// Connect/cut edges at bounding box
public void ClipEdges(BoundingRect bbox)
{
// connect all dangling edges to bounding box
// or get rid of them if it can't be done
// iterate backward so we can splice safely
//while (iEdge--) {
for (int iEdge = this.edges.Count - 1; iEdge >= 0; iEdge--)
{
Edge edge = this.edges[iEdge];
// edge is removed if:
// it is wholly outside the bounding box
// it is actually a point rather than a line
if (!this.ConnectEdge(edge, bbox) ||
!this.ClipEdge(edge, bbox) ||
(Mathf.Abs(edge.va.x - edge.vb.x) < EPSILON && Mathf.Abs(edge.va.y - edge.vb.y) < EPSILON))
{
edge.va = edge.vb = null;
//array_splice(this.edges, iEdge,1);
//this.edges.RemoveAt(iEdge);
this.edges.Remove(edge);
}
}
}
// line-clipping code taken from:
// Liang-Barsky function by Daniel White
// http://www.skytopia.com/project/articles/compsci/clipping.html
// Thanks!
// A bit modified to minimize code paths
public bool ClipEdge(Edge edge, BoundingRect bbox)
{
float ax = edge.va.x;
float ay = edge.va.y;
float bx = edge.vb != null ? edge.vb.x : float.NaN;
float by = edge.vb != null ? edge.vb.y : float.NaN;
float t0 = 0;
float t1 = 1;
float dx = bx - ax;
float dy = by - ay;
// left
float q = ax - bbox.xmin;
if (dx == 0 && q < 0)
{
return(false);
}
float r = -q / dx;
if (dx < 0)
{
if (r < t0)
{
return(false);
}
if (r < t1)
{
t1 = r;
}
}
else if (dx > 0)
{
if (r > t1)
{
return(false);
}
if (r > t0)
{
t0 = r;
}
}
// right
q = bbox.xmax - ax;
if (dx == 0 && q < 0)
{
return(false);
}
r = q / dx;
if (dx < 0)
{
if (r > t1)
{
return(false);
}
if (r > t0)
{
t0 = r;
}
}
else if (dx > 0)
{
if (r < t0)
{
return(false);
}
if (r < t1)
{
t1 = r;
}
}
// top
q = ay - bbox.ymin;
if (dy == 0 && q < 0)
{
return(false);
}
r = -q / dy;
if (dy < 0)
{
if (r < t0)
{
return(false);
}
if (r < t1)
{
t1 = r;
}
}
else if (dy > 0)
{
if (r > t1)
{
return(false);
}
if (r > t0)
{
t0 = r;
}
}
// bottom
q = bbox.ymax - ay;
if (dy == 0 && q < 0)
{
return(false);
}
r = q / dy;
if (dy < 0)
{
if (r > t1)
{
return(false);
}
if (r > t0)
{
t0 = r;
}
}
else if (dy > 0)
{
if (r < t0)
{
return(false);
}
if (r < t1)
{
t1 = r;
}
}
// if we reach this point, Voronoi edge is within bbox
// if t0 > 0, va needs to change
// rhill 2011-06-03: we need to create a new vertex rather
// than modifying the existing one, since the existing
// one is likely shared with at least another edge
if (t0 > 0)
{
edge.va = new Point(ax + t0 * dx, ay + t0 * dy);
}
// if t1 < 1, vb needs to change
// rhill 2011-06-03: we need to create a new vertex rather
// than modifying the existing one, since the existing
// one is likely shared with at least another edge
if (t1 < 1)
{
edge.vb = new Point(ax + t1 * dx, ay + t1 * dy);
}
// va and/or vb were clipped, thus we will need to close
// cells which use this edge.
if (t0 > 0 || t1 < 1)
{
this.cells[edge.lSite.id].closeMe = true;
this.cells[edge.rSite.id].closeMe = true;
}
return(true);
}
// ---------------------------------------------------------------------------
// Diagram completion methods
// connect dangling edges (not if a cursory test tells us
// it is not going to be visible.
// return value:
// false: the dangling va couldn't be connected
// true: the dangling va could be connected
public bool ConnectEdge(Edge edge, BoundingRect bbox)
{
// skip if end point already connected
Point vb = edge.vb;
if (!!vb)
{
return(true);
}
// make local copy for performance purpose
Point va = edge.va;
float xl = bbox.xmin;
float xr = bbox.xmax;
float yt = bbox.ymin;
float yb = bbox.ymax;
Point lSite = edge.lSite;
Point rSite = edge.rSite;
float lx = lSite.x;
float ly = lSite.y;
float rx = rSite.x;
float ry = rSite.y;
float fx = (lx + rx) / 2;
float fy = (ly + ry) / 2;
float fm = float.NaN;
float fb = 0.0f;
// if we reach here, this means cells which use this edge will need
// to be closed, whether because the edge was removed, or because it
// was connected to the bounding box.
