public void LloydRelaxation(int nbIterations)
{
// Reapeat the whole process for the number of iterations asked
for (int i = 0; i < nbIterations; i++)
{
List <Vector2f> newPoints = new List <Vector2f>();
// Go thourgh all sites
sites.ResetListIndex();
Site site = sites.Next();
while (site != null)
{
// Loop all corners of the site to calculate the centroid
List <Vector2f> region = site.Region(plotBounds);
if (region.Count < 1)
{
site = sites.Next();
continue;
}
Vector2f centroid = Vector2f.zero;
float signedArea = 0;
float x0 = 0;
float y0 = 0;
float x1 = 0;
float y1 = 0;
float a = 0;
// For all vertices except last
for (int j = 0; j < region.Count - 1; j++)
{
x0 = region[j].x;
y0 = region[j].y;
x1 = region[j + 1].x;
y1 = region[j + 1].y;
a = x0 * y1 - x1 * y0;
signedArea += a;
centroid.x += (x0 + x1) * a;
centroid.y += (y0 + y1) * a;
}
// Do last vertex
x0 = region[region.Count - 1].x;
y0 = region[region.Count - 1].y;
x1 = region[0].x;
y1 = region[0].y;
a = x0 * y1 - x1 * y0;
signedArea += a;
centroid.x += (x0 + x1) * a;
centroid.y += (y0 + y1) * a;
signedArea *= 0.5f;
centroid.x /= (6 * signedArea);
centroid.y /= (6 * signedArea);
// Move site to the centroid of its Voronoi cell
newPoints.Add(centroid);
site = sites.Next();
}
// Between each replacement of the cendroid of the cell,
// we need to recompute Voronoi diagram:
Rectf origPlotBounds = this.plotBounds;
Dispose();
Init(newPoints, origPlotBounds);
}
}
private void FortunesAlgorithm()
{
Site newSite, bottomSite, topSite, tempSite;
Vertex v, vertex;
Vector2 newIntStar = Vector2.zero;
LR leftRight;
Halfedge lbnd, rbnd, llbnd, rrbnd, bisector;
Edge edge;
Rectf dataBounds = sites.GetSitesBounds();
int sqrtSitesNb = (int)Math.Sqrt(sites.Count() + 4);
HalfedgePriorityQueue heap = new HalfedgePriorityQueue(dataBounds.y, dataBounds.height, sqrtSitesNb);
EdgeList edgeList = new EdgeList(dataBounds.x, dataBounds.width, sqrtSitesNb);
List <Halfedge> halfEdges = new List <Halfedge>();
List <Vertex> vertices = new List <Vertex>();
Site bottomMostSite = sites.Next();
newSite = sites.Next();
while (true)
{
if (!heap.Empty())
{
newIntStar = heap.Min();
}
if (newSite != null &&
(heap.Empty() || CompareByYThenX(newSite, newIntStar) < 0))
{
// New site is smallest
//Debug.Log("smallest: new site " + newSite);
// Step 8:
lbnd = edgeList.EdgeListLeftNeighbor(newSite.Coord); // The halfedge just to the left of newSite
//UnityEngine.Debug.Log("lbnd: " + lbnd);
rbnd = lbnd.edgeListRightNeighbor; // The halfedge just to the right
//UnityEngine.Debug.Log("rbnd: " + rbnd);
bottomSite = RightRegion(lbnd, bottomMostSite); // This is the same as leftRegion(rbnd)
// This Site determines the region containing the new site
//UnityEngine.Debug.Log("new Site is in region of existing site: " + bottomSite);
// Step 9
edge = Edge.CreateBisectingEdge(bottomSite, newSite);
//UnityEngine.Debug.Log("new edge: " + edge);
Edges.Add(edge);
bisector = Halfedge.Create(edge, LR.LEFT);
halfEdges.Add(bisector);
// Inserting two halfedges into edgelist constitutes Step 10:
// Insert bisector to the right of lbnd:
edgeList.Insert(lbnd, bisector);
// First half of Step 11:
if ((vertex = Vertex.Intersect(lbnd, bisector)) != null)
{
vertices.Add(vertex);
heap.Remove(lbnd);
lbnd.vertex = vertex;
lbnd.ystar = vertex.y + newSite.Dist(vertex);
heap.Insert(lbnd);
}
lbnd = bisector;
bisector = Halfedge.Create(edge, LR.RIGHT);
halfEdges.Add(bisector);
// Second halfedge for Step 10::
// Insert bisector to the right of lbnd:
edgeList.Insert(lbnd, bisector);
// Second half of Step 11:
if ((vertex = Vertex.Intersect(bisector, rbnd)) != null)
{
vertices.Add(vertex);
bisector.vertex = vertex;
bisector.ystar = vertex.y + newSite.Dist(vertex);
heap.Insert(bisector);
}
newSite = sites.Next();
}
else if (!heap.Empty())
{
// Intersection is smallest
lbnd = heap.ExtractMin();
llbnd = lbnd.edgeListLeftNeighbor;
rbnd = lbnd.edgeListRightNeighbor;
rrbnd = rbnd.edgeListRightNeighbor;
bottomSite = LeftRegion(lbnd, bottomMostSite);
topSite = RightRegion(rbnd, bottomMostSite);
// These three sites define a Delaunay triangle
// (not actually using these for anything...)
