/* Function: findRightBreakPoint
* ----------------------------
* Finds the breakpoint to the right of the new arc in the beach line.
*/
private float findRightBreakPoint(BeachArc node, float sweepLineY)
{
BeachArc rightArc = node.Next;
if (rightArc)
{
return(findLeftBreakPoint(rightArc, sweepLineY));
}
return((node.site.y == sweepLineY) ? node.site.x : Mathf.Infinity);
}
/* Function: deleteCircleEvent
* ---------------------------
* Deletes a potential circle event associated with a site event
* from the event queue (it is no longer correct).
*/
private void deleteCircleEvent(BeachArc arc)
{
CircleEvent ce = arc.circleEvent;
arc.circleEvent = null;
if (ce != null && sweepLine.Contains(ce))
{
sweepLine.Remove(ce);
usedCircleEvents.Add(ce);
}
}
/* Function: findLeftBreakPoint
* ----------------------------
* Finds the breakpoint to the left of the new arc in the beach line.
*/
private float findLeftBreakPoint(BeachArc node, float sweepLineY)
{
// Right site
Site site = node.site;
float rightFocusX = site.x;
float rightFocusY = site.y;
float rightFocusSweepDiff = rightFocusY - sweepLineY;
// Parabola focus on directrix (sweep line)
if (rightFocusSweepDiff == 0.0f)
{
return(rightFocusX);
}
// New node, don't do anything
BeachArc leftArc = node.Prev;
if (leftArc == null)
{
return(-Mathf.Infinity);
}
// Left site
site = leftArc.site;
float leftFocusX = site.x;
float leftFocusY = site.y;
float leftFocusSweepDiff = leftFocusY - sweepLineY;
// Parabola focus on directrix (sweep line)
if (leftFocusSweepDiff == 0.0f)
{
return(leftFocusX);
}
// Find intersection
float xFocusDiff = leftFocusX - rightFocusX;
float inverseYDiff = 1 / rightFocusSweepDiff - 1 / leftFocusSweepDiff;
float b = xFocusDiff / leftFocusSweepDiff;
// Like quadratic equation centered at rightfocusX and different coefficients
if (inverseYDiff != 0)
{
return((-b + Mathf.Sqrt(b * b - 2 * inverseYDiff * (xFocusDiff * xFocusDiff / (-2 * leftFocusSweepDiff)
- leftFocusY + leftFocusSweepDiff / 2 + rightFocusY - rightFocusSweepDiff / 2)))
/ inverseYDiff + rightFocusX);
}
// Both parabolas are the same distance to sweep line, breakpoint is in middle
return((rightFocusX + leftFocusX) / 2);
}
/* Function: findNewArcPosition
* ----------------------------
* Finds left and right components of arc above the current one to locate
* where new site arc should fall and updates the values.
*/
private void findNewArcPosition(float siteX, float sweepLineY, ref BeachArc leftArc, ref BeachArc rightArc)
{
BeachArc node = beachLine.Root;
float xLeft, xRight;
while (node)
{
xLeft = findLeftBreakPoint(node, sweepLineY) - siteX;
// Left node x-value falls somewhere on the left edge of the beachsection
if (xLeft > EPS)
{
node = node.Left;
}
else
{
xRight = siteX - findRightBreakPoint(node, sweepLineY);
// Right node x-value falls somewhere after the right edge of the beachsection
if (xRight > EPS)
{
if (node.Right == null)
{
leftArc = node;
break;
}
node = node.Right; // continue right
}
else
{
// Left node x-value falls exactly on the left edge of the beachsection
if (xLeft > -EPS)
{
leftArc = node.Prev;
rightArc = node;
}
// Right node x-value falls exactly on the right edge of the beachsection
else if (xRight > -EPS)
{
leftArc = node;
rightArc = node.Next;
}
// Node falls in the middle of the beachsection
else
{
leftArc = rightArc = node;
}
break;
}
}
}
}
/* Method: reset
* -------------
* Resets to compute a new diagram.
