPaths = false;
				}
				//------------------------------------------------------------------------------

				public virtual void Clear()
				{
					DisposeLocalMinimaList();
					int edgesCnt = m_edges.Count;
					for (int i = 0; i < edgesCnt; ++i)
					{
						int edgesIcount = m_edges[i].Count;
						for (int j = 0; j < edgesIcount; ++j)
						{
							m_edges[i][j] = null;
						}
						m_edges[i].Clear();
					}
					m_edges.Clear();
					m_UseFullRange = false;
					m_HasOpenPaths = false;
				}
				//------------------------------------------------------------------------------

				private void DisposeLocalMinimaList()
				{
					while (m_MinimaList != null)
					{
						LocalMinima tmpLm = m_MinimaList.Next;
						m_MinimaList = null;
						m_MinimaList = tmpLm;
					}
					m_CurrentLM = null;
				}
				//------------------------------------------------------------------------------

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

				private void InitEdge(TEdge e, TEdge eNext,
				  TEdge ePrev, IntPoint pt)
				{
					e.Next = eNext;
					e.Prev = ePrev;
					e.Curr = pt;
					e.OutIdx = Unassigned;
				}
				//------------------------------------------------------------------------------

				private void InitEdge2(TEdge e, PolyType polyType)
				{
					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 = polyType;
				}
				//------------------------------------------------------------------------------

				private TEdge FindNextLocMin(TEdge E)
				{
					TEdge E2;
					for (; ; )
					{
						while (E.Bot != E.Prev.Bot || E.Curr == E.Top)
							E = E.Next;
						if (E.Dx != horizontal && E.Prev.Dx != horizontal)
							break;
						while (E.Prev.Dx == horizontal)
							E = E.Prev;
						E2 = E;
						while (E.Dx == horizontal)
							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;
				}
				//------------------------------------------------------------------------------

				private TEdge ProcessBound(TEdge E, bool LeftBoundIsForward)
				{
					TEdge EStart, Result = E;
					TEdge Horz;

					if (Result.OutIdx == Skip)
					{
						//check if there are edges beyond the skip edge in the bound and if so
						//create another LocMin and calling ProcessBound once more ...
						E = Result;
						if (LeftBoundIsForward)
						{
							while (E.Top.Y == E.Next.Bot.Y)
								E = E.Next;
							while (E != Result && E.Dx == horizontal)
								E = E.Prev;
						}
						else
						{
							while (E.Top.Y == E.Prev.Bot.Y)
								E = E.Prev;
							while (E != Result && E.Dx == horizontal)
								E = E.Next;
						}
						if (E == Result)
						{
							if (LeftBoundIsForward)
								Result = E.Next;
							else
								Result = E.Prev;
						}
						else
						{
							//there are more edges in the bound beyond result starting with E
							if (LeftBoundIsForward)
								E = Result.Next;
							else
								E = Result.Prev;
							LocalMinima locMin = new LocalMinima();
							locMin.Next = null;
							locMin.Y = E.Bot.Y;
							locMin.LeftBound = null;
							locMin.RightBound = E;
							E.WindDelta = 0;
							Result = ProcessBound(E, LeftBoundIsForward);
							InsertLocalMinima(locMin);
						}
						return Result;
					}

					if (E.Dx == horizontal)
					{
						//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 (LeftBoundIsForward)
							EStart = E.Prev;
						else
							EStart = E.Next;
						if (EStart.Dx == horizontal) //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 (LeftBoundIsForward)
					{
						while (Result.Top.Y == Result.Next.Bot.Y && Result.Next.OutIdx != Skip)
							Result = Result.Next;
						if (Result.Dx == horizontal && 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 (Horz.Prev.Dx == horizontal)
								Horz = Horz.Prev;
							if (Horz.Prev.Top.X > Result.Next.Top.X)
								Result = Horz.Prev;
						}
						while (E != Result)
						{
							E.NextInLML = E.Next;
							if (E.Dx == horizontal && E != EStart && E.Bot.X != E.Prev.Top.X)
								ReverseHorizontal(E);
							E = E.Next;
						}
						if (E.Dx == horizontal && 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 (Result.Dx == horizontal && Result.Prev.OutIdx != Skip)
						{
							Horz = Result;
							while (Horz.Next.Dx == horizontal)
								Horz = Horz.Next;
							if (Horz.Next.Top.X == Result.Prev.Top.X ||
								Horz.Next.Top.X > Result.Prev.Top.X)
								Result = Horz.Next;
						}

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


				public bool AddPath(Path pg, PolyType polyType, bool Closed)
				{
#if use_lines
					if (!Closed && polyType == PolyType.ptClip)
						throw new ClipperException("AddPath: Open paths must be subject.");
#else
      if (!Closed)
        throw new ClipperException("AddPath: Open paths have been disabled.");
#endif

					int highI = (int)pg.Count - 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 ...
					List<TEdge> edges = new List<TEdge>(highI + 1);
					for (int i = 0; i <= highI; i++)
						edges.Add(new TEdge());

					bool IsFlat = true;

					//1. Basic (first) edge initialization ...
					edges[1].Curr = pg[1];
					RangeTest(pg[0], ref m_UseFullRange);
					RangeTest(pg[highI], ref 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], ref m_UseFullRange);
						InitEdge(edges[i], edges[i + 1], edges[i - 1], pg[i]);
					}
					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) &&
						  (!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)))
						return false;

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

					//3. Do second stage of edge initialization ...
					E = eStart;
					do
					{
						InitEdge2(E, polyType);
						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)
							return false;
						E.Prev.OutIdx = Skip;
						LocalMinima locMin = new LocalMinima();
						locMin.Next = null;
						locMin.Y = E.Bot.Y;
						locMin.LeftBound = null;
						locMin.RightBound = E;
						locMin.RightBound.Side = EdgeSide.esRight;
						locMin.RightBound.WindDelta = 0;
						for (; ; )
						{
							if (E.Bot.X != E.Prev.Top.X)
								ReverseHorizontal(E);
							if (E.Next.OutIdx == Skip)
								break;
							E.NextInLML = E.Next;
							E = E.Next;
						}
						InsertLocalMinima(locMin);
						m_edges.Add(edges);
						return true;
					}

					m_edges.Add(edges);
					bool leftBoundIsForward;
					TEdge EMin = null;

					//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 == null)
							EMin = E;

						//E and E.Prev now share a local minima (left aligned if horizontal).
						//Compare their slopes to find which starts which bound ...
						LocalMinima locMin = new LocalMinima();
						locMin.Next = null;
						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 = EdgeSide.esLeft;
						locMin.RightBound.Side = EdgeSide.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 = null;
						else if (locMin.RightBound.OutIdx == Skip)
							locMin.RightBound = null;
						InsertLocalMinima(locMin);
						if (!leftBoundIsForward)
							E = E2;
					}
					return true;

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

				public bool AddPaths(Paths ppg, PolyType polyType, bool closed)
				{
					bool result = false;
					int ppgCnt = ppg.Count;
					for (int i = 0; i < ppgCnt; ++i)
						if (AddPath(ppg[i], polyType, closed))
							result = true;
					return result;
				}
				//------------------------------------------------------------------------------

				internal bool Pt2IsBetweenPt1AndPt3(IntPoint pt1, IntPoint pt2, 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);
				}
				//------------------------------------------------------------------------------

				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 = null; //flag as removed (see ClipperBase.Clear)
					return result;
				}
				//------------------------------------------------------------------------------

				private 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);
				}
				//---------------------------------------------------------------------------

				private void InsertLocalMinima(LocalMinima newLm)
				{
					if (m_MinimaList == null)
					{
						m_MinimaList = newLm;
					}
					else if (newLm.Y >= m_MinimaList.Y)
					{
						newLm.Next = m_MinimaList;
						m_MinimaList = newLm;
					}
					else
					{
						LocalMinima tmpLm = m_MinimaList;
						while (tmpLm.Next != null && (newLm.Y < tmpLm.Next.Y))
							tmpLm = tmpLm.Next;
						newLm.Next = tmpLm.Next;
						tmpLm.Next = newLm;
					}
				}
				//------------------------------------------------------------------------------

				internal Boolean PopLocalMinima(cInt Y, out LocalMinima current)
				{
					current = m_CurrentLM;
					if (m_CurrentLM != null && m_CurrentLM.Y == Y)
					{
						m_CurrentLM = m_CurrentLM.Next;
						return true;
					}
					return false;
				}
				//------------------------------------------------------------------------------

				private 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(ref e.Top.X, ref e.Bot.X);
#if use_xyz
      Swap(ref e.Top.Z, ref e.Bot.Z);
#endif
				}
				//------------------------------------------------------------------------------

				internal virtual void Reset()
				{
					m_CurrentLM = m_MinimaList;
					if (m_CurrentLM == null)
						return; //ie nothing to process

					//reset all edges ...
					m_Scanbeam = null;
					LocalMinima lm = m_MinimaList;
					while (lm != null)
					{
						InsertScanbeam(lm.Y);
						TEdge e = lm.LeftBound;
						if (e != null)
						{
							e.Curr = e.Bot;
							e.OutIdx = Unassigned;
						}
						e = lm.RightBound;
						if (e != null)
						{
							e.Curr = e.Bot;
							e.OutIdx = Unassigned;
						}
						lm = lm.Next;
					}
					m_ActiveEdges = null;
				}
				//------------------------------------------------------------------------------

				public static IntRect GetBounds(Paths paths)
				{
					int i = 0, cnt = paths.Count;
					while (i < cnt && paths[i].Count == 0)
						i++;
					if (i == cnt)
						return new IntRect(0, 0, 0, 0);
					IntRect result = new IntRect();
					result.left = paths[i][0].X;
					result.right = result.left;
					result.top = paths[i][0].Y;
					result.bottom = result.top;
					for (; i < cnt; i++)
					{
						int pathsIcnt = paths[i].Count;
						for (int j = 0; j < pathsIcnt; j++)
						{
							if (paths[i][j].X < result.left)
								result.left = paths[i][j].X;
							else if (paths[i][j].X > result.right)
								result.right = paths[i][j].X;
							if (paths[i][j].Y < result.top)
								result.top = paths[i][j].Y;
							else if (paths[i][j].Y > result.bottom)
								result.bottom = paths[i][j].Y;
						}
					}
					return result;
				}
				//------------------------------------------------------------------------------

				internal void InsertScanbeam(cInt Y)
				{
					//single-linked list: sorted descending, ignoring dups.
					if (m_Scanbeam == null)
					{
						m_Scanbeam = new Scanbeam();
						m_Scanbeam.Next = null;
						m_Scanbeam.Y = Y;
					}
					else if (Y > m_Scanbeam.Y)
					{
						Scanbeam newSb = new Scanbeam();
						newSb.Y = Y;
						newSb.Next = m_Scanbeam;
						m_Scanbeam = newSb;
					}
					else
					{
						Scanbeam sb2 = m_Scanbeam;
						while (sb2.Next != null && (Y <= sb2.Next.Y))
							sb2 = sb2.Next;
						if (Y == sb2.Y)
							return; //ie ignores duplicates
						Scanbeam newSb = new Scanbeam();
						newSb.Y = Y;
						newSb.Next = sb2.Next;
						sb2.Next = newSb;
					}
				}
				//------------------------------------------------------------------------------

				internal Boolean PopScanbeam(out cInt Y)
				{
					if (m_Scanbeam == null)
					{
						Y = 0;
						return false;
					}
					Y = m_Scanbeam.Y;
					m_Scanbeam = m_Scanbeam.Next;
					return true;
				}
				//------------------------------------------------------------------------------

