public void AddVertex(Vector V)
{
if(VVertexA==Fortune.VVUnkown)
VVertexA = V;
else if(VVertexB==Fortune.VVUnkown)
VVertexB = V;
else throw new Exception("Tried to add third vertex!");
}
internal static Vector CircumCircleCenter(Vector A, Vector B, Vector C)
{
if(A==B || B==C || A==C)
throw new Exception("Need three different points!");
double tx = (A[0] + C[0])/2;
double ty = (A[1] + C[1])/2;
double vx = (B[0] + C[0])/2;
double vy = (B[1] + C[1])/2;
double ux,uy,wx,wy;
if(A[0] == C[0])
{
ux = 1;
uy = 0;
}
else
{
ux = (C[1] - A[1])/(A[0] - C[0]);
uy = 1;
}
if(B[0] == C[0])
{
wx = -1;
wy = 0;
}
else
{
wx = (B[1] - C[1])/(B[0] - C[0]);
wy = -1;
}
double alpha = (wy*(vx-tx)-wx*(vy - ty))/(ux*wy-wx*uy);
return new Vector(tx+alpha*ux,ty+alpha*uy);
}
/// <summary>
/// Add another vector
/// </summary>
/// <param name="V">V</param>
public void Add(Vector V)
{
int i;
for(i=0;i<data.Length;i++)
{
this[i] += V[i];
}
}
/// <summary>
/// Get the distance of two vectors
/// </summary>
public static double Dist(Vector V1, Vector V2)
{
if(V1.Dim != V2.Dim)
return -1;
int i;
double E = 0,D;
for(i=0;i<V1.Dim;i++)
{
D=(V1[i]-V2[i]);
E+=D*D;
}
return E;
}
/// <summary>
/// Subtract two vectors
/// </summary>
public static Vector operator -(Vector A, Vector B)
{
if(A.Dim!=B.Dim)
throw new Exception("Vectors of different dimension!");
Vector Erg = new Vector(A.Dim);
int i;
for(i=0;i<A.Dim;i++)
Erg[i]=A[i]-B[i];
return Erg;
}
/// <summary>
/// Scale one vector
/// </summary>
public static Vector operator *(Vector A, double B)
{
Vector Erg = new Vector(A.Dim);
int i;
for(i=0;i<A.Dim;i++)
Erg[i]=A[i]*B;
return Erg;
}
public void Reset()
{
GL.Enable(EnableCap.LineSmooth);
GL.Enable(EnableCap.PolygonSmooth);
// GL.Enable(EnableCap.DepthTest);
Matrix4 modelview = Matrix4.LookAt(Vector3.Zero, Vector3.UnitZ, Vector3.UnitY);
GL.MatrixMode(MatrixMode.Modelview);
GL.LoadMatrix(ref modelview);
int seeds = 1280;
int extraSeeds = 512;
Vector[] points = new Vector[seeds + extraSeeds];
double thetaOffset = Tau / 4;
for (int i = 0; i < seeds + extraSeeds; i++) {
double theta = (double)(i + 1) * Tau / Phi;
double r = Math.Sqrt(i+1);
double x = (r) * Math.Cos(theta + thetaOffset);
double y = (r) * Math.Sin(theta + thetaOffset);
points[i] = new Vector(new double[] { x, y });
}
VoronoiGraph graph = Fortune.ComputeVoronoiGraph(points);
cells = new SortedDictionary<Vector, List<VoronoiEdge>>();
foreach (VoronoiEdge edge in graph.Edges) {
if (double.IsNaN(edge.VVertexA.X) ||
double.IsNaN(edge.VVertexA.Y) ||
double.IsNaN(edge.VVertexB.X) ||
double.IsNaN(edge.VVertexB.Y)
)
continue;
if (!cells.ContainsKey(edge.LeftData))
cells[edge.LeftData] = new List<VoronoiEdge>();
cells[edge.LeftData].Add(edge);
if (!cells.ContainsKey(edge.RightData))
cells[edge.RightData] = new List<VoronoiEdge>();
cells[edge.RightData].Add(edge);
Complex pA = new Complex(edge.VVertexA.X, edge.VVertexA.Y);
Complex pB = new Complex(edge.VVertexB.X, edge.VVertexB.Y);
int sampleCount = 2;
Complex[] samples = new Complex[sampleCount];
samples[0] = pA;
samples[sampleCount - 1] = pB;
