public static List<Vertices> ConvexPartition(Vertices vertices)
        {
            Polygon poly = new Polygon();

            foreach (Vector2 vertex in vertices)
            {
                poly.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));
            }

            DTSweepContext tcx = new DTSweepContext();
            tcx.PrepareTriangulation(poly);
            DTSweep.Triangulate(tcx);

            List<Vertices> results = new List<Vertices>();

            foreach (DelaunayTriangle triangle in poly.Triangles)
            {
                Vertices v = new Vertices();
                foreach (TriangulationPoint p in triangle.Points)
                {
                    v.Add(new Vector2((float)p.X, (float)p.Y));
                }
                results.Add(v);
            }

            return results;
        }

        /// <summary>
        /// Triangulate simple polygon with holes
        /// </summary>
        public static void Triangulate(DTSweepContext tcx)
        {
            tcx.CreateAdvancingFront();

            Sweep(tcx);

            // Finalize triangulation
            if (tcx.TriangulationMode == TriangulationMode.Polygon)
            {
                FinalizationPolygon(tcx);
            }
            else
            {
                FinalizationConvexHull(tcx);
            }

            tcx.Done();
        }

		/// <summary>
		/// Start sweeping the Y-sorted point set from bottom to top
		/// </summary>
		static void Sweep( DTSweepContext tcx )
		{
			List<TriangulationPoint> points = tcx.Points;

			for( int i = 1; i < points.Count; i++ )
			{
				TriangulationPoint point = points[i];

				AdvancingFrontNode node = PointEvent( tcx, point );

				if( point.HasEdges )
				{
					foreach( DTSweepConstraint e in point.Edges )
					{
						EdgeEvent( tcx, e, node );
					}
				}
				tcx.Update( null );
			}
		}

        /// <summary>
        /// Decompose the polygon into several smaller non-concave polygon.
        /// </summary>
        public static List<Vertices> ConvexPartition(Vertices vertices)
        {
            if (vertices.Count <= 3)
                return new List<Vertices> { vertices };

            Polygon poly = new Polygon();

            foreach (Vector2 vertex in vertices)
                poly.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));

            if (vertices.Holes != null)
            {
                foreach (Vertices holeVertices in vertices.Holes)
                {
                    Polygon hole = new Polygon();

                    foreach (Vector2 vertex in holeVertices)
                        hole.Points.Add(new TriangulationPoint(vertex.X, vertex.Y));

                    poly.AddHole(hole);
                }
            }

            DTSweepContext tcx = new DTSweepContext();
            tcx.PrepareTriangulation(poly);
            DTSweep.Triangulate(tcx);

            List<Vertices> results = new List<Vertices>();

            foreach (DelaunayTriangle triangle in poly.Triangles)
            {
                Vertices v = new Vertices();
                foreach (TriangulationPoint p in triangle.Points)
                {
                    v.Add(new Vector2((float)p.X, (float)p.Y));
                }
                results.Add(v);
            }

            return results;
        }

 private static void FillRightBelowEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
 {
     if (node.Point.X < edge.P.X) // needed?
     {
         if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
         {
             // Concave
             FillRightConcaveEdgeEvent(tcx, edge, node);
         }
         else
         {
             // Convex
             FillRightConvexEdgeEvent(tcx, edge, node);
             // Retry this one
             FillRightBelowEdgeEvent(tcx, edge, node);
         }
     }
 }

 private static void FillRightAboveEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
 {
     while (node.Next.Point.X < edge.P.X)
     {
         // Check if next node is below the edge
         Orientation o1 = TriangulationUtil.Orient2d(edge.Q, node.Next.Point, edge.P);
         if (o1 == Orientation.CCW)
         {
             FillRightBelowEdgeEvent(tcx, edge, node);
         }
         else
         {
             node = node.Next;
         }
     }
 }

        /// <summary>
        /// Creates a new front triangle and legalize it
        /// </summary>
        private static AdvancingFrontNode NewFrontTriangle(DTSweepContext tcx, TriangulationPoint point, AdvancingFrontNode node)
        {
            DelaunayTriangle triangle = new DelaunayTriangle(point, node.Point, node.Next.Point);
            triangle.MarkNeighbor(node.Triangle);
            tcx.Triangles.Add(triangle);