				internal Boolean LocalMinimaPending()
				{
					return (m_CurrentLM != null);
				}
				//------------------------------------------------------------------------------

				internal OutRec CreateOutRec()
				{
					OutRec result = new OutRec();
					result.Idx = Unassigned;
					result.IsHole = false;
					result.IsOpen = false;
					result.FirstLeft = null;
					result.Pts = null;
					result.BottomPt = null;
					result.PolyNode = null;
					m_PolyOuts.Add(result);
					result.Idx = m_PolyOuts.Count - 1;
					return result;
				}
				//------------------------------------------------------------------------------

				internal void DisposeOutRec(int index)
				{
					OutRec outRec = m_PolyOuts[index];
					outRec.Pts = null;
					outRec = null;
					m_PolyOuts[index] = null;
				}
				//------------------------------------------------------------------------------

				internal void UpdateEdgeIntoAEL(ref TEdge e)
				{
					if (e.NextInLML == null)
						throw new ClipperException("UpdateEdgeIntoAEL: invalid call");
					TEdge AelPrev = e.PrevInAEL;
					TEdge AelNext = e.NextInAEL;
					e.NextInLML.OutIdx = e.OutIdx;
					if (AelPrev != null)
						AelPrev.NextInAEL = e.NextInLML;
					else
						m_ActiveEdges = e.NextInLML;
					if (AelNext != null)
						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);
				}
				//------------------------------------------------------------------------------

				internal void 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 != null)
							next.PrevInAEL = edge1;
						TEdge prev = edge1.PrevInAEL;
						if (prev != null)
							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 != null)
							next.PrevInAEL = edge2;
						TEdge prev = edge2.PrevInAEL;
						if (prev != null)
							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 != null)
							edge1.NextInAEL.PrevInAEL = edge1;
						edge1.PrevInAEL = edge2.PrevInAEL;
						if (edge1.PrevInAEL != null)
							edge1.PrevInAEL.NextInAEL = edge1;
						edge2.NextInAEL = next;
						if (edge2.NextInAEL != null)
							edge2.NextInAEL.PrevInAEL = edge2;
						edge2.PrevInAEL = prev;
						if (edge2.PrevInAEL != null)
							edge2.PrevInAEL.NextInAEL = edge2;
					}

					if (edge1.PrevInAEL == null)
						m_ActiveEdges = edge1;
					else if (edge2.PrevInAEL == null)
						m_ActiveEdges = edge2;
				}
				//------------------------------------------------------------------------------

				internal void DeleteFromAEL(TEdge e)
				{
					TEdge AelPrev = e.PrevInAEL;
					TEdge AelNext = e.NextInAEL;
					if (AelPrev == null && AelNext == null && (e != m_ActiveEdges))
						return; //already deleted
					if (AelPrev != null)
						AelPrev.NextInAEL = AelNext;
					else
						m_ActiveEdges = AelNext;
					if (AelNext != null)
						AelNext.PrevInAEL = AelPrev;
					e.NextInAEL = null;
					e.PrevInAEL = null;
				}
				//------------------------------------------------------------------------------

			} //end ClipperBase

			public class Clipper : ClipperBase
			{
				//InitOptions that can be passed to the constructor ...
				public const int ioReverseSolution = 1;
				public const int ioStrictlySimple = 2;
				public const int ioPreserveCollinear = 4;

				private ClipType m_ClipType;
				private Maxima m_Maxima;
				private TEdge m_SortedEdges;
				private List<IntersectNode> m_IntersectList;
				IComparer<IntersectNode> m_IntersectNodeComparer;
				private bool m_ExecuteLocked;
				private PolyFillType m_ClipFillType;
				private PolyFillType m_SubjFillType;
				private List<Join> m_Joins;
				private List<Join> m_GhostJoins;
				private bool m_UsingPolyTree;
#if use_xyz
      public delegate void ZFillCallback(IntPoint bot1, IntPoint top1, 
        IntPoint bot2, IntPoint top2, ref IntPoint pt);
      public ZFillCallback ZFillFunction { get; set; }
#endif
				public Clipper(int InitOptions = 0) : base() //constructor
				{
					m_Scanbeam = null;
					m_Maxima = null;
					m_ActiveEdges = null;
					m_SortedEdges = null;
					m_IntersectList = new List<IntersectNode>();
					m_IntersectNodeComparer = new MyIntersectNodeSort();
					m_ExecuteLocked = false;
					m_UsingPolyTree = false;
					m_PolyOuts = new List<OutRec>();
					m_Joins = new List<Join>();
					m_GhostJoins = new List<Join>();
					ReverseSolution = (ioReverseSolution & InitOptions) != 0;
					StrictlySimple = (ioStrictlySimple & InitOptions) != 0;
					PreserveCollinear = (ioPreserveCollinear & InitOptions) != 0;
#if use_xyz
          ZFillFunction = null;
#endif
				}
				//------------------------------------------------------------------------------

				private void InsertMaxima(cInt X)
				{
					//double-linked list: sorted ascending, ignoring dups.
					Maxima newMax = new Maxima();
					newMax.X = X;
					if (m_Maxima == null)
					{
						m_Maxima = newMax;
						m_Maxima.Next = null;
						m_Maxima.Prev = null;
					}
					else if (X < m_Maxima.X)
					{
						newMax.Next = m_Maxima;
						newMax.Prev = null;
						m_Maxima = newMax;
					}
					else
					{
						Maxima m = m_Maxima;
						while (m.Next != null && (X >= m.Next.X))
							m = m.Next;
						if (X == m.X)
							return; //ie ignores duplicates (& CG to clean up newMax)
									//insert newMax between m and m.Next ...
						newMax.Next = m.Next;
						newMax.Prev = m;
						if (m.Next != null)
							m.Next.Prev = newMax;
						m.Next = newMax;
					}
				}
				//------------------------------------------------------------------------------

				public bool ReverseSolution
				{
					get;
					set;
				}
				//------------------------------------------------------------------------------

				public bool StrictlySimple
				{
					get;
					set;
				}
				//------------------------------------------------------------------------------

				public bool Execute(ClipType clipType, Paths solution,
					PolyFillType FillType = PolyFillType.pftEvenOdd)
				{
					return Execute(clipType, solution, FillType, FillType);
				}
				//------------------------------------------------------------------------------

				public bool Execute(ClipType clipType, PolyTree polytree,
					PolyFillType FillType = PolyFillType.pftEvenOdd)
				{
					return Execute(clipType, polytree, FillType, FillType);
				}
				//------------------------------------------------------------------------------

				public bool Execute(ClipType clipType, Paths solution,
					PolyFillType subjFillType, PolyFillType clipFillType)
				{
					if (m_ExecuteLocked)
						return false;
					if (m_HasOpenPaths)
						throw
	  new ClipperException("Error: PolyTree struct is needed for open path clipping.");

					m_ExecuteLocked = true;
					solution.Clear();
					m_SubjFillType = subjFillType;
					m_ClipFillType = clipFillType;
					m_ClipType = clipType;
					m_UsingPolyTree = false;
					bool succeeded;
					try
					{
						succeeded = ExecuteInternal();
						//build the return polygons ...
						if (succeeded)
							BuildResult(solution);
					}
					finally
					{
						DisposeAllPolyPts();
						m_ExecuteLocked = false;
					}
					return succeeded;
				}
				//------------------------------------------------------------------------------

				public bool 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;
					try
					{
						succeeded = ExecuteInternal();
						//build the return polygons ...
						if (succeeded)
							BuildResult2(polytree);
					}
					finally
					{
						DisposeAllPolyPts();
						m_ExecuteLocked = false;
					}
					return succeeded;
				}
				//------------------------------------------------------------------------------

				internal void FixHoleLinkage(OutRec outRec)
				{
					//skip if an outermost polygon or
					//already already points to the correct FirstLeft ...
					if (outRec.FirstLeft == null ||
						  (outRec.IsHole != outRec.FirstLeft.IsHole &&
						  outRec.FirstLeft.Pts != null))
						return;

					OutRec orfl = outRec.FirstLeft;
					while (orfl != null && ((orfl.IsHole == outRec.IsHole) || orfl.Pts == null))
						orfl = orfl.FirstLeft;
					outRec.FirstLeft = orfl;
				}
				//------------------------------------------------------------------------------

				private bool ExecuteInternal()
				{
					try
					{
						Reset();
						m_SortedEdges = null;
						m_Maxima = null;

						cInt botY, topY;
						if (!PopScanbeam(out botY))
							return false;
						InsertLocalMinimaIntoAEL(botY);
						while (PopScanbeam(out topY) || LocalMinimaPending())
						{
							ProcessHorizontals();
							m_GhostJoins.Clear();
							if (!ProcessIntersections(topY))
								return false;
							ProcessEdgesAtTopOfScanbeam(topY);
							botY = topY;
							InsertLocalMinimaIntoAEL(botY);
						}

						//fix orientations ...
						foreach (OutRec outRec in m_PolyOuts)
						{
							if (outRec.Pts == null || outRec.IsOpen)
								continue;
							if ((outRec.IsHole ^ ReverseSolution) == (Area(outRec) > 0))
								ReversePolyPtLinks(outRec.Pts);
						}

						JoinCommonEdges();

						foreach (OutRec outRec in m_PolyOuts)
						{
							if (outRec.Pts == null)
								continue;
							else if (outRec.IsOpen)
								FixupOutPolyline(outRec);
							else
								FixupOutPolygon(outRec);
						}

						if (StrictlySimple)
							DoSimplePolygons();
						return true;
					}
					//catch { return false; }
					finally
					{
						m_Joins.Clear();
						m_GhostJoins.Clear();
					}
				}
				//------------------------------------------------------------------------------

				private void DisposeAllPolyPts()
				{
					int polyCnt = m_PolyOuts.Count;
					for (int i = 0; i < polyCnt; ++i)
					{
						DisposeOutRec(i);
					}
					m_PolyOuts.Clear();
				}
				//------------------------------------------------------------------------------

				private void AddJoin(OutPt Op1, OutPt Op2, IntPoint OffPt)
				{
					Join j = new Join();
					j.OutPt1 = Op1;
					j.OutPt2 = Op2;
					j.OffPt = OffPt;
					m_Joins.Add(j);
				}
				//------------------------------------------------------------------------------

				private void AddGhostJoin(OutPt Op, IntPoint OffPt)
				{
					Join j = new Join();
					j.OutPt1 = Op;
					j.OffPt = OffPt;
					m_GhostJoins.Add(j);
				}
				//------------------------------------------------------------------------------

#if use_xyz
      internal void SetZ(ref IntPoint pt, TEdge e1, TEdge e2)
      {
        if (pt.Z != 0 || ZFillFunction == null) 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 ZFillFunction(e1.Bot, e1.Top, e2.Bot, e2.Top, ref pt);
      }
      //------------------------------------------------------------------------------
#endif

				private void InsertLocalMinimaIntoAEL(cInt botY)
				{
					LocalMinima lm;
					while (PopLocalMinima(botY, out lm))
					{
						TEdge lb = lm.LeftBound;
						TEdge rb = lm.RightBound;

