summaryrefslogtreecommitdiff
path: root/src/3rdparty/rhill-voronoi-core.js
diff options
context:
space:
mode:
Diffstat (limited to 'src/3rdparty/rhill-voronoi-core.js')
-rw-r--r--src/3rdparty/rhill-voronoi-core.js1723
1 files changed, 1723 insertions, 0 deletions
diff --git a/src/3rdparty/rhill-voronoi-core.js b/src/3rdparty/rhill-voronoi-core.js
new file mode 100644
index 0000000..26dac8f
--- /dev/null
+++ b/src/3rdparty/rhill-voronoi-core.js
@@ -0,0 +1,1723 @@
+/*!
+Copyright (C) 2010-2013 Raymond Hill: https://github.com/gorhill/Javascript-Voronoi
+MIT License: See https://github.com/gorhill/Javascript-Voronoi/LICENSE.md
+*/
+/*
+Author: Raymond Hill (rhill@raymondhill.net)
+Contributor: Jesse Morgan (morgajel@gmail.com)
+File: rhill-voronoi-core.js
+Version: 0.98
+Date: January 21, 2013
+Description: This is my personal Javascript implementation of
+Steven Fortune's algorithm to compute Voronoi diagrams.
+
+License: See https://github.com/gorhill/Javascript-Voronoi/LICENSE.md
+Credits: See https://github.com/gorhill/Javascript-Voronoi/CREDITS.md
+History: See https://github.com/gorhill/Javascript-Voronoi/CHANGELOG.md
+
+## Usage:
+
+ var sites = [{x:300,y:300}, {x:100,y:100}, {x:200,y:500}, {x:250,y:450}, {x:600,y:150}];
+ // xl, xr means x left, x right
+ // yt, yb means y top, y bottom
+ var bbox = {xl:0, xr:800, yt:0, yb:600};
+ var voronoi = new Voronoi();
+ // pass an object which exhibits xl, xr, yt, yb properties. The bounding
+ // box will be used to connect unbound edges, and to close open cells
+ result = voronoi.compute(sites, bbox);
+ // render, further analyze, etc.
+
+Return value:
+ An object with the following properties:
+
+ result.vertices = an array of unordered, unique Voronoi.Vertex objects making
+ up the Voronoi diagram.
+ result.edges = an array of unordered, unique Voronoi.Edge objects making up
+ the Voronoi diagram.
+ result.cells = an array of Voronoi.Cell object making up the Voronoi diagram.
+ A Cell object might have an empty array of halfedges, meaning no Voronoi
+ cell could be computed for a particular cell.
+ result.execTime = the time it took to compute the Voronoi diagram, in
+ milliseconds.
+
+Voronoi.Vertex object:
+ x: The x position of the vertex.
+ y: The y position of the vertex.
+
+Voronoi.Edge object:
+ lSite: the Voronoi site object at the left of this Voronoi.Edge object.
+ rSite: the Voronoi site object at the right of this Voronoi.Edge object (can
+ be null).
+ va: an object with an 'x' and a 'y' property defining the start point
+ (relative to the Voronoi site on the left) of this Voronoi.Edge object.
+ vb: an object with an 'x' and a 'y' property defining the end point
+ (relative to Voronoi site on the left) of this Voronoi.Edge object.
+
+ For edges which are used to close open cells (using the supplied bounding
+ box), the rSite property will be null.
+
+Voronoi.Cell object:
+ site: the Voronoi site object associated with the Voronoi cell.
+ halfedges: an array of Voronoi.Halfedge objects, ordered counterclockwise,
+ defining the polygon for this Voronoi cell.
+
+Voronoi.Halfedge object:
+ site: the Voronoi site object owning this Voronoi.Halfedge object.
+ edge: a reference to the unique Voronoi.Edge object underlying this
+ Voronoi.Halfedge object.
+ getStartpoint(): a method returning an object with an 'x' and a 'y' property
+ for the start point of this halfedge. Keep in mind halfedges are always
+ countercockwise.
+ getEndpoint(): a method returning an object with an 'x' and a 'y' property
+ for the end point of this halfedge. Keep in mind halfedges are always
+ countercockwise.
+
+TODO: Identify opportunities for performance improvement.
+
+TODO: Let the user close the Voronoi cells, do not do it automatically. Not only let
+ him close the cells, but also allow him to close more than once using a different
+ bounding box for the same Voronoi diagram.