// triangles.Add(new Triangle(bottomSite, topSite, RightRegion(lbnd, bottomMostSite)));
v = lbnd.vertex;
v.SetIndex();
lbnd.edge.SetVertex(lbnd.leftRight, v);
rbnd.edge.SetVertex(rbnd.leftRight, v);
edgeList.Remove(lbnd);
heap.Remove(rbnd);
edgeList.Remove(rbnd);
leftRight = LR.LEFT;
if (bottomSite.y > topSite.y)
{
tempSite = bottomSite;
bottomSite = topSite;
topSite = tempSite;
leftRight = LR.RIGHT;
}
edge = Edge.CreateBisectingEdge(bottomSite, topSite);
Edges.Add(edge);
bisector = Halfedge.Create(edge, leftRight);
halfEdges.Add(bisector);
edgeList.Insert(llbnd, bisector);
edge.SetVertex(LR.Other(leftRight), v);
if ((vertex = Vertex.Intersect(llbnd, bisector)) != null)
{
vertices.Add(vertex);
heap.Remove(llbnd);
llbnd.vertex = vertex;
llbnd.ystar = vertex.y + bottomSite.Dist(vertex);
heap.Insert(llbnd);
}
if ((vertex = Vertex.Intersect(bisector, rrbnd)) != null)
{
vertices.Add(vertex);
bisector.vertex = vertex;
bisector.ystar = vertex.y + bottomSite.Dist(vertex);
heap.Insert(bisector);
}
}
else
{
break;
}
}
// Heap should be empty now
heap.Dispose();
edgeList.Dispose();
foreach (Halfedge halfedge in halfEdges)
{
halfedge.ReallyDispose();
}
halfEdges.Clear();
// we need the vertices to clip the edges
foreach (Edge e in Edges)
{
e.ClipVertices(plotBounds);
}
// But we don't actually ever use them again!
foreach (Vertex ve in vertices)
{
ve.Dispose();
}
vertices.Clear();
}
private void FortunesAlgorithm()
{
Site newSite, bottomSite, topSite, tempSite;
Vertex v, vertex;
Vector2f newIntStar = Vector2f.ZERO;
LR leftRight;
Halfedge lbnd, rbnd, llbnd, rrbnd, bisector;
Edge edge;
Rectf dataBounds = this.sitelist.GetSitesBounds();
int sqrtSitesNb = (int)Math.Sqrt(sitelist.Count + 4);
HalfedgePriorityQueue heap = new HalfedgePriorityQueue(dataBounds.Y, dataBounds.Height, sqrtSitesNb);
EdgeList edgeList = new EdgeList(dataBounds.X, dataBounds.Width, sqrtSitesNb);
List <Halfedge> halfEdges = new List <Halfedge>();
List <Vertex> vertices = new List <Vertex>();
Site bottomMostSite = this.sitelist.Next();
newSite = this.sitelist.Next();
while (true)
{
if (!heap.Empty)
{
newIntStar = heap.Min();
}
if (newSite != null && (heap.Empty || CompareByYThenX(newSite, newIntStar) < 0))
{
// Step 8:
lbnd = edgeList.EdgeListLeftNeighbor(newSite.Coord); // The halfedge just to the left of newSite.
rbnd = lbnd.EdgeListRightNeighbor; // The halfedge just to the right.
bottomSite = RightRegion(lbnd, bottomMostSite); // This is the same as leftRegion(rbnd).
