/// <summary>
        /// Will return the new root (unchanged except in start-up)
        /// </summary>
        public static VNode ProcessDataEvent(VDataEvent e, VNode Root, VoronoiGraph VG, double ys, out VDataNode[] CircleCheckList)
        {
            if (Root == null)
            {
                Root            = new VDataNode(e.DataPoint);
                CircleCheckList = new VDataNode[] { (VDataNode)Root };
                return(Root);
            }
            //1. Find the node to be replaced
            VNode C = VNode.FindDataNode(Root, ys, e.DataPoint[0]);
            //2. Create the subtree (ONE Edge, but two VEdgeNodes)
            VoronoiEdge VE = new VoronoiEdge();

            VE.LeftData  = ((VDataNode)C).DataPoint;
            VE.RightData = e.DataPoint;
            VE.VVertexA  = Fortune.VVUnkown;
            VE.VVertexB  = Fortune.VVUnkown;
            VG.Edges.Add(VE);

            VNode SubRoot;

            if (Math.Abs(VE.LeftData[1] - VE.RightData[1]) < 1e-10)
            {
                if (VE.LeftData[0] < VE.RightData[0])
                {
                    SubRoot       = new VEdgeNode(VE, false);
                    SubRoot.Left  = new VDataNode(VE.LeftData);
                    SubRoot.Right = new VDataNode(VE.RightData);
                }
                else
                {
                    SubRoot       = new VEdgeNode(VE, true);
                    SubRoot.Left  = new VDataNode(VE.RightData);
                    SubRoot.Right = new VDataNode(VE.LeftData);
                }
                CircleCheckList = new VDataNode[] { (VDataNode)SubRoot.Left, (VDataNode)SubRoot.Right };
            }
            else
            {
                SubRoot             = new VEdgeNode(VE, false);
                SubRoot.Left        = new VDataNode(VE.LeftData);
                SubRoot.Right       = new VEdgeNode(VE, true);
                SubRoot.Right.Left  = new VDataNode(VE.RightData);
                SubRoot.Right.Right = new VDataNode(VE.LeftData);
                CircleCheckList     = new VDataNode[] { (VDataNode)SubRoot.Left, (VDataNode)SubRoot.Right.Left, (VDataNode)SubRoot.Right.Right };
            }

            //3. Apply subtree
            if (C.Parent == null)
            {
                return(SubRoot);
            }
            C.Parent.Replace(C, SubRoot);
            return(Root);
        }
        public static void CleanUpTree(VNode Root)
        {
            if (Root is VDataNode)
            {
                return;
            }
            VEdgeNode VE = Root as VEdgeNode;

            while (VE.Edge.VVertexB == Fortune.VVUnkown)
            {
                VE.Edge.AddVertex(Fortune.VVInfinite);
//				VE.Flipped = !VE.Flipped;
            }
            if (VE.Flipped)
            {
                Vector T = VE.Edge.LeftData;
                VE.Edge.LeftData  = VE.Edge.RightData;
                VE.Edge.RightData = T;
            }
            VE.Edge.Done = true;
            CleanUpTree(Root.Left);
            CleanUpTree(Root.Right);
        }
        public static VNode ProcessCircleEvent(VCircleEvent e, VNode Root, VoronoiGraph VG, double ys, out VDataNode[] CircleCheckList)
        {
            VDataNode a, b, c;
            VEdgeNode eu, eo;

            b = e.NodeN;
            a = VNode.LeftDataNode(b);
            c = VNode.RightDataNode(b);
            if (a == null || b.Parent == null || c == null || !a.DataPoint.Equals(e.NodeL.DataPoint) || !c.DataPoint.Equals(e.NodeR.DataPoint))
            {
                CircleCheckList = new VDataNode[] {};
                return(Root);                // Abbruch da sich der Graph verändert hat
            }
            eu = (VEdgeNode)b.Parent;
            CircleCheckList = new VDataNode[] { a, c };
            //1. Create the new Vertex
            Vector VNew = new Vector(e.Center[0], e.Center[1]);

//			VNew[0] = Fortune.ParabolicCut(a.DataPoint[0],a.DataPoint[1],c.DataPoint[0],c.DataPoint[1],ys);
//			VNew[1] = (ys + a.DataPoint[1])/2 - 1/(2*(ys-a.DataPoint[1]))*(VNew[0]-a.DataPoint[0])*(VNew[0]-a.DataPoint[0]);
            VG.Vertices.Add(VNew);
            //2. Find out if a or c are in a distand part of the tree (the other is then b's sibling) and assign the new vertex
            if (eu.Left == b)          // c is sibling
            {
                eo = VNode.EdgeToRightDataNode(a);

                // replace eu by eu's Right
                eu.Parent.Replace(eu, eu.Right);
            }
            else             // a is sibling
            {
                eo = VNode.EdgeToRightDataNode(b);

                // replace eu by eu's Left
                eu.Parent.Replace(eu, eu.Left);
            }
            eu.Edge.AddVertex(VNew);
//			///////////////////// uncertain
//			if(eo==eu)
//				return Root;
//			/////////////////////

            //complete & cleanup eo
            eo.Edge.AddVertex(VNew);
            //while(eo.Edge.VVertexB == Fortune.VVUnkown)
            //{
            //    eo.Flipped = !eo.Flipped;
            //    eo.Edge.AddVertex(Fortune.VVInfinite);
            //}
            //if(eo.Flipped)
            //{
            //    Vector T = eo.Edge.LeftData;
            //    eo.Edge.LeftData = eo.Edge.RightData;
            //    eo.Edge.RightData = T;
            //}


            //2. Replace eo by new Edge
            VoronoiEdge VE = new VoronoiEdge();