						OutPt Op1 = null;
						if (lb == null)
						{
							InsertEdgeIntoAEL(rb, null);
							SetWindingCount(rb);
							if (IsContributing(rb))
								Op1 = AddOutPt(rb, rb.Bot);
						}
						else if (rb == null)
						{
							InsertEdgeIntoAEL(lb, null);
							SetWindingCount(lb);
							if (IsContributing(lb))
								Op1 = AddOutPt(lb, lb.Bot);
							InsertScanbeam(lb.Top.Y);
						}
						else
						{
							InsertEdgeIntoAEL(lb, null);
							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 != null)
						{
							if (IsHorizontal(rb))
							{
								if (rb.NextInLML != null)
									InsertScanbeam(rb.NextInLML.Top.Y);
								AddEdgeToSEL(rb);
							}
							else
								InsertScanbeam(rb.Top.Y);
						}

						if (lb == null || rb == null)
							continue;

						//if output polygons share an Edge with a horizontal rb, they'll need joining later ...
						if (Op1 != null && IsHorizontal(rb) &&
						  m_GhostJoins.Count > 0 && rb.WindDelta != 0)
						{
							int ghostCnt = m_GhostJoins.Count;
							for (int i = 0; i < ghostCnt; i++)
							{
								//if the horizontal Rb and a 'ghost' horizontal overlap, then convert
								//the 'ghost' join to a real join ready for later ...
								Join j = m_GhostJoins[i];
								if (HorzSegmentsOverlap(j.OutPt1.Pt.X, j.OffPt.X, rb.Bot.X, rb.Top.X))
									AddJoin(j.OutPt1, Op1, j.OffPt);
							}
						}

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

						if (lb.NextInAEL != rb)
						{

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

							TEdge e = lb.NextInAEL;
							if (e != null)
								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;
								}
						}
					}
				}
				//------------------------------------------------------------------------------

				private void InsertEdgeIntoAEL(TEdge edge, TEdge startEdge)
				{
					if (m_ActiveEdges == null)
					{
						edge.PrevInAEL = null;
						edge.NextInAEL = null;
						m_ActiveEdges = edge;
					}
					else if (startEdge == null && E2InsertsBeforeE1(m_ActiveEdges, edge))
					{
						edge.PrevInAEL = null;
						edge.NextInAEL = m_ActiveEdges;
						m_ActiveEdges.PrevInAEL = edge;
						m_ActiveEdges = edge;
					}
					else
					{
						if (startEdge == null)
							startEdge = m_ActiveEdges;
						while (startEdge.NextInAEL != null &&
						  !E2InsertsBeforeE1(startEdge.NextInAEL, edge))
							startEdge = startEdge.NextInAEL;
						edge.NextInAEL = startEdge.NextInAEL;
						if (startEdge.NextInAEL != null)
							startEdge.NextInAEL.PrevInAEL = edge;
						edge.PrevInAEL = startEdge;
						startEdge.NextInAEL = edge;
					}
				}
				//----------------------------------------------------------------------

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

				private bool IsEvenOddFillType(TEdge edge)
				{
					if (edge.PolyTyp == PolyType.ptSubject)
						return m_SubjFillType == PolyFillType.pftEvenOdd;
					else
						return m_ClipFillType == PolyFillType.pftEvenOdd;
				}
				//------------------------------------------------------------------------------

				private bool IsEvenOddAltFillType(TEdge edge)
				{
					if (edge.PolyTyp == PolyType.ptSubject)
						return m_ClipFillType == PolyFillType.pftEvenOdd;
					else
						return m_SubjFillType == PolyFillType.pftEvenOdd;
				}
				//------------------------------------------------------------------------------

				private bool IsContributing(TEdge edge)
				{
					PolyFillType pft, pft2;
					if (edge.PolyTyp == PolyType.ptSubject)
					{
						pft = m_SubjFillType;
						pft2 = m_ClipFillType;
					}
					else
					{
						pft = m_ClipFillType;
						pft2 = m_SubjFillType;
					}

					switch (pft)
					{
						case PolyFillType.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 PolyFillType.pftNonZero:
							if (Math.Abs(edge.WindCnt) != 1)
								return false;
							break;
						case PolyFillType.pftPositive:
							if (edge.WindCnt != 1)
								return false;
							break;
						default: //PolyFillType.pftNegative
							if (edge.WindCnt != -1)
								return false;
							break;
					}

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

				private void SetWindingCount(TEdge edge)
				{
					TEdge e = edge.PrevInAEL;
					//find the edge of the same polytype that immediately preceeds 'edge' in AEL
					while (e != null && ((e.PolyTyp != edge.PolyTyp) || (e.WindDelta == 0)))
						e = e.PrevInAEL;
					if (e == null)
					{
						PolyFillType pft;
						pft = (edge.PolyTyp == PolyType.ptSubject ? m_SubjFillType : m_ClipFillType);
						if (edge.WindDelta == 0)
							edge.WindCnt = (pft == PolyFillType.pftNegative ? -1 : 1);
						else
							edge.WindCnt = edge.WindDelta;
						edge.WindCnt2 = 0;
						e = m_ActiveEdges; //ie get ready to calc WindCnt2
					}
					else if (edge.WindDelta == 0 && m_ClipType != 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 != null)
							{
								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 (Math.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;
						}
					}
				}
				//------------------------------------------------------------------------------

				private void AddEdgeToSEL(TEdge edge)
				{
					//SEL pointers in PEdge are use to build transient lists of horizontal edges.
					//However, since we don't need to worry about processing order, all additions
					//are made to the front of the list ...
					if (m_SortedEdges == null)
					{
						m_SortedEdges = edge;
						edge.PrevInSEL = null;
						edge.NextInSEL = null;
					}
					else
					{
						edge.NextInSEL = m_SortedEdges;
						edge.PrevInSEL = null;
						m_SortedEdges.PrevInSEL = edge;
						m_SortedEdges = edge;
					}
				}
				//------------------------------------------------------------------------------

				internal Boolean PopEdgeFromSEL(out TEdge e)
				{
					//Pop edge from front of SEL (ie SEL is a FILO list)
					e = m_SortedEdges;
					if (e == null)
						return false;
					TEdge oldE = e;
					m_SortedEdges = e.NextInSEL;
					if (m_SortedEdges != null)
						m_SortedEdges.PrevInSEL = null;
					oldE.NextInSEL = null;
					oldE.PrevInSEL = null;
					return true;
				}
				//------------------------------------------------------------------------------

				private void CopyAELToSEL()
				{
					TEdge e = m_ActiveEdges;
					m_SortedEdges = e;
					while (e != null)
					{
						e.PrevInSEL = e.PrevInAEL;
						e.NextInSEL = e.NextInAEL;
						e = e.NextInAEL;
					}
				}
				//------------------------------------------------------------------------------

				private void SwapPositionsInSEL(TEdge edge1, TEdge edge2)
				{
					if (edge1.NextInSEL == null && edge1.PrevInSEL == null)
						return;
					if (edge2.NextInSEL == null && edge2.PrevInSEL == null)
						return;

					if (edge1.NextInSEL == edge2)
					{
						TEdge next = edge2.NextInSEL;
						if (next != null)
							next.PrevInSEL = edge1;
						TEdge prev = edge1.PrevInSEL;
						if (prev != null)
							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 != null)
							next.PrevInSEL = edge2;
						TEdge prev = edge2.PrevInSEL;
						if (prev != null)
							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 != null)
							edge1.NextInSEL.PrevInSEL = edge1;
						edge1.PrevInSEL = edge2.PrevInSEL;
						if (edge1.PrevInSEL != null)
							edge1.PrevInSEL.NextInSEL = edge1;
						edge2.NextInSEL = next;
						if (edge2.NextInSEL != null)
							edge2.NextInSEL.PrevInSEL = edge2;
						edge2.PrevInSEL = prev;
						if (edge2.PrevInSEL != null)
							edge2.PrevInSEL.NextInSEL = edge2;
					}

					if (edge1.PrevInSEL == null)
						m_SortedEdges = edge1;
					else if (edge2.PrevInSEL == null)
						m_SortedEdges = edge2;
				}
				//------------------------------------------------------------------------------


				private void AddLocalMaxPoly(TEdge e1, TEdge e2, 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);
				}
				//------------------------------------------------------------------------------

				private OutPt AddLocalMinPoly(TEdge e1, TEdge e2, IntPoint pt)
				{
					OutPt result;
					TEdge e, prevE;
					if (IsHorizontal(e2) || (e1.Dx > e2.Dx))
					{
						result = AddOutPt(e1, pt);
						e2.OutIdx = e1.OutIdx;
						e1.Side = EdgeSide.esLeft;
						e2.Side = EdgeSide.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 = EdgeSide.esRight;
						e2.Side = EdgeSide.esLeft;
						e = e2;
						if (e.PrevInAEL == e1)
							prevE = e1.PrevInAEL;
						else
							prevE = e.PrevInAEL;
					}

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

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

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

				private OutPt GetLastOutPt(TEdge e)
				{
					OutRec outRec = m_PolyOuts[e.OutIdx];
					if (e.Side == EdgeSide.esLeft)
						return outRec.Pts;
					else
						return outRec.Pts.Prev;
				}
				//------------------------------------------------------------------------------

				internal void SwapPoints(ref IntPoint pt1, ref IntPoint pt2)
				{
					IntPoint tmp = new IntPoint(pt1);
					pt1 = pt2;
					pt2 = tmp;
				}
				//------------------------------------------------------------------------------

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

				private void SetHoleState(TEdge e, OutRec outRec)
				{
					TEdge e2 = e.PrevInAEL;
					TEdge eTmp = null;
					while (e2 != null)
					{
						if (e2.OutIdx >= 0 && e2.WindDelta != 0)
						{
							if (eTmp == null)
								eTmp = e2;
							else if (eTmp.OutIdx == e2.OutIdx)
								eTmp = null; //paired               
						}
						e2 = e2.PrevInAEL;
					}

					if (eTmp == null)
					{
						outRec.FirstLeft = null;
						outRec.IsHole = false;
					}
					else
					{
						outRec.FirstLeft = m_PolyOuts[eTmp.OutIdx];
						outRec.IsHole = !outRec.FirstLeft.IsHole;
					}
				}
				//------------------------------------------------------------------------------

				private double GetDx(IntPoint pt1, IntPoint pt2)
				{
					if (pt1.Y == pt2.Y)
						return horizontal;
					else
						return (double)(pt2.X - pt1.X) / (pt2.Y - pt1.Y);
				}
				//---------------------------------------------------------------------------

				private bool FirstIsBottomPt(OutPt btmPt1, OutPt btmPt2)
				{
					OutPt p = btmPt1.Prev;
					while ((p.Pt == btmPt1.Pt) && (p != btmPt1))
						p = p.Prev;
					double dx1p = Math.Abs(GetDx(btmPt1.Pt, p.Pt));
					p = btmPt1.Next;
					while ((p.Pt == btmPt1.Pt) && (p != btmPt1))
						p = p.Next;
					double dx1n = Math.Abs(GetDx(btmPt1.Pt, p.Pt));

					p = btmPt2.Prev;
					while ((p.Pt == btmPt2.Pt) && (p != btmPt2))
						p = p.Prev;
					double dx2p = Math.Abs(GetDx(btmPt2.Pt, p.Pt));
					p = btmPt2.Next;
					while ((p.Pt == btmPt2.Pt) && (p != btmPt2))
						p = p.Next;
					double dx2n = Math.Abs(GetDx(btmPt2.Pt, p.Pt));