+*/
+
+/*global Math */
+
+// ---------------------------------------------------------------------------
+
+function Voronoi() {
+ this.vertices = null;
+ this.edges = null;
+ this.cells = null;
+ this.toRecycle = null;
+ this.beachsectionJunkyard = [];
+ this.circleEventJunkyard = [];
+ this.vertexJunkyard = [];
+ this.edgeJunkyard = [];
+ this.cellJunkyard = [];
+ }
+
+// ---------------------------------------------------------------------------
+
+Voronoi.prototype.reset = function() {
+ if (!this.beachline) {
+ this.beachline = new this.RBTree();
+ }
+ // Move leftover beachsections to the beachsection junkyard.
+ if (this.beachline.root) {
+ var beachsection = this.beachline.getFirst(this.beachline.root);
+ while (beachsection) {
+ this.beachsectionJunkyard.push(beachsection); // mark for reuse
+ beachsection = beachsection.rbNext;
+ }
+ }
+ this.beachline.root = null;
+ if (!this.circleEvents) {
+ this.circleEvents = new this.RBTree();
+ }
+ this.circleEvents.root = this.firstCircleEvent = null;
+ this.vertices = [];
+ this.edges = [];
+ this.cells = [];
+ };
+
+Voronoi.prototype.sqrt = Math.sqrt;
+Voronoi.prototype.abs = Math.abs;
+Voronoi.prototype.ε = Voronoi.ε = 1e-9;
+Voronoi.prototype.invε = Voronoi.invε = 1.0 / Voronoi.ε;
+Voronoi.prototype.equalWithEpsilon = function(a,b){return this.abs(a-b)<1e-9;};
+Voronoi.prototype.greaterThanWithEpsilon = function(a,b){return a-b>1e-9;};
+Voronoi.prototype.greaterThanOrEqualWithEpsilon = function(a,b){return b-a<1e-9;};
+Voronoi.prototype.lessThanWithEpsilon = function(a,b){return b-a>1e-9;};
+Voronoi.prototype.lessThanOrEqualWithEpsilon = function(a,b){return a-b<1e-9;};
+
+// ---------------------------------------------------------------------------
+// Red-Black tree code (based on C version of "rbtree" by Franck Bui-Huu
+// https://github.com/fbuihuu/libtree/blob/master/rb.c
+
+Voronoi.prototype.RBTree = function() {
+ this.root = null;
+ };
+
+Voronoi.prototype.RBTree.prototype.rbInsertSuccessor = function(node, successor) {
+ var parent;
+ if (node) {
+ // >>> rhill 2011-05-27: Performance: cache previous/next nodes
+ successor.rbPrevious = node;
+ successor.rbNext = node.rbNext;
+ if (node.rbNext) {
+ node.rbNext.rbPrevious = successor;
+ }
+ node.rbNext = successor;
+ // <<<
+ if (node.rbRight) {
+ // in-place expansion of node.rbRight.getFirst();
+ node = node.rbRight;
+ while (node.rbLeft) {node = node.rbLeft;}
+ node.rbLeft = successor;
+ }
+ else {
+ node.rbRight = successor;
+ }
+ parent = node;
+ }
+ // rhill 2011-06-07: if node is null, successor must be inserted
+ // to the left-most part of the tree
+ else if (this.root) {
+ node = this.getFirst(this.root);
+ // >>> Performance: cache previous/next nodes
+ successor.rbPrevious = null;
+ successor.rbNext = node;
+ node.rbPrevious = successor;
+ // <<<
+ node.rbLeft = successor;
+ parent = node;
+ }
+ else {
+ // >>> Performance: cache previous/next nodes
+ successor.rbPrevious = successor.rbNext = null;
+ // <<<
+ this.root = successor;
+ parent = null;
+ }
+ successor.rbLeft = successor.rbRight = null;
+ successor.rbParent = parent;
+ successor.rbRed = true;
+ // Fixup the modified tree by recoloring nodes and performing
+ // rotations (2 at most) hence the red-black tree properties are
+ // preserved.
