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);
}
}
public List <LineSegment> VoronoiBoundarayForSite(Vector2f coord)
{
return(LineSegment.VisibleLineSegments(Edge.SelectEdgesForSitePoint(coord, edges)));
}
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 = 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 static bool CloseEnough(Vector2f p0, Vector2f p1)
{
return((p0 - p1).magnitude < EPSILON);
}
private void Connect(ref List <Vector2f> points, int j, Rectf bounds, bool closingUp = false)
{
Vector2f rightPoint = points[points.Count - 1];
Edge newEdge = edges[j];
LR newOrientation = edgeOrientations[j];
// The point that must be conected to rightPoint:
Vector2f newPoint = newEdge.ClippedEnds[newOrientation];
if (!CloseEnough(rightPoint, newPoint))
{
// The points do not coincide, so they must have been clipped at the bounds;
// see if they are on the same border of the bounds:
if (rightPoint.x != newPoint.x && rightPoint.y != newPoint.y)
{
// They are on different borders of the bounds;
// insert one or two corners of bounds as needed to hook them up:
// (NOTE this will not be correct if the region should take up more than
// half of the bounds rect, for then we will have gone the wrong way
// around the bounds and included the smaller part rather than the larger)
int rightCheck = BoundsCheck.Check(rightPoint, bounds);
int newCheck = BoundsCheck.Check(newPoint, bounds);
float px, py;
if ((rightCheck & BoundsCheck.RIGHT) != 0)
{
px = bounds.right;
if ((newCheck & BoundsCheck.BOTTOM) != 0)
{
py = bounds.bottom;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.TOP) != 0)
{
py = bounds.top;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.LEFT) != 0)
{
if (rightPoint.y - bounds.y + newPoint.y - bounds.y < bounds.height)
{
py = bounds.top;
}
else
{
py = bounds.bottom;
}
points.Add(new Vector2f(px, py));
points.Add(new Vector2f(bounds.left, py));
}
}
else if ((rightCheck & BoundsCheck.LEFT) != 0)
{
px = bounds.left;
if ((newCheck & BoundsCheck.BOTTOM) != 0)
{
py = bounds.bottom;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.TOP) != 0)
{
py = bounds.top;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.RIGHT) != 0)
{
if (rightPoint.y - bounds.y + newPoint.y - bounds.y < bounds.height)
{
py = bounds.top;
}
else
{
py = bounds.bottom;
}
points.Add(new Vector2f(px, py));
points.Add(new Vector2f(bounds.right, py));
}
}
else if ((rightCheck & BoundsCheck.TOP) != 0)
{
py = bounds.top;
if ((newCheck & BoundsCheck.RIGHT) != 0)
{
px = bounds.right;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.LEFT) != 0)
{
px = bounds.left;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.BOTTOM) != 0)
{
if (rightPoint.x - bounds.x + newPoint.x - bounds.x < bounds.width)
{
px = bounds.left;
}
else
{
px = bounds.right;
}
points.Add(new Vector2f(px, py));
points.Add(new Vector2f(px, bounds.bottom));
}
}
else if ((rightCheck & BoundsCheck.BOTTOM) != 0)
{
py = bounds.bottom;
if ((newCheck & BoundsCheck.RIGHT) != 0)
{
px = bounds.right;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.LEFT) != 0)
{
px = bounds.left;
points.Add(new Vector2f(px, py));
}
else if ((newCheck & BoundsCheck.TOP) != 0)
{
if (rightPoint.x - bounds.x + newPoint.x - bounds.x < bounds.width)
{
px = bounds.left;
}
else
{
px = bounds.right;
}
points.Add(new Vector2f(px, py));
points.Add(new Vector2f(px, bounds.top));
}
}
}
if (closingUp)
{
// newEdge's ends have already been added
return;
}
points.Add(newPoint);
}
Vector2f newRightPoint = newEdge.ClippedEnds[LR.Other(newOrientation)];
if (!CloseEnough(points[0], newRightPoint))
{
points.Add(newRightPoint);
}
}
private void Move(Vector2f p)
{
Clear();
coord = p;
}
public Site(Vector2f p, int index, float weigth)
{
Init(p, index, weigth);
}
public LineSegment(Vector2f p0, Vector2f p1) {
this.P0 = p0;
this.P1 = p1;
}