for (int i = 1; i < sampleCount - 1; i++) {
double ratio = (double)i / sampleCount;
samples[i] = pA * (1 - ratio) + pB * ratio;
}
}
for (int i = 0; i < seeds; i++) {
Queue<VoronoiEdge> edges = new Queue<VoronoiEdge>(cells.Values.ElementAt(i));
var firstEdge = edges.Dequeue();
List<Complex> polygonPoints = new List<Complex>();
polygonPoints.Add(new Complex(firstEdge.VVertexA.X * scale, firstEdge.VVertexA.Y * scale));
polygonPoints.Add(new Complex(firstEdge.VVertexB.X * scale, firstEdge.VVertexB.Y * scale));
while (edges.Count > 0) {
var edge = edges.Dequeue();
Complex pA = new Complex(edge.VVertexA.X * scale, edge.VVertexA.Y * scale);
Complex pB = new Complex(edge.VVertexB.X * scale, edge.VVertexB.Y * scale);
if (polygonPoints[0] == pA) {
polygonPoints.Insert(0, pB);
continue;
}
if (polygonPoints[0] == pB) {
polygonPoints.Insert(0, pA);
continue;
}
if (polygonPoints[polygonPoints.Count - 1] == pA) {
polygonPoints.Add(pB);
continue;
}
if (polygonPoints[polygonPoints.Count - 1] == pB) {
polygonPoints.Add(pA);
continue;
}
edges.Enqueue(edge);
}
polygons.Add(polygonPoints);
}
for (int i = 0; i <= ModuloActor.MaxMod; i++)
ModuloActor.Maps[i] = CreateIndexMap(i, cells);
actors[0] = new ModuloActor(21, 0 / 3, new Color4(1f, 0.5f, 0.5f, 1f));
actors[1] = new ModuloActor(13, 1 / 3, new Color4(0.5f, 1f, 0.5f, 1f));
actors[2] = new ModuloActor(0, 2 / 3, new Color4(0.5f, 0.5f, 1f, 1f));
ModuloActor.AnnounceFibonaccis();
}
public Vector[] GenerateRandom (int seed, double numPoints, double min, double max)
{
//Debug.Log ("Starting to Generate Random Numbers, Max is: " + max);
List<Vector> tempList = new List<Vector> ();
UnityEngine.Random.seed = seed;
Vector p;
while (tempList.Count < numPoints) {
p = new Vector (UnityEngine.Random.Range ((int)min, (int)max), UnityEngine.Random.Range ((int)min, (int)max));
if (!tempList.Contains (p)) {
tempList.Add (p);
}
}
return tempList.ToArray ();
}
public static VoronoiGraph ComputeVoronoiGraph (Vector[] Datapoints)
{
BinaryPriorityQueue PQ = new BinaryPriorityQueue ();
Hashtable CurrentCircles = new Hashtable ();
VoronoiGraph VG = new VoronoiGraph ();
VNode RootNode = null;
foreach (Vector V in Datapoints) {
PQ.Push (new VDataEvent (V));
}
Profiler.BeginSample ("Fortune Compute VoronoiGraph While PQ.Count > 0");
while (PQ.Count>0) {
VEvent VE = PQ.Pop () as VEvent;
VDataNode[] CircleCheckList;
if (VE is VDataEvent) {
RootNode = VNode.ProcessDataEvent (VE as VDataEvent, RootNode, VG, 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, VG, 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) {
Vector DP = ((VDataEvent)VE).DataPoint;
Profiler.BeginSample ("DIST Function");
foreach (VCircleEvent VCE in CurrentCircles.Values) {
if (MathTools.Dist (DP [0], DP [1], VCE.Center [0], VCE.Center [1]) < VCE.Y - VCE.Center [1] && Math.Abs (MathTools.Dist (DP [0], DP [1], VCE.Center [0], VCE.Center [1]) - (VCE.Y - VCE.Center [1])) > 1e-10)
VCE.Valid = false;
}
Profiler.EndSample ();
}
}
Profiler.EndSample ();
VNode.CleanUpTree (RootNode);
foreach (VoronoiEdge VE in VG.Edges) {