            AdvancingFrontNode newNode = new AdvancingFrontNode(point);
            newNode.Next = node.Next;
            newNode.Prev = node;
            node.Next.Prev = newNode;
            node.Next = newNode;

            tcx.AddNode(newNode); // XXX: BST

            if (!Legalize(tcx, triangle))
            {
                tcx.MapTriangleToNodes(triangle);
            }

            return newNode;
        }

        private static bool IsShallow(DTSweepContext tcx, AdvancingFrontNode node)
        {
            double height;

            if (tcx.Basin.leftHighest)
            {
                height = tcx.Basin.leftNode.Point.Y - node.Point.Y;
            }
            else
            {
                height = tcx.Basin.rightNode.Point.Y - node.Point.Y;
            }
            if (tcx.Basin.width > height)
            {
                return true;
            }
            return false;
        }

        private static void FinalizationPolygon(DTSweepContext tcx)
        {
            // Get an Internal triangle to start with
            DelaunayTriangle t = tcx.aFront.Head.Next.Triangle;
            TriangulationPoint p = tcx.aFront.Head.Next.Point;
            while (!t.GetConstrainedEdgeCW(p))
            {
                t = t.NeighborCCW(p);
            }

            // Collect interior triangles constrained by edges
            tcx.MeshClean(t);
        }

        /// <summary>
        /// Adds a triangle to the advancing front to fill a hole.
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="node">middle node, that is the bottom of the hole</param>
        private static void Fill(DTSweepContext tcx, AdvancingFrontNode node)
        {
            DelaunayTriangle triangle = new DelaunayTriangle(node.Prev.Point, node.Point, node.Next.Point);
            // TODO: should copy the cEdge value from neighbor triangles
            //       for now cEdge values are copied during the legalize
            triangle.MarkNeighbor(node.Prev.Triangle);
            triangle.MarkNeighbor(node.Triangle);
            tcx.Triangles.Add(triangle);

            // Update the advancing front
            node.Prev.Next = node.Next;
            node.Next.Prev = node.Prev;
            tcx.RemoveNode(node);

            // If it was legalized the triangle has already been mapped
            if (!Legalize(tcx, triangle))
            {
                tcx.MapTriangleToNodes(triangle);
            }
        }

        private static void EdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle triangle, TriangulationPoint point)
        {
            if (IsEdgeSideOfTriangle(triangle, ep, eq))
                return;

            TriangulationPoint p1 = triangle.PointCCW(point);
            Orientation o1 = TriangulationUtil.Orient2d(eq, p1, ep);
            if (o1 == Orientation.Collinear)
            {
                if (triangle.Contains(eq, p1))
                {
                    triangle.MarkConstrainedEdge(eq, p1);
                    // We are modifying the constraint maybe it would be better to
                    // not change the given constraint and just keep a variable for the new constraint
                    tcx.EdgeEvent.ConstrainedEdge.Q = p1;
                    triangle = triangle.NeighborAcross(point);
                    EdgeEvent(tcx, ep, p1, triangle, p1);
                }
                else
                {
                    throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
                }
                return;
            }

            TriangulationPoint p2 = triangle.PointCW(point);
            Orientation o2 = TriangulationUtil.Orient2d(eq, p2, ep);
            if (o2 == Orientation.Collinear)
            {
                if (triangle.Contains(eq, p2))
                {
                    triangle.MarkConstrainedEdge(eq, p2);
                    // We are modifying the constraint maybe it would be better to
                    // not change the given constraint and just keep a variable for the new constraint
                    tcx.EdgeEvent.ConstrainedEdge.Q = p2;
                    triangle = triangle.NeighborAcross(point);
                    EdgeEvent(tcx, ep, p2, triangle, p2);
                }
                else
                {
                    throw new PointOnEdgeException("EdgeEvent - Point on constrained edge not supported yet");
                }
                return;
            }

            if (o1 == o2)
            {
                // Need to decide if we are rotating CW or CCW to get to a triangle
                // that will cross edge
                if (o1 == Orientation.CW)
                {
                    triangle = triangle.NeighborCCW(point);
                }
                else
                {
                    triangle = triangle.NeighborCW(point);
                }
                EdgeEvent(tcx, ep, eq, triangle, point);
            }
            else
            {
                // This triangle crosses constraint so lets flippin start!
                FlipEdgeEvent(tcx, ep, eq, triangle, point);
            }
        }