					if (Math.Max(dx1p, dx1n) == Math.Max(dx2p, dx2n) &&
					  Math.Min(dx1p, dx1n) == Math.Min(dx2p, dx2n))
						return Area(btmPt1) > 0; //if otherwise identical use orientation
					else
						return (dx1p >= dx2p && dx1p >= dx2n) || (dx1n >= dx2p && dx1n >= dx2n);
				}
				//------------------------------------------------------------------------------

				private OutPt GetBottomPt(OutPt pp)
				{
					OutPt dups = null;
					OutPt p = pp.Next;
					while (p != pp)
					{
						if (p.Pt.Y > pp.Pt.Y)
						{
							pp = p;
							dups = null;
						}
						else if (p.Pt.Y == pp.Pt.Y && p.Pt.X <= pp.Pt.X)
						{
							if (p.Pt.X < pp.Pt.X)
							{
								dups = null;
								pp = p;
							}
							else
							{
								if (p.Next != pp && p.Prev != pp)
									dups = p;
							}
						}
						p = p.Next;
					}
					if (dups != null)
					{
						//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;
				}
				//------------------------------------------------------------------------------

				private OutRec GetLowermostRec(OutRec outRec1, OutRec outRec2)
				{
					//work out which polygon fragment has the correct hole state ...
					if (outRec1.BottomPt == null)
						outRec1.BottomPt = GetBottomPt(outRec1.Pts);
					if (outRec2.BottomPt == null)
						outRec2.BottomPt = GetBottomPt(outRec2.Pts);
					OutPt bPt1 = outRec1.BottomPt;
					OutPt bPt2 = outRec2.BottomPt;
					if (bPt1.Pt.Y > bPt2.Pt.Y)
						return outRec1;
					else if (bPt1.Pt.Y < bPt2.Pt.Y)
						return outRec2;
					else if (bPt1.Pt.X < bPt2.Pt.X)
						return outRec1;
					else if (bPt1.Pt.X > bPt2.Pt.X)
						return outRec2;
					else if (bPt1.Next == bPt1)
						return outRec2;
					else if (bPt2.Next == bPt2)
						return outRec1;
					else if (FirstIsBottomPt(bPt1, bPt2))
						return outRec1;
					else
						return outRec2;
				}
				//------------------------------------------------------------------------------

				bool OutRec1RightOfOutRec2(OutRec outRec1, OutRec outRec2)
				{
					do
					{
						outRec1 = outRec1.FirstLeft;
						if (outRec1 == outRec2)
							return true;
					} while (outRec1 != null);
					return false;
				}
				//------------------------------------------------------------------------------

				private OutRec GetOutRec(int idx)
				{
					OutRec outrec = m_PolyOuts[idx];
					while (outrec != m_PolyOuts[outrec.Idx])
						outrec = m_PolyOuts[outrec.Idx];
					return outrec;
				}
				//------------------------------------------------------------------------------

				private void AppendPolygon(TEdge e1, TEdge e2)
				{
					OutRec outRec1 = m_PolyOuts[e1.OutIdx];
					OutRec outRec2 = m_PolyOuts[e2.OutIdx];

					OutRec holeStateRec;
					if (OutRec1RightOfOutRec2(outRec1, outRec2))
						holeStateRec = outRec2;
					else if (OutRec1RightOfOutRec2(outRec2, outRec1))
						holeStateRec = outRec1;
					else
						holeStateRec = GetLowermostRec(outRec1, outRec2);

					//get the start and ends of both output polygons and
					//join E2 poly onto E1 poly and delete pointers to E2 ...
					OutPt p1_lft = outRec1.Pts;
					OutPt p1_rt = p1_lft.Prev;
					OutPt p2_lft = outRec2.Pts;
					OutPt p2_rt = p2_lft.Prev;

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

					outRec1.BottomPt = null;
					if (holeStateRec == outRec2)
					{
						if (outRec2.FirstLeft != outRec1)
							outRec1.FirstLeft = outRec2.FirstLeft;
						outRec1.IsHole = outRec2.IsHole;
					}
					outRec2.Pts = null;
					outRec2.BottomPt = null;

					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 != null)
					{
						if (e.OutIdx == ObsoleteIdx)
						{
							e.OutIdx = OKIdx;
							e.Side = e1.Side;
							break;
						}
						e = e.NextInAEL;
					}
					outRec2.Idx = outRec1.Idx;
				}
				//------------------------------------------------------------------------------

				private void ReversePolyPtLinks(OutPt pp)
				{
					if (pp == null)
						return;
					OutPt pp1;
					OutPt pp2;
					pp1 = pp;
					do
					{
						pp2 = pp1.Next;
						pp1.Next = pp1.Prev;
						pp1.Prev = pp2;
						pp1 = pp2;
					} while (pp1 != pp);
				}
				//------------------------------------------------------------------------------

				private static void SwapSides(TEdge edge1, TEdge edge2)
				{
					EdgeSide side = edge1.Side;
					edge1.Side = edge2.Side;
					edge2.Side = side;
				}
				//------------------------------------------------------------------------------

				private static void SwapPolyIndexes(TEdge edge1, TEdge edge2)
				{
					int outIdx = edge1.OutIdx;
					edge1.OutIdx = edge2.OutIdx;
					edge2.OutIdx = outIdx;
				}
				//------------------------------------------------------------------------------

				private void IntersectEdges(TEdge e1, TEdge e2, IntPoint pt)
				{
					//e1 will be to the left of e2 BELOW the intersection. Therefore e1 is before
					//e2 in AEL except when e1 is being inserted at the intersection point ...

					bool e1Contributing = (e1.OutIdx >= 0);
					bool e2Contributing = (e2.OutIdx >= 0);

#if use_xyz
          SetZ(ref pt, e1, e2);
#endif

#if 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 == 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)
						{
							if ((e1.WindDelta == 0) && Math.Abs(e2.WindCnt) == 1 &&
							  (m_ClipType != ClipType.ctUnion || e2.WindCnt2 == 0))
							{
								AddOutPt(e1, pt);
								if (e1Contributing)
									e1.OutIdx = Unassigned;
							}
							else if ((e2.WindDelta == 0) && (Math.Abs(e1.WindCnt) == 1) &&
							  (m_ClipType != 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 == PolyType.ptSubject)
					{
						e1FillType = m_SubjFillType;
						e1FillType2 = m_ClipFillType;
					}
					else
					{
						e1FillType = m_ClipFillType;
						e1FillType2 = m_SubjFillType;
					}
					if (e2.PolyTyp == PolyType.ptSubject)
					{
						e2FillType = m_SubjFillType;
						e2FillType2 = m_ClipFillType;
					}
					else
					{
						e2FillType = m_ClipFillType;
						e2FillType2 = m_SubjFillType;
					}

					int e1Wc, e2Wc;
					switch (e1FillType)
					{
						case PolyFillType.pftPositive:
							e1Wc = e1.WindCnt;
							break;
						case PolyFillType.pftNegative:
							e1Wc = -e1.WindCnt;
							break;
						default:
							e1Wc = Math.Abs(e1.WindCnt);
							break;
					}
					switch (e2FillType)
					{
						case PolyFillType.pftPositive:
							e2Wc = e2.WindCnt;
							break;
						case PolyFillType.pftNegative:
							e2Wc = -e2.WindCnt;
							break;
						default:
							e2Wc = Math.Abs(e2.WindCnt);
							break;
					}

					if (e1Contributing && e2Contributing)
					{
						if ((e1Wc != 0 && e1Wc != 1) || (e2Wc != 0 && e2Wc != 1) ||
						  (e1.PolyTyp != e2.PolyTyp && m_ClipType != 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 PolyFillType.pftPositive:
								e1Wc2 = e1.WindCnt2;
								break;
							case PolyFillType.pftNegative:
								e1Wc2 = -e1.WindCnt2;
								break;
							default:
								e1Wc2 = Math.Abs(e1.WindCnt2);
								break;
						}
						switch (e2FillType2)
						{
							case PolyFillType.pftPositive:
								e2Wc2 = e2.WindCnt2;
								break;
							case PolyFillType.pftNegative:
								e2Wc2 = -e2.WindCnt2;
								break;
							default:
								e2Wc2 = Math.Abs(e2.WindCnt2);
								break;
						}

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

				private void DeleteFromSEL(TEdge e)
				{
					TEdge SelPrev = e.PrevInSEL;
					TEdge SelNext = e.NextInSEL;
					if (SelPrev == null && SelNext == null && (e != m_SortedEdges))
						return; //already deleted
					if (SelPrev != null)
						SelPrev.NextInSEL = SelNext;
					else
						m_SortedEdges = SelNext;
					if (SelNext != null)
						SelNext.PrevInSEL = SelPrev;
					e.NextInSEL = null;
					e.PrevInSEL = null;
				}
				//------------------------------------------------------------------------------

				private void ProcessHorizontals()
				{
					TEdge horzEdge; //m_SortedEdges;
					while (PopEdgeFromSEL(out horzEdge))
						ProcessHorizontal(horzEdge);
				}
				//------------------------------------------------------------------------------

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

				private void ProcessHorizontal(TEdge horzEdge)
				{
					Direction dir;
					cInt horzLeft, horzRight;
					bool IsOpen = horzEdge.WindDelta == 0;

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

					TEdge eLastHorz = horzEdge, eMaxPair = null;
					while (eLastHorz.NextInLML != null && IsHorizontal(eLastHorz.NextInLML))
						eLastHorz = eLastHorz.NextInLML;
					if (eLastHorz.NextInLML == null)
						eMaxPair = GetMaximaPair(eLastHorz);

					Maxima currMax = m_Maxima;
					if (currMax != null)
					{
						//get the first maxima in range (X) ...
						if (dir == Direction.dLeftToRight)
						{
							while (currMax != null && currMax.X <= horzEdge.Bot.X)
								currMax = currMax.Next;
							if (currMax != null && currMax.X >= eLastHorz.Top.X)
								currMax = null;
						}
						else
						{
							while (currMax.Next != null && currMax.Next.X < horzEdge.Bot.X)
								currMax = currMax.Next;
							if (currMax.X <= eLastHorz.Top.X)
								currMax = null;
						}
					}

					OutPt op1 = null;
					for (; ; ) //loop through consec. horizontal edges
					{
						bool IsLastHorz = (horzEdge == eLastHorz);
						TEdge e = GetNextInAEL(horzEdge, dir);
						while (e != null)
						{

							//this code block inserts extra coords into horizontal edges (in output
							//polygons) whereever maxima touch these horizontal edges. This helps
							//'simplifying' polygons (ie if the Simplify property is set).
							if (currMax != null)
							{
								if (dir == Direction.dLeftToRight)
								{
									while (currMax != null && currMax.X < e.Curr.X)
									{
										if (horzEdge.OutIdx >= 0 && !IsOpen)
											AddOutPt(horzEdge, new IntPoint(currMax.X, horzEdge.Bot.Y));
										currMax = currMax.Next;
									}
								}
								else
								{
									while (currMax != null && currMax.X > e.Curr.X)
									{
										if (horzEdge.OutIdx >= 0 && !IsOpen)
											AddOutPt(horzEdge, new IntPoint(currMax.X, horzEdge.Bot.Y));
										currMax = currMax.Prev;
									}
								}
							};

							if ((dir == Direction.dLeftToRight && e.Curr.X > horzRight) ||
							  (dir == Direction.dRightToLeft && e.Curr.X < horzLeft))
								break;

