/// <summary>
        /// Creates a new Voronoi Graph given a set of Points
        /// </summary>
        /// <param name="Datapoints">Data points to base the Voronoi Graph around</param>
        /// <returns></returns>
        public static VoronoiGraph GenerateGraph(IEnumerable Datapoints)
        {
            BinaryPriorityQueue PQ = new BinaryPriorityQueue();

            Hashtable CurrentCircles = new Hashtable();

            VoronoiGraph Graph = new VoronoiGraph();

            VNode RootNode = null;

            foreach (Vector2 V in Datapoints)
            {
                PQ.Push(new VDataEvent(V));
            }

            while (PQ.Count > 0)
            {
                VEvent VE = PQ.Pop() as VEvent;
                VDataNode[] CircleCheckList;
                if (VE is VDataEvent)
                {
                    RootNode = VNode.ProcessDataEvent(VE as VDataEvent, RootNode, Graph, VE.Y, out CircleCheckList);
                }
                else if (VE is VCircleEvent)
                {
                    CurrentCircles.Remove(((VCircleEvent)VE).NodeN);
                    if (!((VCircleEvent)VE).Valid)
                        continue;
                    RootNode = VNode.ProcessCircleEvent(VE as VCircleEvent, RootNode, Graph, VE.Y, out CircleCheckList);
                }
                else throw new Exception("Got event of type " + VE.GetType().ToString() + "!");
                foreach (VDataNode VD in CircleCheckList)
                {
                    if (CurrentCircles.ContainsKey(VD))
                    {
                        ((VCircleEvent)CurrentCircles[VD]).Valid = false;
                        CurrentCircles.Remove(VD);
                    }
                    VCircleEvent VCE = VNode.CircleCheckDataNode(VD, VE.Y);
                    if (VCE != null)
                    {
                        PQ.Push(VCE);
                        CurrentCircles[VD] = VCE;
                    }
                }
                if (VE is VDataEvent)
                {
                    Vector2 DP = ((VDataEvent)VE).DataPoint;
                    foreach (VCircleEvent VCE in CurrentCircles.Values)
                    {

                        if (Vector2.Distance(DP, VCE.Center) < VCE.Y - VCE.Center.y && Math.Abs(Vector2.Distance(DP, VCE.Center) - (VCE.Y - VCE.Center.y)) > 1e-10)
                            VCE.Valid = false;
                    }
                }
            }
            return Graph;
        }
        /// <summary>
        /// Will return the new root (unchanged except in start-up)
        /// </summary>
        public static VNode ProcessDataEvent(VDataEvent e, VNode Root, VoronoiGraph VG, float 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.x);
            //2. Create the subtree (ONE Edge, but two VEdgeNodes)
            VoronoiEdge VE = new VoronoiEdge();
            VE.Left = ((VDataNode)C).DataPoint;
            VE.Right = e.DataPoint;
            VE.VVertexA = Fortune.VVUnkown;
            VE.VVertexB = Fortune.VVUnkown;
            VG.Edges.Add(VE);

            VNode SubRoot;
            if (Math.Abs(VE.Left.y - VE.Right.y) < 1e-10)
            {
                if (VE.Left.x < VE.Right.x)
                {
                    SubRoot = new VEdgeNode(VE, false);
                    SubRoot.Left = new VDataNode(VE.Left);
                    SubRoot.Right = new VDataNode(VE.Right);
                }
                else
                {
                    SubRoot = new VEdgeNode(VE, true);
                    SubRoot.Left = new VDataNode(VE.Right);
                    SubRoot.Right = new VDataNode(VE.Left);
                }
                CircleCheckList = new VDataNode[] { (VDataNode)SubRoot.Left, (VDataNode)SubRoot.Right };
            }
            else
            {
                SubRoot = new VEdgeNode(VE, false);
                SubRoot.Left = new VDataNode(VE.Left);
                SubRoot.Right = new VEdgeNode(VE, true);
                SubRoot.Right.Left = new VDataNode(VE.Right);
                SubRoot.Right.Right = new VDataNode(VE.Left);
                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 VNode ProcessCircleEvent(VCircleEvent e, VNode Root, VoronoiGraph VG, float 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
            Vector2 VNew = new Vector2(e.Center.x, e.Center.y);
            //			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;
            //			/////////////////////
            eo.Edge.AddVertex(VNew);
            //2. Replace eo by new Edge
            VoronoiEdge VE = new VoronoiEdge();
            VE.Left = a.DataPoint;
            VE.Right = 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;
        }