 /// <summary>
 /// We will traverse the entire advancing front and fill it to form a convex hull.
 /// </summary>
 private static void TurnAdvancingFrontConvex(DTSweepContext tcx, AdvancingFrontNode b, AdvancingFrontNode c)
 {
     AdvancingFrontNode first = b;
     while (c != tcx.aFront.Tail)
     {
         if (TriangulationUtil.Orient2d(b.Point, c.Point, c.Next.Point) == Orientation.CCW)
         {
             // [b,c,d] Concave - fill around c
             Fill(tcx, c);
             c = c.Next;
         }
         else
         {
             // [b,c,d] Convex
             if (b != first && TriangulationUtil.Orient2d(b.Prev.Point, b.Point, c.Point) == Orientation.CCW)
             {
                 // [a,b,c] Concave - fill around b
                 Fill(tcx, b);
                 b = b.Prev;
             }
             else
             {
                 // [a,b,c] Convex - nothing to fill
                 b = c;
                 c = c.Next;
             }
         }
     }
 }

        /// <summary>
        /// Find closes node to the left of the new point and
        /// create a new triangle. If needed new holes and basins
        /// will be filled to.
        /// </summary>
        private static AdvancingFrontNode PointEvent(DTSweepContext tcx, TriangulationPoint point)
        {
            AdvancingFrontNode node = tcx.LocateNode(point);
            AdvancingFrontNode newNode = NewFrontTriangle(tcx, point, node);

            // Only need to check +epsilon since point never have smaller
            // x value than node due to how we fetch nodes from the front
            if (point.X <= node.Point.X + TriangulationUtil.EPSILON)
            {
                Fill(tcx, node);
            }

            tcx.AddNode(newNode);

            FillAdvancingFront(tcx, newNode);
            return newNode;
        }

		static void FillLeftBelowEdgeEvent( DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node )
		{
			if( node.Point.X > edge.P.X )
			{
				if( TriangulationUtil.Orient2d( node.Point, node.Prev.Point, node.Prev.Prev.Point ) == Orientation.CW )
				{
					// Concave 
					FillLeftConcaveEdgeEvent( tcx, edge, node );
				}
				else
				{
					// Convex
					FillLeftConvexEdgeEvent( tcx, edge, node );
					// Retry this one
					FillLeftBelowEdgeEvent( tcx, edge, node );
				}
			}
		}

 private static void FillRightConvexEdgeEvent(DTSweepContext tcx, DTSweepConstraint edge, AdvancingFrontNode node)
 {
     // Next concave or convex?
     if (TriangulationUtil.Orient2d(node.Next.Point, node.Next.Next.Point, node.Next.Next.Next.Point) ==
         Orientation.CCW)
     {
         // Concave
         FillRightConcaveEdgeEvent(tcx, edge, node.Next);
     }
     else
     {
         // Convex
         // Next above or below edge?
         if (TriangulationUtil.Orient2d(edge.Q, node.Next.Next.Point, edge.P) == Orientation.CCW)
         {
             // Below
             FillRightConvexEdgeEvent(tcx, edge, node.Next);
         }
         else
         {
             // Above
         }
     }
 }

        /// <summary>
        /// If this is a Delaunay Triangulation of a pointset we need to fill so the triangle mesh gets a ConvexHull 
        /// </summary>
        private static void FinalizationConvexHull(DTSweepContext tcx)
        {
            DelaunayTriangle t1, t2;

            AdvancingFrontNode n1 = tcx.aFront.Head.Next;
            AdvancingFrontNode n2 = n1.Next;

            TurnAdvancingFrontConvex(tcx, n1, n2);

            // TODO: implement ConvexHull for lower right and left boundary

            // Lets remove triangles connected to the two "algorithm" points

            // XXX: When the first the nodes are points in a triangle we need to do a flip before
            //      removing triangles or we will lose a valid triangle.
            //      Same for last three nodes!
            // !!! If I implement ConvexHull for lower right and left boundary this fix should not be
            //     needed and the removed triangles will be added again by default
            n1 = tcx.aFront.Tail.Prev;
            if (n1.Triangle.Contains(n1.Next.Point) && n1.Triangle.Contains(n1.Prev.Point))
            {
                t1 = n1.Triangle.NeighborAcross(n1.Point);
                RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
                tcx.MapTriangleToNodes(n1.Triangle);
                tcx.MapTriangleToNodes(t1);
            }
            n1 = tcx.aFront.Head.Next;
            if (n1.Triangle.Contains(n1.Prev.Point) && n1.Triangle.Contains(n1.Next.Point))
            {
                t1 = n1.Triangle.NeighborAcross(n1.Point);
                RotateTrianglePair(n1.Triangle, n1.Point, t1, t1.OppositePoint(n1.Triangle, n1.Point));
                tcx.MapTriangleToNodes(n1.Triangle);
                tcx.MapTriangleToNodes(t1);
            }