+ var grandpa, uncle;
+ node = successor;
+ while (parent && parent.rbRed) {
+ grandpa = parent.rbParent;
+ if (parent === grandpa.rbLeft) {
+ uncle = grandpa.rbRight;
+ if (uncle && uncle.rbRed) {
+ parent.rbRed = uncle.rbRed = false;
+ grandpa.rbRed = true;
+ node = grandpa;
+ }
+ else {
+ if (node === parent.rbRight) {
+ this.rbRotateLeft(parent);
+ node = parent;
+ parent = node.rbParent;
+ }
+ parent.rbRed = false;
+ grandpa.rbRed = true;
+ this.rbRotateRight(grandpa);
+ }
+ }
+ else {
+ uncle = grandpa.rbLeft;
+ if (uncle && uncle.rbRed) {
+ parent.rbRed = uncle.rbRed = false;
+ grandpa.rbRed = true;
+ node = grandpa;
+ }
+ else {
+ if (node === parent.rbLeft) {
+ this.rbRotateRight(parent);
+ node = parent;
+ parent = node.rbParent;
+ }
+ parent.rbRed = false;
+ grandpa.rbRed = true;
+ this.rbRotateLeft(grandpa);
+ }
+ }
+ parent = node.rbParent;
+ }
+ this.root.rbRed = false;
+ };
+
+Voronoi.prototype.RBTree.prototype.rbRemoveNode = function(node) {
+ // >>> rhill 2011-05-27: Performance: cache previous/next nodes
+ if (node.rbNext) {
+ node.rbNext.rbPrevious = node.rbPrevious;
+ }
+ if (node.rbPrevious) {
+ node.rbPrevious.rbNext = node.rbNext;
+ }
+ node.rbNext = node.rbPrevious = null;
+ // <<<
+ var parent = node.rbParent,
+ left = node.rbLeft,
+ right = node.rbRight,
+ next;
+ if (!left) {
+ next = right;
+ }
+ else if (!right) {
+ next = left;
+ }
+ else {
+ next = this.getFirst(right);
+ }
+ if (parent) {
+ if (parent.rbLeft === node) {
+ parent.rbLeft = next;
+ }
+ else {
+ parent.rbRight = next;
+ }
+ }
+ else {
+ this.root = next;
+ }
+ // enforce red-black rules
+ var isRed;
+ if (left && right) {
+ isRed = next.rbRed;
+ next.rbRed = node.rbRed;
+ next.rbLeft = left;
+ left.rbParent = next;
+ if (next !== right) {
+ parent = next.rbParent;
+ next.rbParent = node.rbParent;
+ node = next.rbRight;
+ parent.rbLeft = node;
+ next.rbRight = right;
+ right.rbParent = next;
+ }
+ else {
+ next.rbParent = parent;
+ parent = next;
+ node = next.rbRight;
+ }
+ }
+ else {
+ isRed = node.rbRed;
+ node = next;
+ }
+ // 'node' is now the sole successor's child and 'parent' its
+ // new parent (since the successor can have been moved)
+ if (node) {
+ node.rbParent = parent;
+ }
+ // the 'easy' cases
+ if (isRed) {return;}
+ if (node && node.rbRed) {
+ node.rbRed = false;
+ return;
+ }
+ // the other cases
+ var sibling;
+ do {
+ if (node === this.root) {
+ break;
+ }
+ if (node === parent.rbLeft) {
+ sibling = parent.rbRight;
+ if (sibling.rbRed) {
+ sibling.rbRed = false;
+ parent.rbRed = true;
+ this.rbRotateLeft(parent);
+ sibling = parent.rbRight;
+ }
+ if ((sibling.rbLeft && sibling.rbLeft.rbRed) || (sibling.rbRight && sibling.rbRight.rbRed)) {
+ if (!sibling.rbRight || !sibling.rbRight.rbRed) {
+ sibling.rbLeft.rbRed = false;
+ sibling.rbRed = true;
+ this.rbRotateRight(sibling);
+ sibling = parent.rbRight;
+ }
+ sibling.rbRed = parent.rbRed;
+ parent.rbRed = sibling.rbRight.rbRed = false;
+ this.rbRotateLeft(parent);
+ node = this.root;
+ break;
+ }
+ }
+ else {
+ sibling = parent.rbLeft;
+ if (sibling.rbRed) {
+ sibling.rbRed = false;
+ parent.rbRed = true;
+ this.rbRotateRight(parent);
+ sibling = parent.rbLeft;
+ }
+ if ((sibling.rbLeft && sibling.rbLeft.rbRed) || (sibling.rbRight && sibling.rbRight.rbRed)) {
+ if (!sibling.rbLeft || !sibling.rbLeft.rbRed) {
+ sibling.rbRight.rbRed = false;
+ sibling.rbRed = true;
+ this.rbRotateLeft(sibling);
+ sibling = parent.rbLeft;
+ }
+ sibling.rbRed = parent.rbRed;
