public EdgeList( SiteList siteList) {
Edges = new List<HalfEdge>();
_siteList = siteList;
LeftEnd = new HalfEdge(null, Side.Left);
RightEnd = new HalfEdge(null, Side.Left);
LeftEnd.Right = RightEnd;
RightEnd.Left = LeftEnd;
Edges.Add(LeftEnd);
Edges.Add(RightEnd);
}
public void Insert(HalfEdge he, Site site, float offset) {
he.Vertex = site;
he.YStar = site.Y + offset;
int i;
for (i = 0; i < _events.Count; i++) {
var next = _events[i];
if (he.YStar > next.YStar || (Math.Abs(he.YStar - next.YStar) < Geometry.Tolerance && site.X > next.Vertex.X)) {
continue;
}
break;
}
_events.Insert(i, he);
}
public static bool RightOf(HalfEdge he, Site p) {
var e = he.Edge;
var topSite = e.Region[Side.Right];
var rightOfSite = (p.X > topSite.X);
if (rightOfSite && (he.Side == Side.Left)) {
return true;
}
if (!rightOfSite && (he.Side == Side.Right)) {
return false;
}
bool above;
if (Math.Abs(e.A - 1) < Tolerance) {
var dyp = p.Y - topSite.Y;
var dxp = p.X - topSite.X;
var fast = false;
if ((!rightOfSite && (e.B < 0)) || (rightOfSite && (e.B >= 0))) {
above = fast = (dyp >= e.B*dxp);
} else {
above = ((p.X + p.Y*e.B) > e.C);
if (e.B < 0) {
above = !above;
}
if (!above) {
fast = true;
}
}
if (!fast) {
var dxs = topSite.X - e.Region[Side.Left].X;
above = (e.B*(dxp*dxp - dyp*dyp)) < (dxs*dyp*(1 + 2*dxp/dxs + e.B*e.B));
if (e.B < 0) {
above = !above;
}
}
} else { // e.b == 1
var y1 = e.C - e.A*p.X;
var t1 = p.Y - y1;
var t2 = p.X - topSite.X;
var t3 = y1 - topSite.Y;
above = (t1*t1) > (t2*t2 + t3*t3);
}
return he.Side == Side.Left ? above : !above;
}
public static Site Intersect(HalfEdge el1, HalfEdge el2) {
var e1 = el1.Edge;
var e2 = el2.Edge;
if (e1 == null || e2 == null) {
return null;
}
if (e1.Region[Side.Right] == e2.Region[Side.Right]) {
return null;
}
var d = (e1.A*e2.B) - (e1.B*e2.A);
if (Math.Abs(d) < Tolerance) {
return null;
}
var xint = (e1.C*e2.B - e2.C*e1.B)/d;
var yint = (e2.C*e1.A - e1.C*e2.A)/d;
var e1Region = e1.Region[Side.Right];
var e2Region = e2.Region[Side.Right];
HalfEdge el;
Edge e;
if ((e1Region.Y < e2Region.Y) || Math.Abs(e1Region.Y - e2Region.Y) < Tolerance && e1Region.X < e2Region.X) {
el = el1;
e = e1;
} else {
el = el2;
e = e2;
}
var rightOfSite = (xint >= e.Region[Side.Right].X);
if ((rightOfSite && (el.Side == Side.Left)) || (!rightOfSite && (el.Side == Side.Right))) {
return null;
}
var vertex = new Site(xint, yint);
//vertex.AddEdge(e1);
//vertex.AddEdge(e2);
return vertex;
}
public VoronoiGraph StepVoronoi() {
_graph.ResetNewItems();
if (!_edgeFixup) {
if (!_eventQueue.IsEmpty) {
_newIntStar = _eventQueue.Min();
}
if (_newSite != null && (_eventQueue.IsEmpty || /*Geometry.CompareByYThenX(_newSite, _newIntStar)*/ _newSite.CompareTo(_newIntStar) < 0 )) {
_graph.PlotSite(_newSite);
var lbnd = _edgeList.LeftBound(_newSite);
var rbnd = lbnd.Right;
var bot = _edgeList.RightRegion(lbnd);
var e = Edge.CreateBisectingEdge(bot, _newSite);
_graph.PlotBisector(e);
var bisector = new HalfEdge(e, Side.Left);
EdgeList.Insert(lbnd, bisector);