							//Also break if we've got to the end of an intermediate horizontal edge ...
							//nb: Smaller Dx's are to the right of larger Dx's ABOVE the horizontal.
							if (e.Curr.X == horzEdge.Top.X && horzEdge.NextInLML != null &&
							  e.Dx < horzEdge.NextInLML.Dx)
								break;

							if (horzEdge.OutIdx >= 0 && !IsOpen)  //note: may be done multiple times
							{
								op1 = AddOutPt(horzEdge, e.Curr);
								TEdge eNextHorz = m_SortedEdges;
								while (eNextHorz != null)
								{
									if (eNextHorz.OutIdx >= 0 &&
									  HorzSegmentsOverlap(horzEdge.Bot.X,
									  horzEdge.Top.X, eNextHorz.Bot.X, eNextHorz.Top.X))
									{
										OutPt op2 = GetLastOutPt(eNextHorz);
										AddJoin(op2, op1, eNextHorz.Top);
									}
									eNextHorz = eNextHorz.NextInSEL;
								}
								AddGhostJoin(op1, horzEdge.Bot);
							}

							//OK, so far we're still in range of the horizontal Edge  but make sure
							//we're at the last of consec. horizontals when matching with eMaxPair
							if (e == eMaxPair && IsLastHorz)
							{
								if (horzEdge.OutIdx >= 0)
									AddLocalMaxPoly(horzEdge, eMaxPair, horzEdge.Top);
								DeleteFromAEL(horzEdge);
								DeleteFromAEL(eMaxPair);
								return;
							}

							if (dir == Direction.dLeftToRight)
							{
								IntPoint Pt = new IntPoint(e.Curr.X, horzEdge.Curr.Y);
								IntersectEdges(horzEdge, e, Pt);
							}
							else
							{
								IntPoint Pt = new IntPoint(e.Curr.X, horzEdge.Curr.Y);
								IntersectEdges(e, horzEdge, Pt);
							}
							TEdge eNext = GetNextInAEL(e, dir);
							SwapPositionsInAEL(horzEdge, e);
							e = eNext;
						} //end while(e != null)

						//Break out of loop if HorzEdge.NextInLML is not also horizontal ...
						if (horzEdge.NextInLML == null || !IsHorizontal(horzEdge.NextInLML))
							break;

						UpdateEdgeIntoAEL(ref horzEdge);
						if (horzEdge.OutIdx >= 0)
							AddOutPt(horzEdge, horzEdge.Bot);
						GetHorzDirection(horzEdge, out dir, out horzLeft, out horzRight);

					} //end for (;;)

					if (horzEdge.OutIdx >= 0 && op1 == null)
					{
						op1 = GetLastOutPt(horzEdge);
						TEdge eNextHorz = m_SortedEdges;
						while (eNextHorz != null)
						{
							if (eNextHorz.OutIdx >= 0 &&
							  HorzSegmentsOverlap(horzEdge.Bot.X,
							  horzEdge.Top.X, eNextHorz.Bot.X, eNextHorz.Top.X))
							{
								OutPt op2 = GetLastOutPt(eNextHorz);
								AddJoin(op2, op1, eNextHorz.Top);
							}
							eNextHorz = eNextHorz.NextInSEL;
						}
						AddGhostJoin(op1, horzEdge.Top);
					}

					if (horzEdge.NextInLML != null)
					{
						if (horzEdge.OutIdx >= 0)
						{
							op1 = AddOutPt(horzEdge, horzEdge.Top);

							UpdateEdgeIntoAEL(ref horzEdge);
							if (horzEdge.WindDelta == 0)
								return;
							//nb: HorzEdge is no longer horizontal here
							TEdge ePrev = horzEdge.PrevInAEL;
							TEdge eNext = horzEdge.NextInAEL;
							if (ePrev != null && 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 != null && 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(ref horzEdge);
					}
					else
					{
						if (horzEdge.OutIdx >= 0)
							AddOutPt(horzEdge, horzEdge.Top);
						DeleteFromAEL(horzEdge);
					}
				}
				//------------------------------------------------------------------------------

				private TEdge GetNextInAEL(TEdge e, Direction Direction)
				{
					return Direction == Direction.dLeftToRight ? e.NextInAEL : e.PrevInAEL;
				}
				//------------------------------------------------------------------------------

				private bool IsMinima(TEdge e)
				{
					return e != null && (e.Prev.NextInLML != e) && (e.Next.NextInLML != e);
				}
				//------------------------------------------------------------------------------

				private bool IsMaxima(TEdge e, double Y)
				{
					return (e != null && e.Top.Y == Y && e.NextInLML == null);
				}
				//------------------------------------------------------------------------------

				private bool IsIntermediate(TEdge e, double Y)
				{
					return (e.Top.Y == Y && e.NextInLML != null);
				}
				//------------------------------------------------------------------------------

				internal TEdge GetMaximaPair(TEdge e)
				{
					if ((e.Next.Top == e.Top) && e.Next.NextInLML == null)
						return e.Next;
					else if ((e.Prev.Top == e.Top) && e.Prev.NextInLML == null)
						return e.Prev;
					else
						return null;
				}
				//------------------------------------------------------------------------------

				internal TEdge GetMaximaPairEx(TEdge e)
				{
					//as above but returns null if MaxPair isn't in AEL (unless it's horizontal)
					TEdge result = GetMaximaPair(e);
					if (result == null || result.OutIdx == Skip ||
					  ((result.NextInAEL == result.PrevInAEL) && !IsHorizontal(result)))
						return null;
					return result;
				}
				//------------------------------------------------------------------------------

				private bool ProcessIntersections(cInt topY)
				{
					if (m_ActiveEdges == null)
						return true;
					try
					{
						BuildIntersectList(topY);
						if (m_IntersectList.Count == 0)
							return true;
						if (m_IntersectList.Count == 1 || FixupIntersectionOrder())
							ProcessIntersectList();
						else
							return false;
					}
					catch
					{
						m_SortedEdges = null;
						m_IntersectList.Clear();
						throw new ClipperException("ProcessIntersections error");
					}
					m_SortedEdges = null;
					return true;
				}
				//------------------------------------------------------------------------------

				private void BuildIntersectList(cInt topY)
				{
					if (m_ActiveEdges == null)
						return;

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

					//bubblesort ...
					bool isModified = true;
					while (isModified && m_SortedEdges != null)
					{
						isModified = false;
						e = m_SortedEdges;
						while (e.NextInSEL != null)
						{
							TEdge eNext = e.NextInSEL;
							IntPoint pt;
							if (e.Curr.X > eNext.Curr.X)
							{
								IntersectPoint(e, eNext, out pt);
								if (pt.Y < topY)
									pt = new IntPoint(TopX(e, topY), topY);
								IntersectNode newNode = new IntersectNode();
								newNode.Edge1 = e;
								newNode.Edge2 = eNext;
								newNode.Pt = pt;
								m_IntersectList.Add(newNode);

								SwapPositionsInSEL(e, eNext);
								isModified = true;
							}
							else
								e = eNext;
						}
						if (e.PrevInSEL != null)
							e.PrevInSEL.NextInSEL = null;
						else
							break;
					}
					m_SortedEdges = null;
				}
				//------------------------------------------------------------------------------

				private bool EdgesAdjacent(IntersectNode inode)
				{
					return (inode.Edge1.NextInSEL == inode.Edge2) ||
					  (inode.Edge1.PrevInSEL == inode.Edge2);
				}
				//------------------------------------------------------------------------------

				private static int IntersectNodeSort(IntersectNode node1, IntersectNode node2)
				{
					//the following typecast is safe because the differences in Pt.Y will
					//be limited to the height of the scanbeam.
					return (int)(node2.Pt.Y - node1.Pt.Y);
				}
				//------------------------------------------------------------------------------

				private bool 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 ...
					m_IntersectList.Sort(m_IntersectNodeComparer);

					CopyAELToSEL();
					int cnt = m_IntersectList.Count;
					for (int i = 0; i < cnt; i++)
					{
						if (!EdgesAdjacent(m_IntersectList[i]))
						{
							int j = i + 1;
							while (j < cnt && !EdgesAdjacent(m_IntersectList[j]))
								j++;
							if (j == cnt)
								return false;

							IntersectNode tmp = m_IntersectList[i];
							m_IntersectList[i] = m_IntersectList[j];
							m_IntersectList[j] = tmp;

						}
						SwapPositionsInSEL(m_IntersectList[i].Edge1, m_IntersectList[i].Edge2);
					}
					return true;
				}
				//------------------------------------------------------------------------------

				private void ProcessIntersectList()
				{
					int intersectCnt = m_IntersectList.Count;
					for (int i = 0; i < intersectCnt; i++)
					{
						IntersectNode iNode = m_IntersectList[i];
						{
							IntersectEdges(iNode.Edge1, iNode.Edge2, iNode.Pt);
							SwapPositionsInAEL(iNode.Edge1, iNode.Edge2);
						}
					}
					m_IntersectList.Clear();
				}
				//------------------------------------------------------------------------------

				internal static cInt Round(double value)
				{
					return value < 0 ? (cInt)(value - 0.5) : (cInt)(value + 0.5);
				}
				//------------------------------------------------------------------------------

				private static cInt TopX(TEdge edge, cInt currentY)
				{
					if (currentY == edge.Top.Y)
						return edge.Top.X;
					return edge.Bot.X + Round(edge.Dx * (currentY - edge.Bot.Y));
				}
				//------------------------------------------------------------------------------

				private void IntersectPoint(TEdge edge1, TEdge edge2, out IntPoint ip)
				{
					ip = new IntPoint();
					double b1, b2;
					//nb: with very large coordinate values, it's possible for SlopesEqual() to 
					//return false but for the edge.Dx value be equal due to double precision rounding.
					if (edge1.Dx == edge2.Dx)
					{
						ip.Y = edge1.Curr.Y;
						ip.X = TopX(edge1, ip.Y);
						return;
					}

					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 (Math.Abs(edge1.Dx) < Math.Abs(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 (Math.Abs(edge1.Dx) < Math.Abs(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;
						//better to use the more vertical edge to derive X ...
						if (Math.Abs(edge1.Dx) > Math.Abs(edge2.Dx))
							ip.X = TopX(edge2, ip.Y);
						else
							ip.X = TopX(edge1, ip.Y);
					}
				}
				//------------------------------------------------------------------------------

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

						if (IsMaximaEdge)
						{
							TEdge eMaxPair = GetMaximaPairEx(e);
							IsMaximaEdge = (eMaxPair == null || !IsHorizontal(eMaxPair));
						}

						if (IsMaximaEdge)
						{
							if (StrictlySimple)
								InsertMaxima(e.Top.X);
							TEdge ePrev = e.PrevInAEL;
							DoMaxima(e);
							if (ePrev == null)
								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(ref e);
								if (e.OutIdx >= 0)
									AddOutPt(e, e.Bot);
								AddEdgeToSEL(e);
							}
							else
							{
								e.Curr.X = TopX(e, topY);
								e.Curr.Y = topY;
							}

							//When StrictlySimple and 'e' is being touched by another edge, then
							//make sure both edges have a vertex here ...
							if (StrictlySimple)
							{
								TEdge ePrev = e.PrevInAEL;
								if ((e.OutIdx >= 0) && (e.WindDelta != 0) && ePrev != null &&
								  (ePrev.OutIdx >= 0) && (ePrev.Curr.X == e.Curr.X) &&
								  (ePrev.WindDelta != 0))
								{
									IntPoint ip = new IntPoint(e.Curr);
#if use_xyz
                SetZ(ref ip, ePrev, e);
#endif
									OutPt op = AddOutPt(ePrev, ip);
									OutPt op2 = AddOutPt(e, ip);
									AddJoin(op, op2, ip); //StrictlySimple (type-3) join
								}
							}

							e = e.NextInAEL;
						}
					}

					//3. Process horizontals at the Top of the scanbeam ...
					ProcessHorizontals();
					m_Maxima = null;

