/// <summary>
/// Visualization of 2D Voronoi map.
/// </summary>
/// <param name="weight">Weight of result image.</param>
/// <param name="height">Height of result image.</param>
/// <param name="Datapoints">Array of data points.</param>
/// <returns>Result bitmap.</returns>
public static Bitmap GetVoronoyMap(int weight, int height, IEnumerable Datapoints)
{
Bitmap bmp = new Bitmap(weight, height);
VoronoiGraph graph = Fortune.ComputeVoronoiGraph(Datapoints);
Graphics g = Graphics.FromImage(bmp);
foreach (object o in graph.Vertizes)
{
Vector3 v = (Vector3)o;
g.DrawEllipse(Pens.Black, (int)v[0] - 2, (int)v[1] - 2, 4, 4);
}
foreach (object o in Datapoints)
{
Vector3 v = (Vector3)o;
g.DrawEllipse(Pens.Red, (int)v[0] - 1, (int)v[1] - 1, 2, 2);
}
foreach (object o in graph.Edges)
{
VoronoiEdge edge = (VoronoiEdge)o;
try
{
g.DrawLine(Pens.Brown, (int)edge.VVertexA[0], (int)edge.VVertexA[1], (int)edge.VVertexB[0], (int)edge.VVertexB[1]);
}
catch { }
}
return(bmp);
}
/// <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[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);
}
/// <summary>
/// Visualization of Delaunay Triangulation
/// </summary>
/// <param name="weight">Weight of result image.</param>
/// <param name="height">Height of result image.</param>
/// <param name="Datapoints">Result bitmap.</param>
/// <returns></returns>
public static List <Triangle> GetDelaunayTriangulation(IEnumerable Datapoints)
{
System.Collections.Generic.List <Triangle> list = new System.Collections.Generic.List <Triangle>();
VoronoiGraph voronoiGraph = Fortune.ComputeVoronoiGraph(Datapoints);
//Graphics g = Graphics.FromImage(bmp);
List <Triangle> triangles = new List <Triangle>();
for (int i = voronoiGraph.Edges.Count - 1; i >= 0; i--)
{
VoronoiEdge edge1 = voronoiGraph.Edges[i];
for (int j = 0; j < i; j++)
{
VoronoiEdge edge2 = voronoiGraph.Edges[j];
//if (edge1.LeftData.Index == edge2.LeftData.Index)
//{
// triangles.Add(new Triangle(edge1.LeftData.Index, edge1.RightData.Index, edge2.RightData.Index));
//}
//if (edge1.RightData.Index == edge2.RightData.Index)
//{
// triangles.Add(new Triangle(edge1.LeftData.Index, edge1.RightData.Index, edge2.LeftData.Index));
//}
//if (edge1.RightData.Index == edge2.LeftData.Index)
//{
// triangles.Add(new Triangle(edge1.LeftData.Index, edge1.RightData.Index, edge2.RightData.Index));
//}
//if (edge1.LeftData.Index == edge2.RightData.Index)
//{
// triangles.Add(new Triangle(edge1.LeftData.Index, edge1.RightData.Index, edge2.LeftData.Index));
//}
}
//if ((edge.LeftData[0] == v[0]) & (edge.LeftData[1] == v[1]))
//{
// g.DrawLine(Pens.Black, (int)edge.LeftData[0], (int)edge.LeftData[1], (int)edge.RightData[0], (int)edge.RightData[1]);
//}
}
////Graphics g = Graphics.FromImage(bmp);
//foreach (object o in Datapoints)
//{
// Vector3 v = (Vector3)o;
// //g.DrawEllipse(Pens.Red, (int)v[0] - 1, (int)v[1] - 1, 2, 2);
// foreach (object obj in voronoiGraph.Edges)
// {
// VoronoiEdge edge = (VoronoiEdge)obj;
// if ((edge.LeftData[0] == v[0]) & (edge.LeftData[1] == v[1]))
// {
// g.DrawLine(Pens.Black, (int)edge.LeftData[0], (int)edge.LeftData[1], (int)edge.RightData[0], (int)edge.RightData[1]);
// }
// }
//}
return(triangles);
}