var p = Site.CreateIntersectingSite(lbnd, bisector);
if (p != null) {
_eventQueue.Delete(lbnd);
if (_graph.Debug) {
Console.WriteLine("Inserting {0}", p);
}
_eventQueue.Insert(lbnd, p, Site.Distance(p, _newSite));
}
lbnd = bisector;
bisector = new HalfEdge(e, Side.Right);
EdgeList.Insert(lbnd, bisector);
p = Site.CreateIntersectingSite(bisector, rbnd);
if (p != null) {
if (_graph.Debug) {
Console.WriteLine("Inserting {0}", p);
}
_eventQueue.Insert(bisector, p, Site.Distance(p, _newSite));
}
_newSite = _sites.ExtractMin();
if (_newSite !=null && _newSite.Y > _graph.SweepLine) {
_graph.SweepLine = _newSite.Y;
} else if (_newSite == null) {
_graph.SweepLine = _graph.Height;
}
} else if (!_eventQueue.IsEmpty) { // intersection is smallest
var lbnd = _eventQueue.ExtractMin();
var llbnd = lbnd.Left;
var rbnd = lbnd.Right;
var rrbnd = rbnd.Right;
var bot = _edgeList.LeftRegion(lbnd);
var top = _edgeList.RightRegion(rbnd);
_graph.PlotTriple(bot, top, _edgeList.RightRegion(lbnd));
var v = lbnd.Vertex;
_graph.PlotVertex(v);
_graph.EndPoint(lbnd.Edge, lbnd.Side, v);
_graph.EndPoint(rbnd.Edge, rbnd.Side, v);
EdgeList.Delete(lbnd);
_eventQueue.Delete(rbnd);
EdgeList.Delete(rbnd);
var pm = Side.Left;
if (bot.Y > top.Y) {
var temp = bot;
bot = top;
top = temp;
pm = Side.Right;
}
var e = Edge.CreateBisectingEdge(bot, top);
_graph.PlotBisector(e);
var bisector = new HalfEdge(e, pm);
EdgeList.Insert(llbnd, bisector);
_graph.EndPoint(e, pm == Side.Left ? Side.Right : Side.Left, v);
var p = Site.CreateIntersectingSite(llbnd, bisector);
if (p != null) {
_eventQueue.Delete(llbnd);
if (_graph.Debug) {
Console.WriteLine("Inserting {0}", p);
}
_eventQueue.Insert(llbnd, p, Site.Distance(p, bot));
}
p = Site.CreateIntersectingSite(bisector, rrbnd);
if (p != null) {
if (_graph.Debug) {
Console.WriteLine("Inserting {0}", p);
}
_eventQueue.Insert(bisector, p, Site.Distance(p, bot));
}
} else {
_edgeFixup = true;
}
StepNumber++;
} else {
var lbnd = _edgeList.LeftEnd.Right;
if (lbnd != _edgeList.RightEnd) {
var e = lbnd.Edge;
_graph.PlotEndpoint(e);
EdgeList.Delete(lbnd);
StepNumber++;
} else {
foreach (var edge in _graph.Edges) {
edge.ClipVertices(new Rectangle(0, 0, _graph.Width, _graph.Height));
}
if (_graph.Debug) {
Console.WriteLine("Done computing graph!");
}
}
}
if (_graph.Debug) {
Console.WriteLine("Step: " + StepNumber);
}
return _graph;
}
public static VoronoiGraph ComputeVoronoi(IEnumerable<PointF> points, int w = 800, int h = 600, bool debug=false) {
var sites = new SiteList(points);
sites.LogSites();
var graph = new VoronoiGraph(w, h) { Debug = debug };
try {
var edgeList = new EdgeList(sites);
var eventQueue = new EventQueue();
sites.BottomSite = sites.ExtractMin();
graph.PlotSite(sites.BottomSite);
var newSite = sites.ExtractMin();
var newIntStar = new Site(float.MaxValue, float.MaxValue);
while (true) {
if (!eventQueue.IsEmpty) {
newIntStar = eventQueue.Min();
}
// new site is smallest
if (newSite != null &&