            // Lower right boundary
            TriangulationPoint first = tcx.aFront.Head.Point;
            n2 = tcx.aFront.Tail.Prev;
            t1 = n2.Triangle;
            TriangulationPoint p1 = n2.Point;
            n2.Triangle = null;
            do
            {
                tcx.RemoveFromList(t1);
                p1 = t1.PointCCW(p1);
                if (p1 == first) break;
                t2 = t1.NeighborCCW(p1);
                t1.Clear();
                t1 = t2;
            } while (true);

            // Lower left boundary
            first = tcx.aFront.Head.Next.Point;
            p1 = t1.PointCW(tcx.aFront.Head.Point);
            t2 = t1.NeighborCW(tcx.aFront.Head.Point);
            t1.Clear();
            t1 = t2;
            while (p1 != first) //TODO: Port note. This was do while before.
            {
                tcx.RemoveFromList(t1);
                p1 = t1.PointCCW(p1);
                t2 = t1.NeighborCCW(p1);
                t1.Clear();
                t1 = t2;
            }

            // Remove current head and tail node now that we have removed all triangles attached
            // to them. Then set new head and tail node points
            tcx.aFront.Head = tcx.aFront.Head.Next;
            tcx.aFront.Head.Prev = null;
            tcx.aFront.Tail = tcx.aFront.Tail.Prev;
            tcx.aFront.Tail.Next = null;

            tcx.FinalizeTriangulation();
        }

        /// <summary>
        /// Fills holes in the Advancing Front
        /// </summary>
        private static void FillAdvancingFront(DTSweepContext tcx, AdvancingFrontNode n)
        {
            double angle;

            // Fill right holes
            AdvancingFrontNode node = n.Next;
            while (node.HasNext)
            {
                // if HoleAngle exceeds 90 degrees then break.
                if (LargeHole_DontFill(node))
                    break;

                Fill(tcx, node);
                node = node.Next;
            }

            // Fill left holes
            node = n.Prev;
            while (node.HasPrev)
            {
                // if HoleAngle exceeds 90 degrees then break.
                if (LargeHole_DontFill(node))
                    break;

                angle = HoleAngle(node);
                if (angle > PI_div2 || angle < -PI_div2)
                {
                    break;
                }
                Fill(tcx, node);
                node = node.Prev;
            }

            // Fill right basins
            if (n.HasNext && n.Next.HasNext)
            {
                angle = BasinAngle(n);
                if (angle < PI_3div4)
                {
                    FillBasin(tcx, n);
                }
            }
        }

        private static void FlipEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle t, TriangulationPoint p)
        {
            DelaunayTriangle ot = t.NeighborAcross(p);
            TriangulationPoint op = ot.OppositePoint(t, p);

            if (ot == null)
            {
                // If we want to integrate the fillEdgeEvent do it here
                // With current implementation we should never get here
                throw new InvalidOperationException("[BUG:FIXME] FLIP failed due to missing triangle");
            }

            if (t.GetConstrainedEdgeAcross(p))
            {
                throw new Exception("Intersecting Constraints");
            }

            bool inScanArea = TriangulationUtil.InScanArea(p, t.PointCCW(p), t.PointCW(p), op);
            if (inScanArea)
            {
                // Lets rotate shared edge one vertex CW
                RotateTrianglePair(t, p, ot, op);
                tcx.MapTriangleToNodes(t);
                tcx.MapTriangleToNodes(ot);

                if (p == eq && op == ep)
                {
                    if (eq == tcx.EdgeEvent.ConstrainedEdge.Q
                        && ep == tcx.EdgeEvent.ConstrainedEdge.P)
                    {
                        t.MarkConstrainedEdge(ep, eq);
                        ot.MarkConstrainedEdge(ep, eq);
                        Legalize(tcx, t);
                        Legalize(tcx, ot);
                    }
                    else
                    {
                        // XXX: I think one of the triangles should be legalized here?
                    }
                }
                else
                {
                    // TODO: remove
                    Orientation o = TriangulationUtil.Orient2d(eq, op, ep);
                    t = NextFlipTriangle(tcx, o, t, ot, p, op);
                    FlipEdgeEvent(tcx, ep, eq, t, p);
                }
            }
            else
            {
                TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
                FlipScanEdgeEvent(tcx, ep, eq, t, ot, newP);
                EdgeEvent(tcx, ep, eq, t, p);
            }
        }

