private static void CheckCircle(RedBlackTreeNode <BeachSection> section, MinHeap <FortuneEvent> eventQueue)
{
RedBlackTreeNode <BeachSection> left = section.previous;
RedBlackTreeNode <BeachSection> right = section.next;
if (left == null || right == null)
{
return;
}
FortuneSite leftSite = left.data.site;
FortuneSite centerSite = section.data.site;
FortuneSite rightSite = right.data.site;
if (leftSite == rightSite)
{
return;
}
double bX = centerSite.x;
double bY = centerSite.y;
double aX = leftSite.x - bX;
double aY = leftSite.y - bY;
double cX = rightSite.x - bX;
double cY = rightSite.y - bY;
double delta = aX * cY - aY * cX;
if (delta.ApproxGreaterThanOrEqualTo(0))
{
return;
}
double magnitudeA = aX * aX + aY * aY;
double magnitudeC = cX * cX + cY * cY;
double x = (cY * magnitudeA - aY * magnitudeC) / (2 * delta);
double y = (aX * magnitudeC - cX * magnitudeA) / (2 * delta);
double yCenter = y + bY;
FortuneCircleEvent circleEvent = new FortuneCircleEvent(
new Point(x + bX, yCenter + Math.Sqrt(x * x + y * y)),
yCenter, section
);
section.data.circleEvent = circleEvent;
eventQueue.Insert(circleEvent);
}
private static void CheckCircle(RBTreeNode <BeachSection> section, MinHeap <FortuneEvent> eventQueue)
{
//if (section == null)
// return;
var left = section.Previous;
var right = section.Next;
if (left == null || right == null)
{
return;
}
var leftSite = left.Data.Site;
var centerSite = section.Data.Site;
var rightSite = right.Data.Site;
//if the left arc and right arc are defined by the same
//focus, the two arcs cannot converge
if (leftSite == rightSite)
{
return;
}
// http://mathforum.org/library/drmath/view/55002.html
// because every piece of this program needs to be demoed in maple >.<
//MATH HACKS: place center at origin and
//draw vectors a and c to
//left and right respectively
double bx = centerSite.X,
by = centerSite.Y,
ax = leftSite.X - bx,
ay = leftSite.Y - by,
cx = rightSite.X - bx,
cy = rightSite.Y - by;
//The center beach section can only dissapear when
//the angle between a and c is negative
var d = ax * cy - ay * cx;
if (d.ApproxGreaterThanOrEqualTo(0))
{
return;
}
var magnitudeA = ax * ax + ay * ay;
var magnitudeC = cx * cx + cy * cy;
var x = (cy * magnitudeA - ay * magnitudeC) / (2 * d);
var y = (ax * magnitudeC - cx * magnitudeA) / (2 * d);
//add back offset
var ycenter = y + by;
//y center is off
var circleEvent = new FortuneCircleEvent(
new Point(x + bx, ycenter + Math.Sqrt(x * x + y * y)),
ycenter, section
);
section.Data.CircleEvent = circleEvent;
eventQueue.Insert(circleEvent);
}
internal void RemoveBeachSection(FortuneCircleEvent circle, MinHeap <FortuneEvent> eventQueue, HashSet <FortuneCircleEvent> deleted, LinkedList <VoronoiEdge> edges)
{
var section = circle.ToDelete;
var x = circle.X;
var y = circle.YCenter;
var vertex = new Point(x, y);
//multiple edges could end here
var toBeRemoved = new List <RBTreeNode <BeachSection> >();
//look left
var prev = section.Previous;
while (prev.Data.CircleEvent != null &&
(x - prev.Data.CircleEvent.X).ApproxEqual(0) &&
(y - prev.Data.CircleEvent.Y).ApproxEqual(0))
{
toBeRemoved.Add(prev);
prev = prev.Previous;
}
var next = section.Next;
while (next.Data.CircleEvent != null &&
(x - next.Data.CircleEvent.X).ApproxEqual(0) &&
(y - next.Data.CircleEvent.Y).ApproxEqual(0))
{
toBeRemoved.Add(next);
next = next.Next;
}
section.Data.Edge.EndPoint = vertex;
section.Next.Data.Edge.EndPoint = vertex;
section.Data.CircleEvent = null;
//odds are this double writes a few edges but this is clean...