this.cells[lSite.id].closeMe = true;
this.cells[rSite.id].closeMe = true;
// get the line equation of the bisector if line is not vertical
if (ry != ly)
{
fm = (lx - rx) / (ry - ly);
fb = fy - fm * fx;
}
// remember, direction of line (relative to left site):
// upward: left.x < right.x
// downward: left.x > right.x
// horizontal: left.x == right.x
// upward: left.x < right.x
// rightward: left.y < right.y
// leftward: left.y > right.y
// vertical: left.y == right.y
// depending on the direction, find the best side of the
// bounding box to use to determine a reasonable start point
// rhill 2013-12-02:
// While at it, since we have the values which define the line,
// clip the end of va if it is outside the bbox.
// https://github.com/gorhill/Javascript-Voronoi/issues/15
// TODO: Do all the clipping here rather than rely on Liang-Barsky
// which does not do well sometimes due to loss of arithmetic
// precision. The code here doesn't degrade if one of the vertex is
// at a huge distance.
// special case: vertical line
if (float.IsNaN(fm))
{
// doesn't intersect with viewport
if (fx < xl || fx >= xr)
{
return(false);
}
// downward
if (lx > rx)
{
if (!va || va.y < yt)
{
//Debug.Log(yt);
va = new Point(fx, yt);
}
else if (va.y >= yb)
{
//Debug.Log(yb);
return(false);
}
vb = new Point(fx, yb);
}
// upward
else
{
if (!va || va.y > yb)
{
//Debug.Log(yb);
va = new Point(fx, yb);
}
else if (va.y < yt)
{
//Debug.Log(yt);
return(false);
}
vb = new Point(fx, yt);
}
}
// closer to vertical than horizontal, connect start point to the
// top or bottom side of the bounding box
else if (fm < -1 || fm > 1)
{
// downward
if (lx > rx)
{
if (!va || va.y < yt)
{
//Debug.Log(va.y + " yt: " + yt);
va = new Point((yt - fb) / fm, yt);
}
else if (va.y >= yb)
{
//Debug.Log(va.y + " yb: " + yb);
return(false);
}
vb = new Point((yb - fb) / fm, yb);
}
// upward
else
{
if (!va || va.y > yb)
{
//Debug.Log(va.y + " yb: " + yb);
va = new Point((yb - fb) / fm, yb);
}
else if (va.y < yt)
{
//Debug.Log(va.y + " yt: " + yt);
return(false);
}
vb = new Point((yt - fb) / fm, yt);
}
}
// closer to horizontal than vertical, connect start point to the
// left or right side of the bounding box
else
{
// rightward
if (ly < ry)
{
if (!va || va.x < xl)
{
//Debug.Log(va.x + " xl: " + xl);
va = new Point(xl, fm * xl + fb);
}
else if (va.x >= xr)
{
//Debug.Log(va.x + " xr: " + xr);
return(false);
}
vb = new Point(xr, fm * xr + fb);
}
// leftward
else
{
if (!va || va.x > xr)
{
//Debug.Log(va.x + " xr: " + xr);
va = new Point(xr, fm * xr + fb);
}
else if (va.x < xl)
{
//Debug.Log(va.x + " xl: " + xl);
return(false);
}
vb = new Point(xl, fm * xl + fb);
}
}
edge.va = va;
edge.vb = vb;
return(true);
}
public VoronoiGraph Compute(List <Point> sites, BoundingRect bbox)
{
this.Reset();
// Initialize site event queue
var siteEvents = sites.Take(sites.Count).ToList();
/*siteEvents.Sort((a, b) =>
* {
* float r = b.y - a.y;
* if (r != 0) { return Mathf.CeilToInt(r); }
* return Mathf.CeilToInt(b.x - a.x);
* });*/
siteEvents = siteEvents.OrderByDescending(s => s.y).ToList();
// process queue
Point site = siteEvents.Last();
siteEvents.Remove(site);
int siteid = 0;
float xsitex = -Mathf.Infinity;
float xsitey = -Mathf.Infinity;
// main loop
for (; ;)
{
// we need to figure whether we handle a site or circle event
// for this we find out if there is a site event and it is
// 'earlier' than the circle event
CircleEvent circle = this.firstCircleEvent;
// add beach section
if (site && (!circle || site.y < circle.y || (site.y == circle.y && site.x < circle.x)))
{
// only if site is not a duplicate
if (site.x != xsitex || site.y != xsitey)
{
// first create cell for new site
//this.cells[siteid] = new Cell(site);
this.cells.Insert(siteid, new Cell(site));
site.id = siteid++;
// then create a beachsection for that site
this.AddBeachSection(site);
// remember last site coords to detect duplicate
xsitey = site.y;
xsitex = site.x;
}
site = siteEvents.Count > 0 ? siteEvents.Last() : null;
if (siteEvents.Count > 0)
{
siteEvents.Remove(site);
}
}
// remove beach section
else if (circle)
{
this.RemoveBeachSection(circle.arc);
}
// all done, quit
else
{
break;
}
}
// wrapping-up
this.ClipEdges(bbox);
this.CloseCells(bbox);
VoronoiGraph graph = new VoronoiGraph();
graph.sites = sites;
graph.cells = this.cells;
graph.edges = this.edges;
this.Reset();
return(graph);
}
// Close the cells.