            VE.LeftData  = a.DataPoint;
            VE.RightData = c.DataPoint;
            VE.AddVertex(VNew);
            VG.Edges.Add(VE);

            VEdgeNode VEN = new VEdgeNode(VE, false);

            VEN.Left  = eo.Left;
            VEN.Right = eo.Right;
            if (eo.Parent == null)
            {
                return(VEN);
            }
            eo.Parent.Replace(eo, VEN);
            return(Root);
        }
		public static VNode ProcessCircleEvent(VCircleEvent e, VNode Root, VoronoiGraph VG, double ys, out VDataNode[] CircleCheckList)
		{
			VDataNode a,b,c;
			VEdgeNode eu,eo;
			b = e.NodeN;
			a = VNode.LeftDataNode(b);
			c = VNode.RightDataNode(b);
			if(a==null || b.Parent==null || c==null || !a.DataPoint.Equals(e.NodeL.DataPoint) || !c.DataPoint.Equals(e.NodeR.DataPoint))
			{
				CircleCheckList = new VDataNode[]{};
				return Root; // Abbruch da sich der Graph verändert hat
			}
			eu = (VEdgeNode)b.Parent;
			CircleCheckList = new VDataNode[] {a,c};
			//1. Create the new Vertex
			Vector VNew = new Vector(e.Center[0],e.Center[1]);
//			VNew[0] = Fortune.ParabolicCut(a.DataPoint[0],a.DataPoint[1],c.DataPoint[0],c.DataPoint[1],ys);
//			VNew[1] = (ys + a.DataPoint[1])/2 - 1/(2*(ys-a.DataPoint[1]))*(VNew[0]-a.DataPoint[0])*(VNew[0]-a.DataPoint[0]);
			VG.Vertizes.Add(VNew);
			//2. Find out if a or c are in a distand part of the tree (the other is then b's sibling) and assign the new vertex
			if(eu.Left==b) // c is sibling
			{
				eo = VNode.EdgeToRightDataNode(a);

				// replace eu by eu's Right
				eu.Parent.Replace(eu,eu.Right);
			}
			else // a is sibling
			{
				eo = VNode.EdgeToRightDataNode(b);

				// replace eu by eu's Left
				eu.Parent.Replace(eu,eu.Left);
			}
			eu.Edge.AddVertex(VNew);
//			///////////////////// uncertain
//			if(eo==eu)
//				return Root;
//			/////////////////////
			
			//complete & cleanup eo
			eo.Edge.AddVertex(VNew);
			//while(eo.Edge.VVertexB == Fortune.VVUnkown)
			//{
			//    eo.Flipped = !eo.Flipped;
			//    eo.Edge.AddVertex(Fortune.VVInfinite);
			//}
			//if(eo.Flipped)
			//{
			//    Vector T = eo.Edge.LeftData;
			//    eo.Edge.LeftData = eo.Edge.RightData;
			//    eo.Edge.RightData = T;
			//}


			//2. Replace eo by new Edge
			VoronoiEdge VE = new VoronoiEdge();
			VE.LeftData = a.DataPoint;
			VE.RightData = c.DataPoint;
			VE.AddVertex(VNew);
			VG.Edges.Add(VE);

			VEdgeNode VEN = new VEdgeNode(VE, false);
			VEN.Left = eo.Left;
			VEN.Right = eo.Right;
			if(eo.Parent == null)
				return VEN;
			eo.Parent.Replace(eo,VEN);
			return Root;
		}
		/// <summary>
		/// Will return the new root (unchanged except in start-up)
		/// </summary>
		public static VNode ProcessDataEvent(VDataEvent e, VNode Root, VoronoiGraph VG, double ys, out VDataNode[] CircleCheckList)
		{
			if(Root==null)
			{
				Root = new VDataNode(e.DataPoint);
				CircleCheckList = new VDataNode[] {(VDataNode)Root};
				return Root;
			}
			//1. Find the node to be replaced
			VNode C = VNode.FindDataNode(Root, ys, e.DataPoint[0]);
			//2. Create the subtree (ONE Edge, but two VEdgeNodes)
			VoronoiEdge VE = new VoronoiEdge();
			VE.LeftData = ((VDataNode)C).DataPoint;
			VE.RightData = e.DataPoint;
			VE.VVertexA = Fortune.VVUnkown;
			VE.VVertexB = Fortune.VVUnkown;
			VG.Edges.Add(VE);

			VNode SubRoot;
			if(Math.Abs(VE.LeftData[1]-VE.RightData[1])<1e-10)
			{
				if(VE.LeftData[0]<VE.RightData[0])
				{
					SubRoot = new VEdgeNode(VE,false);
					SubRoot.Left = new VDataNode(VE.LeftData);
					SubRoot.Right = new VDataNode(VE.RightData);
				}
				else
				{
					SubRoot = new VEdgeNode(VE,true);
					SubRoot.Left = new VDataNode(VE.RightData);
					SubRoot.Right = new VDataNode(VE.LeftData);
				}
				CircleCheckList = new VDataNode[] {(VDataNode)SubRoot.Left,(VDataNode)SubRoot.Right};
			}
			else
			{
				SubRoot = new VEdgeNode(VE,false);
				SubRoot.Left = new VDataNode(VE.LeftData);
				SubRoot.Right = new VEdgeNode(VE,true);
				SubRoot.Right.Left = new VDataNode(VE.RightData);
				SubRoot.Right.Right = new VDataNode(VE.LeftData);
				CircleCheckList = new VDataNode[] {(VDataNode)SubRoot.Left,(VDataNode)SubRoot.Right.Left,(VDataNode)SubRoot.Right.Right};
			}

			//3. Apply subtree
			if(C.Parent == null)
				return SubRoot;
			C.Parent.Replace(C,SubRoot);
			return Root;
		}