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

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

				private void DoMaxima(TEdge e)
				{
					TEdge eMaxPair = GetMaximaPairEx(e);
					if (eMaxPair == null)
					{
						if (e.OutIdx >= 0)
							AddOutPt(e, e.Top);
						DeleteFromAEL(e);
						return;
					}

					TEdge eNext = e.NextInAEL;
					while (eNext != null && 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);
					}
#if 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 new ClipperException("DoMaxima error");
				}
				//------------------------------------------------------------------------------

				public static void ReversePaths(Paths polys)
				{
					foreach (var poly in polys) { poly.Reverse(); }
				}
				//------------------------------------------------------------------------------

				public static bool Orientation(Path poly)
				{
					return Area(poly) >= 0;
				}
				//------------------------------------------------------------------------------

				private int PointCount(OutPt pts)
				{
					if (pts == null)
						return 0;
					int result = 0;
					OutPt p = pts;
					do
					{
						result++;
						p = p.Next;
					}
					while (p != pts);
					return result;
				}
				//------------------------------------------------------------------------------

				private void BuildResult(Paths polyg)
				{
					polyg.Clear();
					polyg.Capacity = m_PolyOuts.Count;
					int polyCnt = m_PolyOuts.Count;
					for (int i = 0; i < polyCnt; i++)
					{
						OutRec outRec = m_PolyOuts[i];
						if (outRec.Pts == null)
							continue;
						OutPt p = outRec.Pts.Prev;
						int cnt = PointCount(p);
						if (cnt < 2)
							continue;
						Path pg = new Path(cnt);
						for (int j = 0; j < cnt; j++)
						{
							pg.Add(p.Pt);
							p = p.Prev;
						}
						polyg.Add(pg);
					}
				}
				//------------------------------------------------------------------------------

				private void BuildResult2(PolyTree polytree)
				{
					polytree.Clear();

					//add each output polygon/contour to polytree ...
					polytree.m_AllPolys.Capacity = m_PolyOuts.Count;
					int polyCnt = m_PolyOuts.Count;
					for (int i = 0; i < polyCnt; 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();
						polytree.m_AllPolys.Add(pn);
						outRec.PolyNode = pn;
						pn.m_polygon.Capacity = cnt;
						OutPt op = outRec.Pts.Prev;
						for (int j = 0; j < cnt; j++)
						{
							pn.m_polygon.Add(op.Pt);
							op = op.Prev;
						}
					}

					//fixup PolyNode links etc ...
					polytree.m_Childs.Capacity = m_PolyOuts.Count;
					polyCnt = m_PolyOuts.Count;
					for (int i = 0; i < polyCnt; i++)
					{
						OutRec outRec = m_PolyOuts[i];
						if (outRec.PolyNode == null)
							continue;
						else if (outRec.IsOpen)
						{
							outRec.PolyNode.IsOpen = true;
							polytree.AddChild(outRec.PolyNode);
						}
						else if (outRec.FirstLeft != null &&
						  outRec.FirstLeft.PolyNode != null)
							outRec.FirstLeft.PolyNode.AddChild(outRec.PolyNode);
						else
							polytree.AddChild(outRec.PolyNode);
					}
				}
				//------------------------------------------------------------------------------

				private void FixupOutPolyline(OutRec outrec)
				{
					OutPt pp = outrec.Pts;
					OutPt lastPP = pp.Prev;
					while (pp != lastPP)
					{
						pp = pp.Next;
						if (pp.Pt == pp.Prev.Pt)
						{
							if (pp == lastPP)
								lastPP = pp.Prev;
							OutPt tmpPP = pp.Prev;
							tmpPP.Next = pp.Next;
							pp.Next.Prev = tmpPP;
							pp = tmpPP;
						}
					}
					if (pp == pp.Prev)
						outrec.Pts = null;
				}
				//------------------------------------------------------------------------------

				private void FixupOutPolygon(OutRec outRec)
				{
					//FixupOutPolygon() - removes duplicate points and simplifies consecutive
					//parallel edges by removing the middle vertex.
					OutPt lastOK = null;
					outRec.BottomPt = null;
					OutPt pp = outRec.Pts;
					bool preserveCol = PreserveCollinear || StrictlySimple;
					for (; ; )
					{
						if (pp.Prev == pp || pp.Prev == pp.Next)
						{
							outRec.Pts = null;
							return;
						}
						//test for duplicate points and collinear edges ...
						if ((pp.Pt == pp.Next.Pt) || (pp.Pt == pp.Prev.Pt) ||
						  (SlopesEqual(pp.Prev.Pt, pp.Pt, pp.Next.Pt, m_UseFullRange) &&
						  (!preserveCol || !Pt2IsBetweenPt1AndPt3(pp.Prev.Pt, pp.Pt, pp.Next.Pt))))
						{
							lastOK = null;
							pp.Prev.Next = pp.Next;
							pp.Next.Prev = pp.Prev;
							pp = pp.Prev;
						}
						else if (pp == lastOK)
							break;
						else
						{
							if (lastOK == null)
								lastOK = pp;
							pp = pp.Next;
						}
					}
					outRec.Pts = pp;
				}
				//------------------------------------------------------------------------------

				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 GetOverlap(cInt a1, cInt a2, cInt b1, cInt b2, out cInt Left, out cInt Right)
				{
					if (a1 < a2)
					{
						if (b1 < b2) { Left = Math.Max(a1, b1); Right = Math.Min(a2, b2); } else { Left = Math.Max(a1, b2); Right = Math.Min(a2, b1); }
					}
					else
					{
						if (b1 < b2) { Left = Math.Max(a2, b1); Right = Math.Min(a1, b2); } else { Left = Math.Max(a2, b2); Right = Math.Min(a1, b1); }
					}
					return Left < Right;
				}
				//------------------------------------------------------------------------------

				bool JoinHorz(OutPt op1, OutPt op1b, OutPt op2, OutPt op2b,
				  IntPoint Pt, bool DiscardLeft)
				{
					Direction Dir1 = (op1.Pt.X > op1b.Pt.X ?
					  Direction.dRightToLeft : Direction.dLeftToRight);
					Direction Dir2 = (op2.Pt.X > op2b.Pt.X ?
					  Direction.dRightToLeft : Direction.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 == Direction.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 == Direction.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 == Direction.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;
				}
				//------------------------------------------------------------------------------

				private bool JoinPoints(Join j, OutRec outRec1, OutRec outRec2)
				{
					OutPt op1 = j.OutPt1, op1b;
					OutPt op2 = j.OutPt2, op2b;

					//There are 3 kinds of joins for output polygons ...
					//1. Horizontal joins where Join.OutPt1 & Join.OutPt2 are vertices anywhere
					//along (horizontal) collinear edges (& Join.OffPt is on the same horizontal).
					//2. Non-horizontal joins where Join.OutPt1 & Join.OutPt2 are at the same
					//location at the Bottom of the overlapping segment (& Join.OffPt is above).
					//3. StrictlySimple 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, out Left, out 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;
						}
					}
				}
				//----------------------------------------------------------------------

				public static int PointInPolygon(IntPoint pt, 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, cnt = path.Count;
					if (cnt < 3)
						return 0;
					IntPoint ip = path[0];
					for (int 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 == 0)
										return -1;
									else 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 == 0)
										return -1;
									else if ((d > 0) == (ipNext.Y > ip.Y))
										result = 1 - result;
								}
							}
						}
						ip = ipNext;
					}
					return result;
				}
				//------------------------------------------------------------------------------

				//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
				private static int PointInPolygon(IntPoint pt, OutPt op)
				{
					//returns 0 if false, +1 if true, -1 if pt ON polygon boundary
					int result = 0;
					OutPt startOp = op;
					cInt ptx = pt.X, pty = pt.Y;
					cInt poly0x = op.Pt.X, poly0y = op.Pt.Y;
					do
					{
						op = op.Next;
						cInt poly1x = op.Pt.X, poly1y = op.Pt.Y;

						if (poly1y == pty)
						{
							if ((poly1x == ptx) || (poly0y == pty &&
							  ((poly1x > ptx) == (poly0x < ptx))))
								return -1;
						}
						if ((poly0y < pty) != (poly1y < pty))
						{
							if (poly0x >= ptx)
							{
								if (poly1x > ptx)
									result = 1 - result;
								else
								{
									double d = (double)(poly0x - ptx) * (poly1y - pty) -
									  (double)(poly1x - ptx) * (poly0y - pty);
									if (d == 0)
										return -1;
									if ((d > 0) == (poly1y > poly0y))
										result = 1 - result;
								}
							}
							else
							{
								if (poly1x > ptx)
								{
									double d = (double)(poly0x - ptx) * (poly1y - pty) -
									  (double)(poly1x - ptx) * (poly0y - pty);
									if (d == 0)
										return -1;
									if ((d > 0) == (poly1y > poly0y))
										result = 1 - result;
								}
							}
						}
						poly0x = poly1x;
						poly0y = poly1y;
					} while (startOp != op);
					return result;
				}
				//------------------------------------------------------------------------------

				private static 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;
				}
				//----------------------------------------------------------------------

				private void FixupFirstLefts1(OutRec OldOutRec, OutRec NewOutRec)
				{
					foreach (OutRec outRec in m_PolyOuts)
					{
						OutRec firstLeft = ParseFirstLeft(outRec.FirstLeft);
						if (outRec.Pts != null && firstLeft == OldOutRec)
						{
							if (Poly2ContainsPoly1(outRec.Pts, NewOutRec.Pts))
								outRec.FirstLeft = NewOutRec;
						}
					}
				}
				//----------------------------------------------------------------------

				private void FixupFirstLefts2(OutRec innerOutRec, OutRec outerOutRec)
				{
					//A polygon has split into two such that one is now the inner of the other.
					//It's possible that these polygons now wrap around other polygons, so check
					//every polygon that's also contained by OuterOutRec's FirstLeft container
					//(including nil) to see if they've become inner to the new inner polygon ...
					OutRec orfl = outerOutRec.FirstLeft;
					foreach (OutRec outRec in m_PolyOuts)
					{
						if (outRec.Pts == null || outRec == outerOutRec || outRec == innerOutRec)
							continue;
						OutRec firstLeft = ParseFirstLeft(outRec.FirstLeft);
						if (firstLeft != orfl && firstLeft != innerOutRec && firstLeft != outerOutRec)
							continue;
						if (Poly2ContainsPoly1(outRec.Pts, innerOutRec.Pts))
							outRec.FirstLeft = innerOutRec;
						else if (Poly2ContainsPoly1(outRec.Pts, outerOutRec.Pts))
							outRec.FirstLeft = outerOutRec;
						else if (outRec.FirstLeft == innerOutRec || outRec.FirstLeft == outerOutRec)
							outRec.FirstLeft = orfl;
					}
				}
				//----------------------------------------------------------------------

				private void FixupFirstLefts3(OutRec OldOutRec, OutRec NewOutRec)
				{
					//same as FixupFirstLefts1 but doesn't call Poly2ContainsPoly1()
					foreach (OutRec outRec in m_PolyOuts)
					{
						if (outRec.Pts != null && outRec.FirstLeft == OldOutRec)
							outRec.FirstLeft = NewOutRec;
					}
				}
				//----------------------------------------------------------------------

				private static OutRec ParseFirstLeft(OutRec FirstLeft)
				{
					while (FirstLeft != null && FirstLeft.Pts == null)
						FirstLeft = FirstLeft.FirstLeft;
					return FirstLeft;
				}
				//------------------------------------------------------------------------------

				private void JoinCommonEdges()
				{
					int joinCnt = m_Joins.Count;
					for (int i = 0; i < joinCnt; i++)
					{
						Join join = m_Joins[i];