*/
public void reset()
{
// Leftover beach sections to the used list
if (beachLine.Root)
{
BeachArc arc = beachLine.GetFirst(beachLine.Root);
while (arc)
{
usedBeachArcs.Add(arc);
arc = arc.Next;
}
}
beachLine.Root = null;
// Reset sweep line (should be empty)
sweepLine.Clear();
}
/* Function: createNewBeachArc
* ---------------------------
* Creates new beach arc from provided site. Attempts to find
* 'used' one to minimize memory costs.
*/
private BeachArc createNewBeachArc(Site site)
{
// See if used arc available for repurposing
BeachArc arc = (usedBeachArcs.Count > 0) ? usedBeachArcs.Last() : null;
if (arc)
{
usedBeachArcs.Remove(arc);
arc.site = site;
}
// Otherwise create new one
else
{
arc = new BeachArc(site);
}
return(arc);
}
/* Function: getTripleArcCircleEvent
* ---------------------------------
* Checks sites of three arcs for convergence of breakpoints, i.e. beach will
* collapse giving rise to a circle event. If true, gets a circle event and
* updates its fields on the receiving arc and event queue.
*
* Note: Calculation of circle event based on Jeremie St-Amand's:
* https://github.com/jesta88/Unity-Voronoi/blob/master/Assets/Voronoi/FortuneVoronoi.cs
*/
private void getTripleArcCircleEvent(Site left, ref BeachArc center, Site right)
{
float cx = center.site.x;
float cy = center.site.y;
float lx = left.x - cx;
float ly = left.y - cy;
float rx = right.x - cx;
float ry = right.y - cy;
float orientation = 2 * (lx * ry - ly * rx);
// Points are CW, beach section does not collapse so no event
if (orientation >= -2e-12)
{
return;
}
float lLengthSquared = lx * lx + ly * ly;
float rLengthSquared = rx * rx + ry * ry;
float x = (ry * lLengthSquared - ly * rLengthSquared) / orientation;
float y = (lx * rLengthSquared - rx * lLengthSquared) / orientation;
float yCenter = y + cy; // at or below sweepline
// Get circle event to setup
CircleEvent circleEvent = null;
if (usedCircleEvents.Count > 0)
{
circleEvent = usedCircleEvents.Last();
usedCircleEvents.Remove(circleEvent);
}
else
{
circleEvent = new CircleEvent();
}
// Update fields
circleEvent.site = center.site;
circleEvent.arc = center;
circleEvent.setPosition(x + cx, yCenter + Mathf.Sqrt(x * x + y * y), yCenter);
center.circleEvent = circleEvent;
// Add to event queue
sweepLine.Enqueue(circleEvent, circleEvent);
}
/* Function: findPotentialCircleEvent
* ----------------------------------
* Checks for a potential circle event after a site event and adds it
* to the event queue and references it on the arc if found. Done by checking
* if triple of consecutive arcs (including new one) have breakpoints that
* converge.
*/
private void findPotentialCircleEvent(BeachArc arc)
{
BeachArc leftArc = arc.Prev;
BeachArc rightArc = arc.Next;
// Handle missing edge (shouldn't happen)
if (leftArc == null || rightArc == null)
{
//Debug.LogError("Error attaching potential circle event, a surrounding arc is null.");
return;
}
// No convergence, arc sides same
if (leftArc.site == rightArc.site)
{
return;
}
// If left, center, right site locations are CW no event, else event returned
getTripleArcCircleEvent(leftArc.site, ref arc, rightArc.site);
}
/* Function: handleCircleEvent
* ---------------------------
* Handles circle event.