(eventQueue.IsEmpty || newSite.Y < newIntStar.Y || (Math.Abs(newSite.Y - newIntStar.Y) < Geometry.Tolerance && newSite.X < newIntStar.X))) {
graph.PlotSite(newSite);
var lbnd = edgeList.LeftBound(newSite);
var rbnd = lbnd.Right;
var bot = edgeList.RightRegion(lbnd);
var e = Geometry.Bisect(bot, newSite);
graph.PlotBisector(e);
var bisector = new HalfEdge(e, Side.Left);
edgeList.Insert(lbnd, bisector);
var p = Geometry.Intersect(lbnd, bisector);
if (p != null) {
eventQueue.Delete(lbnd);
if (debug) {
Console.WriteLine("Inserting {0}", p);
}
eventQueue.Insert(lbnd, p, Geometry.Distance(p, newSite));
}
lbnd = bisector;
bisector = new HalfEdge(e, Side.Right);
edgeList.Insert(lbnd, bisector);
p = Geometry.Intersect(bisector, rbnd);
if (p != null) {
if (debug) {
Console.WriteLine("Inserting {0}", p);
}
eventQueue.Insert(bisector, p, Geometry.Distance(p, newSite));
}
newSite = sites.ExtractMin();
} else if (!eventQueue.IsEmpty) { // intersection is smallest
var lbnd = eventQueue.ExtractMin();
var llbnd = lbnd.Left;
var rbnd = lbnd.Right;
var rrbnd = rbnd.Right;
var bot = edgeList.LeftRegion(lbnd);
var top = edgeList.RightRegion(rbnd);
graph.PlotTriple(bot, top, edgeList.RightRegion(lbnd));
var v = lbnd.Vertex;
graph.PlotVertex(v);
Geometry.EndPoint(lbnd.Edge, lbnd.Side, v, graph);
Geometry.EndPoint(rbnd.Edge, rbnd.Side, v, graph);
edgeList.Delete(lbnd);
eventQueue.Delete(rbnd);
edgeList.Delete(rbnd);
var pm = Side.Left;
if (bot.Y > top.Y) {
var temp = bot;
bot = top;
top = temp;
pm = Side.Right;
}
var e = Geometry.Bisect(bot, top);
graph.PlotBisector(e);
var bisector = new HalfEdge(e, pm);
edgeList.Insert(llbnd, bisector);
Geometry.EndPoint(e, Side.Other(pm), v, graph);
var p = Geometry.Intersect(llbnd, bisector);
if (p != null) {
eventQueue.Delete(llbnd);
if (debug) {
Console.WriteLine("Inserting {0}", p);
}
eventQueue.Insert(llbnd, p, Geometry.Distance(p, bot));
}
p = Geometry.Intersect(bisector, rrbnd);
if (p != null) {
if (debug) {
Console.WriteLine("Inserting {0}", p);
}
eventQueue.Insert(bisector, p, Geometry.Distance(p, bot));
}
} else {
break;
}
}
for (var lbnd = edgeList.LeftEnd.Right; lbnd != edgeList.RightEnd; lbnd = lbnd.Right) {
var e = lbnd.Edge;
graph.PlotEndpoint(e);
}
} catch (Exception ex) {
Console.WriteLine("########################################");
Console.WriteLine(ex.Message);
Console.WriteLine(ex.StackTrace);
}
graph.SweepLine = graph.Height;
graph.ResetNewItems();
foreach (var edge in graph.Edges) {
edge.ClipVertices(new Rectangle(0,0, w, h));
}
return graph;
}
public void Delete(HalfEdge he)
{
_events.Remove(he);
}
public Site RightRegion(HalfEdge he) {
if (he.Edge == null) {
return _siteList.BottomSite;
}
return he.Side == Side.Left ? he.Edge.Region[Side.Right] : he.Edge.Region[Side.Left];
}
public void Delete(HalfEdge he) {
he.Left.Right = he.Right;
he.Right.Left = he.Left;
he.Edge = null;
}
public void Insert(HalfEdge lb, HalfEdge he) {
he.Left = lb;
he.Right = lb.Right;
lb.Right.Left = he;
lb.Right = he;
}
public void Delete(HalfEdge he) {
_events.Remove(he);
}