						OutRec outRec1 = GetOutRec(join.OutPt1.Idx);
						OutRec outRec2 = GetOutRec(join.OutPt2.Idx);

						if (outRec1.Pts == null || outRec2.Pts == null)
							continue;
						if (outRec1.IsOpen || outRec2.IsOpen)
							continue;

						//get the polygon fragment with the correct hole state (FirstLeft)
						//before calling JoinPoints() ...
						OutRec holeStateRec;
						if (outRec1 == outRec2)
							holeStateRec = outRec1;
						else if (OutRec1RightOfOutRec2(outRec1, outRec2))
							holeStateRec = outRec2;
						else if (OutRec1RightOfOutRec2(outRec2, outRec1))
							holeStateRec = outRec1;
						else
							holeStateRec = GetLowermostRec(outRec1, outRec2);

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

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

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

							if (Poly2ContainsPoly1(outRec2.Pts, outRec1.Pts))
							{
								//outRec1 contains outRec2 ...
								outRec2.IsHole = !outRec1.IsHole;
								outRec2.FirstLeft = outRec1;

								if (m_UsingPolyTree)
									FixupFirstLefts2(outRec2, outRec1);

								if ((outRec2.IsHole ^ ReverseSolution) == (Area(outRec2) > 0))
									ReversePolyPtLinks(outRec2.Pts);

							}
							else if (Poly2ContainsPoly1(outRec1.Pts, outRec2.Pts))
							{
								//outRec2 contains outRec1 ...
								outRec2.IsHole = outRec1.IsHole;
								outRec1.IsHole = !outRec2.IsHole;
								outRec2.FirstLeft = outRec1.FirstLeft;
								outRec1.FirstLeft = outRec2;

								if (m_UsingPolyTree)
									FixupFirstLefts2(outRec1, outRec2);

								if ((outRec1.IsHole ^ ReverseSolution) == (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 = null;
							outRec2.BottomPt = null;
							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)
								FixupFirstLefts3(outRec2, outRec1);
						}
					}
				}
				//------------------------------------------------------------------------------

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

				private void DoSimplePolygons()
				{
					int i = 0;
					while (i < m_PolyOuts.Count)
					{
						OutRec outrec = m_PolyOuts[i++];
						OutPt op = outrec.Pts;
						if (op == null || 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);
					}
				}
				//------------------------------------------------------------------------------

				public static double Area(Path poly)
				{
					int cnt = (int)poly.Count;
					if (cnt < 3)
						return 0;
					double a = 0;
					for (int i = 0, j = cnt - 1; i < cnt; ++i)
					{
						a += ((double)poly[j].X + poly[i].X) * ((double)poly[j].Y - poly[i].Y);
						j = i;
					}
					return -a * 0.5;
				}
				//------------------------------------------------------------------------------

				internal double Area(OutRec outRec)
				{
					return Area(outRec.Pts);
				}
				//------------------------------------------------------------------------------

				internal double Area(OutPt op)
				{
					OutPt opFirst = op;
					if (op == null)
						return 0;
					double a = 0;
					do
					{
						a = a + (double)(op.Prev.Pt.X + op.Pt.X) * (double)(op.Prev.Pt.Y - op.Pt.Y);
						op = op.Next;
					} while (op != opFirst);
					return a * 0.5;
				}

				//------------------------------------------------------------------------------
				// SimplifyPolygon functions ...
				// Convert self-intersecting polygons into simple polygons
				//------------------------------------------------------------------------------

				public static Paths SimplifyPolygon(Path poly,
					  PolyFillType fillType = PolyFillType.pftEvenOdd)
				{
					Paths result = new Paths();
					Clipper c = new Clipper();
					c.StrictlySimple = true;
					c.AddPath(poly, PolyType.ptSubject, true);
					c.Execute(ClipType.ctUnion, result, fillType, fillType);
					return result;
				}
				//------------------------------------------------------------------------------

				public static Paths SimplifyPolygons(Paths polys,
					PolyFillType fillType = PolyFillType.pftEvenOdd)
				{
					Paths result = new Paths();
					Clipper c = new Clipper();
					c.StrictlySimple = true;
					c.AddPaths(polys, PolyType.ptSubject, true);
					c.Execute(ClipType.ctUnion, result, fillType, fillType);
					return result;
				}
				//------------------------------------------------------------------------------

				private static double DistanceSqrd(IntPoint pt1, IntPoint pt2)
				{
					double dx = ((double)pt1.X - pt2.X);
					double dy = ((double)pt1.Y - pt2.Y);
					return (dx * dx + dy * dy);
				}
				//------------------------------------------------------------------------------

				private static double DistanceFromLineSqrd(IntPoint pt, IntPoint ln1, 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 = ln1.Y - ln2.Y;
					double B = 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);
				}
				//---------------------------------------------------------------------------

				private static bool SlopesNearCollinear(IntPoint pt1,
					IntPoint pt2, 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.  
					//nb: with 'spikes', either pt1 or pt3 is geometrically between the other pts                    
					if (Math.Abs(pt1.X - pt2.X) > Math.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;
					}
				}
				//------------------------------------------------------------------------------

				private static 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);
				}
				//------------------------------------------------------------------------------

				private static OutPt ExcludeOp(OutPt op)
				{
					OutPt result = op.Prev;
					result.Next = op.Next;
					op.Next.Prev = result;
					result.Idx = 0;
					return result;
				}
				//------------------------------------------------------------------------------

				public static Path CleanPolygon(Path path, double distance = 1.415)
				{
					//distance = proximity in units/pixels below which vertices will be stripped. 
					//Default ~= sqrt(2) so when adjacent vertices or semi-adjacent vertices have 
					//both x & y coords within 1 unit, then the second vertex will be stripped.

					int cnt = path.Count;

					if (cnt == 0)
						return new Path();

					OutPt[] outPts = new OutPt[cnt];
					for (int i = 0; i < cnt; ++i)
						outPts[i] = new OutPt();

					for (int i = 0; i < cnt; ++i)
					{
						outPts[i].Pt = path[i];
						outPts[i].Next = outPts[(i + 1) % cnt];
						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);
							cnt--;
						}
						else if (PointsAreClose(op.Prev.Pt, op.Next.Pt, distSqrd))
						{
							ExcludeOp(op.Next);
							op = ExcludeOp(op);
							cnt -= 2;
						}
						else if (SlopesNearCollinear(op.Prev.Pt, op.Pt, op.Next.Pt, distSqrd))
						{
							op = ExcludeOp(op);
							cnt--;
						}
						else
						{
							op.Idx = 1;
							op = op.Next;
						}
					}

					if (cnt < 3)
						cnt = 0;
					Path result = new Path(cnt);
					for (int i = 0; i < cnt; ++i)
					{
						result.Add(op.Pt);
						op = op.Next;
					}
					outPts = null;
					return result;
				}
				//------------------------------------------------------------------------------

				public static Paths CleanPolygons(Paths polys,
					double distance = 1.415)
				{
					Paths result = new Paths(polys.Count);
					int polyCnt = polys.Count;
					for (int i = 0; i < polyCnt; i++)
					{
						result.Add(CleanPolygon(polys[i], distance));
					}
					return result;
				}
				//------------------------------------------------------------------------------

				internal static Paths Minkowski(Path pattern, Path path, bool IsSum, bool IsClosed)
				{
					int delta = (IsClosed ? 1 : 0);
					int polyCnt = pattern.Count;
					int pathCnt = path.Count;
					Paths result = new Paths(pathCnt);
					if (IsSum)
						for (int i = 0; i < pathCnt; i++)
						{
							Path p = new Path(polyCnt);
							foreach (IntPoint ip in pattern)
								p.Add(new IntPoint(path[i].X + ip.X, path[i].Y + ip.Y));
							result.Add(p);
						}
					else
						for (int i = 0; i < pathCnt; i++)
						{
							Path p = new Path(polyCnt);
							foreach (IntPoint ip in pattern)
								p.Add(new IntPoint(path[i].X - ip.X, path[i].Y - ip.Y));
							result.Add(p);
						}

					Paths quads = new Paths((pathCnt + delta) * (polyCnt + 1));
					for (int i = 0; i < pathCnt - 1 + delta; i++)
						for (int j = 0; j < polyCnt; j++)
						{
							Path quad = new Path(4);
							quad.Add(result[i % pathCnt][j % polyCnt]);
							quad.Add(result[(i + 1) % pathCnt][j % polyCnt]);
							quad.Add(result[(i + 1) % pathCnt][(j + 1) % polyCnt]);
							quad.Add(result[i % pathCnt][(j + 1) % polyCnt]);
							if (!Orientation(quad))
								quad.Reverse();
							quads.Add(quad);
						}
					return quads;
				}
				//------------------------------------------------------------------------------

				public static Paths MinkowskiSum(Path pattern, Path path, bool pathIsClosed)
				{
					Paths paths = Minkowski(pattern, path, true, pathIsClosed);
					Clipper c = new Clipper();
					c.AddPaths(paths, PolyType.ptSubject, true);
					c.Execute(ClipType.ctUnion, paths, PolyFillType.pftNonZero, PolyFillType.pftNonZero);
					return paths;
				}
				//------------------------------------------------------------------------------

				private static Path TranslatePath(Path path, IntPoint delta)
				{
					int pathCnt = path.Count;
					Path outPath = new Path(pathCnt);
					for (int i = 0; i < pathCnt; i++)
					{
						outPath.Add(new IntPoint(path[i].X + delta.X, path[i].Y + delta.Y));
					}
					return outPath;
				}
				//------------------------------------------------------------------------------

				public static Paths MinkowskiSum(Path pattern, Paths paths, bool pathIsClosed)
				{
					Paths solution = new Paths();
					Clipper c = new Clipper();
					int pathCnt = paths.Count;
					for (int i = 0; i < pathCnt; ++i)
					{
						Paths tmp = Minkowski(pattern, paths[i], true, pathIsClosed);
						c.AddPaths(tmp, PolyType.ptSubject, true);
						if (pathIsClosed)
						{
							Path path = TranslatePath(paths[i], pattern[0]);
							c.AddPath(path, PolyType.ptClip, true);
						}
					}
					c.Execute(ClipType.ctUnion, solution,
					  PolyFillType.pftNonZero, PolyFillType.pftNonZero);
					return solution;
				}
				//------------------------------------------------------------------------------

				public static Paths MinkowskiDiff(Path poly1, Path poly2)
				{
					Paths paths = Minkowski(poly1, poly2, false, true);
					Clipper c = new Clipper();
					c.AddPaths(paths, PolyType.ptSubject, true);
					c.Execute(ClipType.ctUnion, paths, PolyFillType.pftNonZero, PolyFillType.pftNonZero);
					return paths;
				}
				//------------------------------------------------------------------------------

				internal enum NodeType { ntAny, ntOpen, ntClosed };

				public static Paths PolyTreeToPaths(PolyTree polytree)
				{

					Paths result = new Paths();
					result.Capacity = polytree.Total;
					AddPolyNodeToPaths(polytree, NodeType.ntAny, result);
					return result;
				}
				//------------------------------------------------------------------------------

				internal static void AddPolyNodeToPaths(PolyNode polynode, NodeType nt, Paths paths)
				{
					bool match = true;
					switch (nt)
					{
						case NodeType.ntOpen:
							return;
						case NodeType.ntClosed:
							match = !polynode.IsOpen;
							break;
						default:
							break;
					}

					if (polynode.m_polygon.Count > 0 && match)
						paths.Add(polynode.m_polygon);
					foreach (PolyNode pn in polynode.Childs)
						AddPolyNodeToPaths(pn, nt, paths);
				}
				//------------------------------------------------------------------------------

				public static Paths OpenPathsFromPolyTree(PolyTree polytree)
				{
					Paths result = new Paths();
					result.Capacity = polytree.ChildCount;
					for (int i = 0; i < polytree.ChildCount; i++)
						if (polytree.Childs[i].IsOpen)
							result.Add(polytree.Childs[i].m_polygon);
					return result;
				}
				//------------------------------------------------------------------------------

				public static Paths ClosedPathsFromPolyTree(PolyTree polytree)
				{
					Paths result = new Paths();
					result.Capacity = polytree.Total;
					AddPolyNodeToPaths(polytree, NodeType.ntClosed, result);
					return result;
				}
				//------------------------------------------------------------------------------