public VEdgeNode(VoronoiEdge E, bool Flipped)
{
this.Edge = E;
this.Flipped = Flipped;
}
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
Vector3 VNew = new Vector3(e.Center[0], e.Center[1], 0);
// 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;
// /////////////////////
eo.Edge.AddVertex(VNew);
//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)
{
VEdgeNode eo;
var b = e.NodeN;
var a = LeftDataNode(b);
var c = RightDataNode(b);
if (a == null || b.Parent == null || c == null || a.DataPoint != e.NodeL.DataPoint || c.DataPoint != e.NodeR.DataPoint)
{
circleCheckList = new VDataNode[] { };
return(root); // Abbruch da sich der Graph verändert hat
}
var eu = (VEdgeNode)b.Parent;
circleCheckList = new[] { a, c };
//1. Create the new Vertex
var 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 = EdgeToRightDataNode(a);
// replace eu by eu's Right
eu.Parent.Replace(eu, eu.Right);
}
else // a is sibling
{
eo = 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
var ve = new VoronoiEdge {
LeftData = a.DataPoint,
RightData = c.DataPoint
};
ve.AddVertex(vNew);
vg.Edges.Add(ve);
var ven = new VEdgeNode(ve, false)
{
Left = eo.Left,
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)root };
return(root);
}
//1. Find the node to be replaced
VNode c = FindDataNode(root, ys, e.DataPoint[0]);
//2. Create the subtree (ONE Edge, but two VEdgeNodes)
var ve = new VoronoiEdge {
LeftData = ((VDataNode)c).DataPoint,
RightData = e.DataPoint,
VVertexA = Fortune.VvUnkown,
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)
{
Left = new VDataNode(ve.LeftData),
Right = new VDataNode(ve.RightData)
};
}
else
{
subRoot = new VEdgeNode(ve, true)
{
Left = new VDataNode(ve.RightData),
Right = new VDataNode(ve.LeftData)
};
}
circleCheckList = new[] { (VDataNode)subRoot.Left, (VDataNode)subRoot.Right };
}
else
{
subRoot = new VEdgeNode(ve, false)
{
Left = new VDataNode(ve.LeftData),
Right = new VEdgeNode(ve, true)
{
Left = new VDataNode(ve.RightData),
Right = new VDataNode(ve.LeftData)
}
};
circleCheckList = new[] { (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);
}
/// <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.X);
//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.Y-VE.RightData.Y)<1e-10)
{
if(VE.LeftData.X<VE.RightData.X)
{
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 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
Point VNew = new Point(e.Center.X,e.Center.Y);
// VNew.X = Fortune.ParabolicCut(a.DataPoint.X,a.DataPoint.Y,c.DataPoint.X,c.DataPoint.Y,ys);
// VNew.Y = (ys + a.DataPoint.Y)/2 - 1/(2*(ys-a.DataPoint.Y))*(VNew.X-a.DataPoint.X)*(VNew.X-a.DataPoint.X);
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;
}
public VEdgeNode(VoronoiEdge E, bool Flipped)
{
this.Edge = E;
this.Flipped = Flipped;
}
void Start()
{
var meshFilter = gameObject.AddComponent<MeshFilter>();
var edges = CellData.Edges.Select(e =>
{
var vA = e.VVertexA;
var vB = e.VVertexB;
var dA = vA - CellData.Site;
var dB = vB - CellData.Site;
var atanA = Mathf.Atan2((float)dA.Y, (float)dA.X);
var atanB = Mathf.Atan2((float)dB.Y, (float)dB.X);
VoronoiEdge edge;
if (atanA > 0f)
{
if (atanA < atanB)
{