foreach (var remove in toBeRemoved)
{
remove.Data.Edge.EndPoint = vertex;
remove.Next.Data.Edge.EndPoint = vertex;
deleted.Add(remove.Data.CircleEvent);
remove.Data.CircleEvent = null;
}
//need to delete all upcoming circle events with this node
if (prev.Data.CircleEvent != null)
{
deleted.Add(prev.Data.CircleEvent);
prev.Data.CircleEvent = null;
}
if (next.Data.CircleEvent != null)
{
deleted.Add(next.Data.CircleEvent);
next.Data.CircleEvent = null;
}
//create a new edge with start point at the vertex and assign it to next
var newEdge = new VoronoiEdge(vertex, next.Data.Site, prev.Data.Site);
next.Data.Edge = newEdge;
edges.AddFirst(newEdge);
//add neighbors for delaunay
prev.Data.Site.Neighbours.Add(next.Data.Site);
next.Data.Site.Neighbours.Add(prev.Data.Site);
//remove the sectionfrom the tree
beachLine.RemoveNode(section);
foreach (var remove in toBeRemoved)
{
beachLine.RemoveNode(remove);
}
CheckCircle(prev, eventQueue);
CheckCircle(next, eventQueue);
}
internal BeachSection(FSite site)
{
Site = site;
CircleEvent = null;
}
public void RemoveBeachSection(FortuneCircleEvent circle, MinHeap <FortuneEvent> eventQueue, HashSet <FortuneCircleEvent> deleted, LinkedList <Edge> edges)
{
RedBlackTreeNode <BeachSection> section = circle.toDelete;
double x = circle.x;
double y = circle.yCenter;
Point vertex = new Point(x, y);
List <RedBlackTreeNode <BeachSection> > toBeRemoved = new List <RedBlackTreeNode <BeachSection> >();
RedBlackTreeNode <BeachSection> previous = section.previous;
while (previous.data.circleEvent != null && (x - previous.data.circleEvent.x).ApproxEqual(0) && (y - previous.data.circleEvent.y).ApproxEqual(0))
{
toBeRemoved.Add(previous);
previous = previous.previous;
}
RedBlackTreeNode <BeachSection> next = section.next;
while (next.data.circleEvent != null && (x - next.data.circleEvent.x).ApproxEqual(0) && (y - next.data.circleEvent.y).ApproxEqual(0))
{
toBeRemoved.Add(next);
next = next.next;
}
section.data.edge.end = vertex;
section.next.data.edge.end = vertex;
section.data.circleEvent = null;
foreach (RedBlackTreeNode <BeachSection> toRemove in toBeRemoved)
{
toRemove.data.edge.end = vertex;
toRemove.next.data.edge.end = vertex;
deleted.Add(toRemove.data.circleEvent);
toRemove.data.circleEvent = null;
}
if (previous.data.circleEvent != null)
{
deleted.Add(previous.data.circleEvent);
previous.data.circleEvent = null;
}
if (next.data.circleEvent != null)
{
deleted.Add(next.data.circleEvent);
next.data.circleEvent = null;
}
Edge newEdge = new Edge(vertex, next.data.site, previous.data.site);
next.data.edge = newEdge;
edges.AddFirst(newEdge);
previous.data.site.neighbours.Add(next.data.site);
next.data.site.neighbours.Add(previous.data.site);
sections.Remove(section);
foreach (RedBlackTreeNode <BeachSection> toRemove in toBeRemoved)
{
sections.Remove(toRemove);
}
CheckCircle(previous, eventQueue);
CheckCircle(next, eventQueue);
}
public BeachSection(FortuneSite site)
{
this.site = site;
this.circleEvent = null;
}