// Step 9:
edge = Edge.CreateBisectingEdge(bottomSite, newSite);
edges.Add(edge);
bisector = Halfedge.Create(edge, LR.LEFT);
halfEdges.Add(bisector);
// Inserting two halfedges into edgelist constitutes Step 10:
// Insert bisector to the right of lbnd.
edgeList.Insert(lbnd, bisector);
// First half of Step 11:
if ((vertex = Vertex.Intersect(lbnd, bisector)) != null)
{
vertices.Add(vertex);
heap.Remove(lbnd);
lbnd.Vertex = vertex;
lbnd.Ystar = vertex.Y + newSite.Dist(vertex);
heap.Insert(lbnd);
}
lbnd = bisector;
bisector = Halfedge.Create(edge, LR.RIGHT);
halfEdges.Add(bisector);
// Second halfedge for Step 10:
// Insert bisector to the right of lbnd.
edgeList.Insert(lbnd, bisector);
// Second half of Step 11:
if ((vertex = Vertex.Intersect(bisector, rbnd)) != null)
{
vertices.Add(vertex);
bisector.Vertex = vertex;
bisector.Ystar = vertex.Y + newSite.Dist(vertex);
heap.Insert(bisector);
}
newSite = sitelist.Next();
}
else if (!heap.Empty)
{
// Intersection is smallest.
lbnd = heap.ExtractMin();
llbnd = lbnd.EdgeListLeftNeighbor;
rbnd = lbnd.EdgeListRightNeighbor;
rrbnd = rbnd.EdgeListRightNeighbor;
bottomSite = LeftRegion(lbnd, bottomMostSite);
topSite = RightRegion(rbnd, bottomMostSite);
// These three sites define a Delaunay triangle
// (not actually using these for anything...)
// triangles.Add(new Triangle(bottomSite, topSite, RightRegion(lbnd, bottomMostSite)));
v = lbnd.Vertex;
v.SetIndex();
lbnd.Edge.SetVertex(lbnd.LeftRight, v);
rbnd.Edge.SetVertex(rbnd.LeftRight, v);
edgeList.Remove(lbnd);
heap.Remove(rbnd);
edgeList.Remove(rbnd);
leftRight = LR.LEFT;
if (bottomSite.Y > topSite.Y)
{
tempSite = bottomSite;
bottomSite = topSite;
topSite = tempSite;
leftRight = LR.RIGHT;
}
edge = Edge.CreateBisectingEdge(bottomSite, topSite);
edges.Add(edge);
bisector = Halfedge.Create(edge, leftRight);
halfEdges.Add(bisector);
edgeList.Insert(llbnd, bisector);
edge.SetVertex(LR.Other(leftRight), v);
if ((vertex = Vertex.Intersect(llbnd, bisector)) != null)
{
vertices.Add(vertex);
heap.Remove(llbnd);
llbnd.Vertex = vertex;
llbnd.Ystar = vertex.Y + bottomSite.Dist(vertex);
heap.Insert(llbnd);
}
if ((vertex = Vertex.Intersect(bisector, rrbnd)) != null)
{
vertices.Add(vertex);
bisector.Vertex = vertex;
bisector.Ystar = vertex.Y + bottomSite.Dist(vertex);
heap.Insert(bisector);
}
}
else
{
break;
}
}
// Heap should be empty now.
heap.Dispose();
edgeList.Dispose();
foreach (Halfedge halfedge in halfEdges)
{
halfedge.ReallyDispose();
}
halfEdges.Clear();
// We need the vertices to clip the edges.
foreach (Edge e in edges)
{
e.ClipVertices(this.PlotBounds);
}
}