edge = new VoronoiEdge { VVertexA = vB - CellData.Site, VVertexB = vA - CellData.Site };
}
else
{
if (atanA - atanB > Mathf.PI)
{
edge = new VoronoiEdge { VVertexA = vB - CellData.Site, VVertexB = vA - CellData.Site };
}
else
{
edge = new VoronoiEdge { VVertexA = vA - CellData.Site, VVertexB = vB - CellData.Site };
}
}
}
else
{
if (atanA > atanB)
{
edge = new VoronoiEdge { VVertexA = vA - CellData.Site, VVertexB = vB - CellData.Site };
}
else
{
if (atanB - atanA > Mathf.PI)
{
edge = new VoronoiEdge { VVertexA = vA - CellData.Site, VVertexB = vB - CellData.Site };
}
else
{
edge = new VoronoiEdge { VVertexA = vB - CellData.Site, VVertexB = vA - CellData.Site };
}
}
}
return edge;
}).ToArray();
var maxDistFromCenter = edges.Max(e => Mathf.Max((float)e.VVertexA.Length, (float)e.VVertexB.Length));
if (edges[0].VVertexA.Length > maxDistFromCenter)
{
maxDistFromCenter = (float)edges[0].VVertexA.Length;
}
maxDistFromCenter *= 2; // To make sure that UV coords will be in [-0.5; 0.5] range
Mesh mesh = new Mesh();
mesh.name = "cellMesh";
var cellCorners = new Vector3[edges.Length * 2 + 1];
var triangles = new int[edges.Length * 3];
var uvs = new Vector2[edges.Length * 2 + 1];
cellCorners[0] = Vector3.zero; // Placing Cell Center at Origin of new GameObjects
//verts [1] = new Vector3 (edges [0].Start.x, edges [0].Start.y, 0f);
var shift = new Vector2(0.5f, 0.5f); // Shifting texture coords origin
uvs[0] = shift;
uvs[1] = new Vector2(((float)edges[0].VVertexA.X + shift.x) / maxDistFromCenter, ((float)edges[0].VVertexA.Y + shift.y) / maxDistFromCenter);
for (int i = 0; i < edges.Length; i++)
{
var edge = edges[i];
cellCorners[2 * i + 1] = new Vector3((float)edges[i].VVertexA.X, (float)edges[i].VVertexA.Y, 0f);
cellCorners[2 * i + 2] = new Vector3((float)edges[i].VVertexB.X, (float)edges[i].VVertexB.Y, 0f);
var uvStart = shift + new Vector2((float)edge.VVertexA.X / maxDistFromCenter, (float)edge.VVertexA.Y / maxDistFromCenter);
var uvEnd = shift + new Vector2((float)edge.VVertexB.X / maxDistFromCenter, (float)edge.VVertexB.Y / maxDistFromCenter);
uvs[2 * i + 1] = new Vector3(uvStart.x, uvStart.y, 0f);
uvs[2 * i + 2] = new Vector3(uvEnd.x, uvEnd.y, 0f);
triangles[3 * i] = 0;
triangles[3 * i + 1] = 2 * i + 1;
triangles[3 * i + 2] = 2 * i + 2;
}
mesh.vertices = cellCorners;
mesh.uv = uvs;
mesh.triangles = triangles;
mesh.RecalculateNormals();
mesh.RecalculateBounds();
mesh.Optimize();
mesh.RecalculateTangents();
meshFilter.sharedMesh = mesh;
var meshRenderer = gameObject.AddComponent<MeshRenderer>();
if (MeshMaterial == null)
{
meshRenderer.material.color = Color.green;
}
else
{
meshRenderer.material = MeshMaterial;
}
var polyCollider = gameObject.AddComponent<EdgeCollider2D>();
polyCollider.points = cellCorners.Skip(1).Select(c => new Vector2(c.x, c.y)).ToArray();
}
public VEdgeNode(VoronoiEdge e, bool flipped)
{
Edge = e;
Flipped = flipped;
}
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
Point VNew = new Point(e.Center.X, e.Center.Y);
// VNew.X = Fortune.ParabolicCut(a.DataPoint.X,a.DataPoint.Y,c.DataPoint.X,c.DataPoint.Y,ys);
// VNew.Y = (ys + a.DataPoint.Y)/2 - 1/(2*(ys-a.DataPoint.Y))*(VNew.X-a.DataPoint.X)*(VNew.X-a.DataPoint.X);
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);
}