*/
private void handleCircleEvent(BeachArc arc)
{
CircleEvent circleEvent = arc.circleEvent;
Vertex center = new Vertex(circleEvent.x, circleEvent.yCircleCenter);
BeachArc prev = arc.Prev;
BeachArc next = arc.Next;
LinkedList <BeachArc> disappearingTransitions = new LinkedList <BeachArc>();
disappearingTransitions.AddLast(arc);
deleteBeachArc(arc);
// Handle collapse left
BeachArc leftArc = prev;
while (leftArc.circleEvent != null && Mathf.Abs(center.x - leftArc.circleEvent.x) < EPS &&
Mathf.Abs(center.y - leftArc.circleEvent.yCircleCenter) < EPS)
{
prev = leftArc.Prev;
disappearingTransitions.AddFirst(leftArc);
deleteBeachArc(leftArc);
leftArc = prev;
}
// New left arc not dissappearing, but used in edge updates
disappearingTransitions.AddFirst(leftArc);
deleteCircleEvent(leftArc);
// Hanlde collapse right
BeachArc rightArc = next;
while (rightArc.circleEvent != null && Mathf.Abs(center.x - rightArc.circleEvent.x) < EPS &&
Mathf.Abs(center.y - rightArc.circleEvent.yCircleCenter) < EPS)
{
next = rightArc.Next;
disappearingTransitions.AddLast(rightArc);
deleteBeachArc(rightArc);
rightArc = next;
}
// New right arc not dissappearing, but used in edge updates
disappearingTransitions.AddLast(rightArc);
deleteCircleEvent(rightArc);
// Link existing edges at start point
int nArcs = disappearingTransitions.Count;
for (int i = 1; i < nArcs; i++)
{
rightArc = disappearingTransitions.ElementAt(i);
leftArc = disappearingTransitions.ElementAt(i - 1);
rightArc.edge.setStartVertex(leftArc.site, rightArc.site, center);
}
// Create new edge between previously non-adjacent arcs
// New vertex defines end point relative to site on the left
leftArc = disappearingTransitions.ElementAt(0);
rightArc = disappearingTransitions.ElementAt(nArcs - 1);
rightArc.edge = createNewEdge(leftArc.site, rightArc.site, null, center);
// Update circle events for arcs
findPotentialCircleEvent(leftArc);
findPotentialCircleEvent(rightArc);
}
/* Function: deleteBeachArc
* ------------------------
* Deletes an arc and associated circle event from the beach line.
*/
private void deleteBeachArc(BeachArc arc)
{
deleteCircleEvent(arc);
beachLine.Remove(arc);
usedBeachArcs.Add(arc);
}
/* Function: handleSiteEvent
* -------------------------
* Handles site event.
*/
private void handleSiteEvent(Site site)
{
// Locate arc above new site (binary search tree on x-coord)
BeachArc leftArc = null;
BeachArc rightArc = null;
findNewArcPosition(site.x, site.y, ref leftArc, ref rightArc);
// Create a new site event for the site and add it to RB-tree
BeachArc newArc = createNewBeachArc(site);
beachLine.Insert(leftArc, newArc); // if leftArc null, newArc set as root
// First element in beach line, do nothing
if (!leftArc && !rightArc)
{
return;
}
// Node falls in middle of existing beach section arc
else if (leftArc == rightArc)
{
// Delete potential circle event of now split section
deleteCircleEvent(leftArc);
// Split beach section in two
rightArc = createNewBeachArc(leftArc.site);
beachLine.Insert(newArc, rightArc);
// New edge between new site and the one that created split old arc (from new breakpoint)
newArc.edge = rightArc.edge = createNewEdge(leftArc.site, newArc.site);
// Check for potential circle events and add to the event queue
findPotentialCircleEvent(leftArc);
findPotentialCircleEvent(rightArc);
}
// Node falls last on beach line to the right
else if (leftArc && rightArc == null)
{
newArc.edge = createNewEdge(leftArc.site, newArc.site);
}
// Only occurs if no nodes in tree yet (no left curve yet), handled above
else if (leftArc == null && rightArc)
{
Debug.LogError("Error inserting first element into beachline tree.");
}
// Node falls inbetween two other beach section arcs
else if (leftArc != rightArc)
{
deleteCircleEvent(leftArc);
deleteCircleEvent(rightArc);
// Find new cell vertex
Vertex v = findNewVertex(site, leftArc.site, rightArc.site);
// Connect vertex to arcs
rightArc.edge.setStartVertex(leftArc.site, rightArc.site, v);
newArc.edge = createNewEdge(leftArc.site, site, null, v);
rightArc.edge = createNewEdge(site, rightArc.site, null, v);
// Check for potential circle events and add to the event queue
findPotentialCircleEvent(leftArc);
findPotentialCircleEvent(rightArc);
}
}