			} //end Clipper

			public class ClipperOffset
			{
				private Paths m_destPolys;
				private Path m_srcPoly;
				private Path m_destPoly;
				private List<DoublePoint> m_normals = new List<DoublePoint>();
				private double m_delta, m_sinA, m_sin, m_cos;
				private double m_miterLim, m_StepsPerRad;

				private IntPoint m_lowest;
				private PolyNode m_polyNodes = new PolyNode();

				public double ArcTolerance { get; set; }
				public double MiterLimit { get; set; }

				private const double two_pi = Math.PI * 2;
				private const double def_arc_tolerance = 0.25;

				public ClipperOffset(
				  double miterLimit = 2.0, double arcTolerance = def_arc_tolerance)
				{
					MiterLimit = miterLimit;
					ArcTolerance = arcTolerance;
					m_lowest.X = -1;
				}
				//------------------------------------------------------------------------------

				public void Clear()
				{
					m_polyNodes.Childs.Clear();
					m_lowest.X = -1;
				}
				//------------------------------------------------------------------------------

				internal static cInt Round(double value)
				{
					return value < 0 ? (cInt)(value - 0.5) : (cInt)(value + 0.5);
				}
				//------------------------------------------------------------------------------

				public void AddPath(Path path, JoinType joinType, EndType endType)
				{
					int highI = path.Count - 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 == EndType.etClosedLine || endType == EndType.etClosedPolygon)
						while (highI > 0 && path[0] == path[highI])
							highI--;
					newNode.m_polygon.Capacity = highI + 1;
					newNode.m_polygon.Add(path[0]);
					int j = 0, k = 0;
					for (int i = 1; i <= highI; i++)
						if (newNode.m_polygon[j] != path[i])
						{
							j++;
							newNode.m_polygon.Add(path[i]);
							if (path[i].Y > newNode.m_polygon[k].Y ||
							  (path[i].Y == newNode.m_polygon[k].Y &&
							  path[i].X < newNode.m_polygon[k].X))
								k = j;
						}
					if (endType == EndType.etClosedPolygon && j < 2)
						return;

					m_polyNodes.AddChild(newNode);

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

				public void AddPaths(Paths paths, JoinType joinType, EndType endType)
				{
					foreach (Path p in paths)
						AddPath(p, joinType, endType);
				}
				//------------------------------------------------------------------------------

				private void 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 &&
					  !Clipper.Orientation(m_polyNodes.Childs[(int)m_lowest.X].m_polygon))
					{
						for (int i = 0; i < m_polyNodes.ChildCount; i++)
						{
							PolyNode node = m_polyNodes.Childs[i];
							if (node.m_endtype == EndType.etClosedPolygon ||
							  (node.m_endtype == EndType.etClosedLine &&
							  Clipper.Orientation(node.m_polygon)))
								node.m_polygon.Reverse();
						}
					}
					else
					{
						for (int i = 0; i < m_polyNodes.ChildCount; i++)
						{
							PolyNode node = m_polyNodes.Childs[i];
							if (node.m_endtype == EndType.etClosedLine &&
							  !Clipper.Orientation(node.m_polygon))
								node.m_polygon.Reverse();
						}
					}
				}
				//------------------------------------------------------------------------------

				internal static DoublePoint GetUnitNormal(IntPoint pt1, IntPoint pt2)
				{
					double dx = (pt2.X - pt1.X);
					double dy = (pt2.Y - pt1.Y);
					if ((dx == 0) && (dy == 0))
						return new DoublePoint();

					double f = 1 * 1.0 / Math.Sqrt(dx * dx + dy * dy);
					dx *= f;
					dy *= f;

					return new DoublePoint(dy, -dx);
				}
				//------------------------------------------------------------------------------

				private void DoOffset(double delta)
				{
					m_destPolys = new Paths();
					m_delta = delta;

					//if Zero offset, just copy any CLOSED polygons to m_p and return ...
					if (ClipperBase.near_zero(delta))
					{
						m_destPolys.Capacity = m_polyNodes.ChildCount;
						for (int i = 0; i < m_polyNodes.ChildCount; i++)
						{
							PolyNode node = m_polyNodes.Childs[i];
							if (node.m_endtype == EndType.etClosedPolygon)
								m_destPolys.Add(node.m_polygon);
						}
						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 > Math.Abs(delta) * def_arc_tolerance)
						y = Math.Abs(delta) * def_arc_tolerance;
					else
						y = ArcTolerance;
					//see offset_triginometry2.svg in the documentation folder ...
					double steps = Math.PI / Math.Acos(1 - y / Math.Abs(delta));
					m_sin = Math.Sin(two_pi / steps);
					m_cos = Math.Cos(two_pi / steps);
					m_StepsPerRad = steps / two_pi;
					if (delta < 0.0)
						m_sin = -m_sin;

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

						int len = m_srcPoly.Count;

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

						m_destPoly = new Path();

						if (len == 1)
						{
							if (node.m_jointype == JoinType.jtRound)
							{
								double X = 1.0, Y = 0.0;
								for (int j = 1; j <= steps; j++)
								{
									m_destPoly.Add(new 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.Add(new 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.Add(m_destPoly);
							continue;
						}

						//build m_normals ...
						m_normals.Clear();
						m_normals.Capacity = len;
						for (int j = 0; j < len - 1; j++)
							m_normals.Add(GetUnitNormal(m_srcPoly[j], m_srcPoly[j + 1]));
						if (node.m_endtype == EndType.etClosedLine ||
						  node.m_endtype == EndType.etClosedPolygon)
							m_normals.Add(GetUnitNormal(m_srcPoly[len - 1], m_srcPoly[0]));
						else
							m_normals.Add(new DoublePoint(m_normals[len - 2]));

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

							IntPoint pt1;
							if (node.m_endtype == EndType.etOpenButt)
							{
								int j = len - 1;
								pt1 = new 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.Add(pt1);
								pt1 = new 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.Add(pt1);
							}
							else
							{
								int j = len - 1;
								k = len - 2;
								m_sinA = 0;
								m_normals[j] = new DoublePoint(-m_normals[j].X, -m_normals[j].Y);
								if (node.m_endtype == EndType.etOpenSquare)
									DoSquare(j, k);
								else
									DoRound(j, k);
							}

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

							m_normals[0] = new DoublePoint(-m_normals[1].X, -m_normals[1].Y);

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

							if (node.m_endtype == EndType.etOpenButt)
							{
								pt1 = new 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.Add(pt1);
								pt1 = new 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.Add(pt1);
							}
							else
							{
								k = 1;
								m_sinA = 0;
								if (node.m_endtype == EndType.etOpenSquare)
									DoSquare(0, 1);
								else
									DoRound(0, 1);
							}
							m_destPolys.Add(m_destPoly);
						}
					}
				}
				//------------------------------------------------------------------------------

				public void Execute(ref Paths solution, double delta)
				{
					solution.Clear();
					FixOrientations();
					DoOffset(delta);
					//now clean up 'corners' ...
					Clipper clpr = new Clipper();
					clpr.AddPaths(m_destPolys, PolyType.ptSubject, true);
					if (delta > 0)
					{
						clpr.Execute(ClipType.ctUnion, solution,
						  PolyFillType.pftPositive, PolyFillType.pftPositive);
					}
					else
					{
						IntRect r = Clipper.GetBounds(m_destPolys);
						Path outer = new Path(4);

						outer.Add(new IntPoint(r.left - 10, r.bottom + 10));
						outer.Add(new IntPoint(r.right + 10, r.bottom + 10));
						outer.Add(new IntPoint(r.right + 10, r.top - 10));
						outer.Add(new IntPoint(r.left - 10, r.top - 10));

						clpr.AddPath(outer, PolyType.ptSubject, true);
						clpr.ReverseSolution = true;
						clpr.Execute(ClipType.ctUnion, solution, PolyFillType.pftNegative, PolyFillType.pftNegative);
						if (solution.Count > 0)
							solution.RemoveAt(0);
					}
				}
				//------------------------------------------------------------------------------

				public void Execute(ref PolyTree solution, double delta)
				{
					solution.Clear();
					FixOrientations();
					DoOffset(delta);

					//now clean up 'corners' ...
					Clipper clpr = new Clipper();
					clpr.AddPaths(m_destPolys, PolyType.ptSubject, true);
					if (delta > 0)
					{
						clpr.Execute(ClipType.ctUnion, solution,
						  PolyFillType.pftPositive, PolyFillType.pftPositive);
					}
					else
					{
						IntRect r = Clipper.GetBounds(m_destPolys);
						Path outer = new Path(4);

						outer.Add(new IntPoint(r.left - 10, r.bottom + 10));
						outer.Add(new IntPoint(r.right + 10, r.bottom + 10));
						outer.Add(new IntPoint(r.right + 10, r.top - 10));
						outer.Add(new IntPoint(r.left - 10, r.top - 10));

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

				void OffsetPoint(int j, ref 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 (Math.Abs(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.Add(new 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.Add(new 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.Add(m_srcPoly[j]);
						m_destPoly.Add(new 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 JoinType.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 JoinType.jtSquare:
								DoSquare(j, k);
								break;
							case JoinType.jtRound:
								DoRound(j, k);
								break;
						}
					k = j;
				}
				//------------------------------------------------------------------------------

				internal void DoSquare(int j, int k)
				{
					double dx = Math.Tan(Math.Atan2(m_sinA,
						m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y) / 4);
					m_destPoly.Add(new 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.Add(new 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))));
				}
				//------------------------------------------------------------------------------

				internal void DoMiter(int j, int k, double r)
				{
					double q = m_delta / r;
					m_destPoly.Add(new 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)));
				}
				//------------------------------------------------------------------------------

				internal void DoRound(int j, int k)
				{
					double a = Math.Atan2(m_sinA,
					m_normals[k].X * m_normals[j].X + m_normals[k].Y * m_normals[j].Y);
					int steps = Math.Max((int)Round(m_StepsPerRad * Math.Abs(a)), 1);

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

			class ClipperException : Exception
			{
				public ClipperException(string description) : base(description) { }
			}
			//------------------------------------------------------------------------------

		}
	} //end ClipperLib namespace

}