if (VE.Done)
continue;
if (VE.VVertexB == Fortune.VVUnkown) {
VE.AddVertex (Fortune.VVInfinite);
Profiler.BeginSample ("Infinite Function");
if (Math.Abs (VE.LeftData [1] - VE.RightData [1]) < 1e-10 && VE.LeftData [0] < VE.RightData [0]) {
Vector T = VE.LeftData;
VE.LeftData = VE.RightData;
VE.RightData = T;
}
Profiler.EndSample ();
}
}
ArrayList MinuteEdges = new ArrayList ();
foreach (VoronoiEdge VE in VG.Edges) {
if (!VE.IsPartlyInfinite && VE.VVertexA.Equals (VE.VVertexB)) {
MinuteEdges.Add (VE);
// prevent rounding errors from expanding to holes
foreach (VoronoiEdge VE2 in VG.Edges) {
if (VE2.VVertexA.Equals (VE.VVertexA))
VE2.VVertexA = VE.VVertexA;
if (VE2.VVertexB.Equals (VE.VVertexA))
VE2.VVertexB = VE.VVertexA;
}
}
}
foreach (VoronoiEdge VE in MinuteEdges)
VG.Edges.Remove (VE);
return VG;
}
public VDataEvent(Vector DP)
{
this.DataPoint = DP;
}
public VDataNode(Vector DP)
{
this.DataPoint = DP;
}
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;
}
public Cell (Vector Site)
{
site = Site;
Reset ();
}
/// <summary>
/// Reset all elements with ransom values from the given range
/// </summary>
/// <param name="MinMax">MinMax[0] - Min
/// MinMax[1] - Max</param>
public void Randomize(Vector[] MinMax)
{
int i;
for(i=0;i<data.Length;i++)
{
this[i] = MinMax[0][i] + (MinMax[1][i]-MinMax[0][i])*MathTools.R.NextDouble();
}
}
// Lloyd Relax the points here to get more even distribution.
// First we need to know the N number of Voronoi Verts that make up each cell.
// Then we can find the centroid of each of those cells, and move the Site that created this cell to that centroid.
public Vector[] LloydRelax (Vector[] sites, VoronoiGraph graph)
{
List<Vector> RelaxedSites = new List<Vector> ();
for (int s =0; s < sites.Length; s++) {
List<Vector> cellVerts = new List<Vector> ();
foreach (VoronoiEdge edge in graph.Edges) {
if (edge.LeftData == sites [s]) {
// Check if one or more of the edge verts is infinity
if (edge.IsPartlyInfinite) {
if (edge.VVertexA == Fortune.VVInfinite) {
edge.VVertexA = (edge.FixedPoint + (edge.DirectionVector * InfinityLength));
}
if (edge.VVertexB == Fortune.VVInfinite) {
edge.VVertexB = (edge.FixedPoint + (edge.DirectionVector * InfinityLength));
}
}
edge.Clamp (Border, Max - Border);
cellVerts.Add (edge.VVertexA);
cellVerts.Add (edge.VVertexB);
}
// If we didn't find a LeftData for this edge just put that site back uncentered.
Vector centroid = sites [s];
if (cellVerts.Count > 0) {
centroid = math_utilities.Compute2DPolygonCentroid (cellVerts);
centroid.Clamp (Border, Max - Border);// lets hope this works better.
}
if (!RelaxedSites.Contains (centroid)) {
RelaxedSites.Add (centroid);
}
}
}
return RelaxedSites.ToArray ();
}
/// <summary>
/// Build a new vector as a copy of an existing one
/// </summary>
/// <param name="O">The existing vector</param>
public Vector(Vector O)
: this(O.data)
{
}
public static Vector operator / (Vector A, double B)
{
Vector Erg = new Vector(A.Dim);
for (int i = 0; i < A.Dim; i++)
{
Erg[i] = A[i] / B;
}
return Erg;
}