        /// <summary>
        /// Fills a basin that has formed on the Advancing Front to the right
        /// of given node.
        /// First we decide a left,bottom and right node that forms the 
        /// boundaries of the basin. Then we do a reqursive fill.
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="node">starting node, this or next node will be left node</param>
        private static void FillBasin(DTSweepContext tcx, AdvancingFrontNode node)
        {
            if (TriangulationUtil.Orient2d(node.Point, node.Next.Point, node.Next.Next.Point) == Orientation.CCW)
            {
                // tcx.basin.leftNode = node.next.next;
                tcx.Basin.leftNode = node;
            }
            else
            {
                tcx.Basin.leftNode = node.Next;
            }

            // Find the bottom and right node
            tcx.Basin.bottomNode = tcx.Basin.leftNode;
            while (tcx.Basin.bottomNode.HasNext && tcx.Basin.bottomNode.Point.Y >= tcx.Basin.bottomNode.Next.Point.Y)
            {
                tcx.Basin.bottomNode = tcx.Basin.bottomNode.Next;
            }

            if (tcx.Basin.bottomNode == tcx.Basin.leftNode)
            {
                // No valid basins
                return;
            }

            tcx.Basin.rightNode = tcx.Basin.bottomNode;
            while (tcx.Basin.rightNode.HasNext && tcx.Basin.rightNode.Point.Y < tcx.Basin.rightNode.Next.Point.Y)
            {
                tcx.Basin.rightNode = tcx.Basin.rightNode.Next;
            }

            if (tcx.Basin.rightNode == tcx.Basin.bottomNode)
            {
                // No valid basins
                return;
            }

            tcx.Basin.width = tcx.Basin.rightNode.Point.X - tcx.Basin.leftNode.Point.X;
            tcx.Basin.leftHighest = tcx.Basin.leftNode.Point.Y > tcx.Basin.rightNode.Point.Y;

            FillBasinReq(tcx, tcx.Basin.bottomNode);
        }

        /// <summary>
        /// Scan part of the FlipScan algorithm<br>
        /// When a triangle pair isn't flippable we will scan for the next 
        /// point that is inside the flip triangle scan area. When found 
        /// we generate a new flipEdgeEvent
        /// </summary>
        /// <param name="tcx"></param>
        /// <param name="ep">last point on the edge we are traversing</param>
        /// <param name="eq">first point on the edge we are traversing</param>
        /// <param name="flipTriangle">the current triangle sharing the point eq with edge</param>
        /// <param name="t"></param>
        /// <param name="p"></param>
        private static void FlipScanEdgeEvent(DTSweepContext tcx, TriangulationPoint ep, TriangulationPoint eq, DelaunayTriangle flipTriangle, DelaunayTriangle t, TriangulationPoint p)
        {
            DelaunayTriangle ot = t.NeighborAcross(p);
            TriangulationPoint op = ot.OppositePoint(t, p);

            if (ot == null)
            {
                // If we want to integrate the fillEdgeEvent do it here
                // With current implementation we should never get here
                throw new Exception("[BUG:FIXME] FLIP failed due to missing triangle");
            }

            bool inScanArea = TriangulationUtil.InScanArea(eq, flipTriangle.PointCCW(eq), flipTriangle.PointCW(eq), op);
            if (inScanArea)
            {
                // flip with new edge op->eq
                FlipEdgeEvent(tcx, eq, op, ot, op);
                // TODO: Actually I just figured out that it should be possible to
                //       improve this by getting the next ot and op before the the above
                //       flip and continue the flipScanEdgeEvent here
                // set new ot and op here and loop back to inScanArea test
                // also need to set a new flipTriangle first
                // Turns out at first glance that this is somewhat complicated
                // so it will have to wait.
            }
            else
            {
                TriangulationPoint newP = NextFlipPoint(ep, eq, ot, op);
                FlipScanEdgeEvent(tcx, ep, eq, flipTriangle, ot, newP);
            }
        }