// The cells are bound by the supplied bounding box.
// Each cell refers to its associated site, and a list
// of halfedges ordered counterclockwise.
public void CloseCells(BoundingRect bbox)
{
// prune, order halfedges, then add missing ones
// required to close cells
float xl = bbox.xmin;
float xr = bbox.xmax;
float yt = bbox.ymin;
float yb = bbox.ymax;
int badIterations = 0;
for (int iCell = this.cells.Count - 1; iCell >= 0; iCell--)
{
Cell cell = this.cells[iCell];
// prune, order halfedges counterclockwise, then add missing ones
// required to close cells
if (cell.Prepare() <= 0)
{
continue;
}
if (!cell.closeMe)
{
continue;
}
// close open cells
// step 1: find first 'unclosed' point, if any.
// an 'unclosed' point will be the end point of a halfedge which
// does not match the start point of the following halfedge
int nHalfedges = cell.halfEdges.Count;
// special case: only one site, in which case, the viewport is the cell
// ...
// all other cases
int iLeft = 0;
int iter = 0;
while (iLeft < nHalfedges)// && iter < 10)
{
iter++;
/*int iRight = (iLeft+1) % nHalfedges;
* Point va = cell.halfEdges[iLeft].Getva();
* Point vz = cell.halfEdges[iRight].Getvz();*/
Point va = cell.halfEdges[iLeft].GetEndPoint();
Point vz = cell.halfEdges[(iLeft + 1) % nHalfedges].GetStartPoint();
// if end point is not equal to start point, we need to add the missing
// halfedge(s) to close the cell
if ((Mathf.Abs(va.x - vz.x) >= EPSILON || Mathf.Abs(va.y - vz.y) >= EPSILON))
{
// rhill 2013-12-02:
// "Holes" in the halfedges are not necessarily always adjacent.
// https://github.com/gorhill/Javascript-Voronoi/issues/16
bool lastBorderSegment = false;
Point vb;
Edge edge;
// walk downward along left side
if (equalWithEpsilon(va.x, xl) && lessThanWithEpsilon(va.y, yb))
{
lastBorderSegment = this.equalWithEpsilon(vz.x, xl);
vb = new Point(xl, lastBorderSegment ? vz.y : yb);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk rightward along bottom side
if (!lastBorderSegment && this.equalWithEpsilon(va.y, yb) && this.lessThanWithEpsilon(va.x, xr))
{
lastBorderSegment = this.equalWithEpsilon(vz.y, yb);
vb = new Point(lastBorderSegment ? vz.x : xr, yb);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk upward along right side
if (!lastBorderSegment && this.equalWithEpsilon(va.x, xr) && this.greaterThanWithEpsilon(va.y, yt))
{
lastBorderSegment = this.equalWithEpsilon(vz.x, xr);
vb = new Point(xr, lastBorderSegment ? vz.y : yt);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk leftward along top side
if (!lastBorderSegment && this.equalWithEpsilon(va.y, yt) && this.greaterThanWithEpsilon(va.x, xl))
{
lastBorderSegment = this.equalWithEpsilon(vz.y, yt);
vb = new Point(lastBorderSegment ? vz.x : xl, yt);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk downward along left side
if (!lastBorderSegment)
{
lastBorderSegment = this.equalWithEpsilon(vz.x, xl);
vb = new Point(xl, lastBorderSegment ? vz.y : yb);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk rightward along bottom side
if (!lastBorderSegment)
{
lastBorderSegment = this.equalWithEpsilon(vz.y, yb);
vb = new Point(lastBorderSegment ? vz.x : xr, yb);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
if (!lastBorderSegment)
{
va = vb;
}
}
// walk upward along right side
if (!lastBorderSegment)
{
lastBorderSegment = this.equalWithEpsilon(vz.x, xr);
vb = new Point(xr, lastBorderSegment ? vz.y : yt);
edge = this.CreateBorderEdge(cell.site, va, vb);
iLeft++;
//halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
cell.halfEdges.Insert(iLeft, new HalfEdge(edge, cell.site, null));
nHalfedges++;
}
if (!lastBorderSegment)
{
Debug.LogError("This makes no sense");
badIterations++;
}
}
iLeft++;
}
cell.closeMe = false;
}
if (badIterations > 0)
{
this.valid = false;
}
else
{
this.valid = true;
}
}