+ parent.rbRed = sibling.rbLeft.rbRed = false;
+ this.rbRotateRight(parent);
+ node = this.root;
+ break;
+ }
+ }
+ sibling.rbRed = true;
+ node = parent;
+ parent = parent.rbParent;
+ } while (!node.rbRed);
+ if (node) {node.rbRed = false;}
+ };
+
+Voronoi.prototype.RBTree.prototype.rbRotateLeft = function(node) {
+ var p = node,
+ q = node.rbRight, // can't be null
+ parent = p.rbParent;
+ if (parent) {
+ if (parent.rbLeft === p) {
+ parent.rbLeft = q;
+ }
+ else {
+ parent.rbRight = q;
+ }
+ }
+ else {
+ this.root = q;
+ }
+ q.rbParent = parent;
+ p.rbParent = q;
+ p.rbRight = q.rbLeft;
+ if (p.rbRight) {
+ p.rbRight.rbParent = p;
+ }
+ q.rbLeft = p;
+ };
+
+Voronoi.prototype.RBTree.prototype.rbRotateRight = function(node) {
+ var p = node,
+ q = node.rbLeft, // can't be null
+ parent = p.rbParent;
+ if (parent) {
+ if (parent.rbLeft === p) {
+ parent.rbLeft = q;
+ }
+ else {
+ parent.rbRight = q;
+ }
+ }
+ else {
+ this.root = q;
+ }
+ q.rbParent = parent;
+ p.rbParent = q;
+ p.rbLeft = q.rbRight;
+ if (p.rbLeft) {
+ p.rbLeft.rbParent = p;
+ }
+ q.rbRight = p;
+ };
+
+Voronoi.prototype.RBTree.prototype.getFirst = function(node) {
+ while (node.rbLeft) {
+ node = node.rbLeft;
+ }
+ return node;
+ };
+
+Voronoi.prototype.RBTree.prototype.getLast = function(node) {
+ while (node.rbRight) {
+ node = node.rbRight;
+ }
+ return node;
+ };
+
+// ---------------------------------------------------------------------------
+// Diagram methods
+
+Voronoi.prototype.Diagram = function(site) {
+ this.site = site;
+ };
+
+// ---------------------------------------------------------------------------
+// Cell methods
+
+Voronoi.prototype.Cell = function(site) {
+ this.site = site;
+ this.halfedges = [];
+ this.closeMe = false;
+ };
+
+Voronoi.prototype.Cell.prototype.init = function(site) {
+ this.site = site;
+ this.halfedges = [];
+ this.closeMe = false;
+ return this;
+ };
+
+Voronoi.prototype.createCell = function(site) {
+ var cell = this.cellJunkyard.pop();
+ if ( cell ) {
+ return cell.init(site);
+ }
+ return new this.Cell(site);
+ };
+
+Voronoi.prototype.Cell.prototype.prepareHalfedges = function() {
+ var halfedges = this.halfedges,
+ iHalfedge = halfedges.length,
+ edge;
+ // get rid of unused halfedges
+ // rhill 2011-05-27: Keep it simple, no point here in trying
+ // to be fancy: dangling edges are a typically a minority.
+ while (iHalfedge--) {
+ edge = halfedges[iHalfedge].edge;
+ if (!edge.vb || !edge.va) {
+ halfedges.splice(iHalfedge,1);
+ }
+ }
+
+ // rhill 2011-05-26: I tried to use a binary search at insertion
+ // time to keep the array sorted on-the-fly (in Cell.addHalfedge()).
+ // There was no real benefits in doing so, performance on
+ // Firefox 3.6 was improved marginally, while performance on
+ // Opera 11 was penalized marginally.
+ halfedges.sort(function(a,b){return b.angle-a.angle;});
+ return halfedges.length;
+ };
+
+// Return a list of the neighbor Ids
+Voronoi.prototype.Cell.prototype.getNeighborIds = function() {
+ var neighbors = [],
+ iHalfedge = this.halfedges.length,
+ edge;
+ while (iHalfedge--){
+ edge = this.halfedges[iHalfedge].edge;
+ if (edge.lSite !== null && edge.lSite.voronoiId != this.site.voronoiId) {
+ neighbors.push(edge.lSite.voronoiId);
+ }
+ else if (edge.rSite !== null && edge.rSite.voronoiId != this.site.voronoiId){
+ neighbors.push(edge.rSite.voronoiId);
+ }
+ }
+ return neighbors;
+ };
+
+// Compute bounding box
+//
+Voronoi.prototype.Cell.prototype.getBbox = function() {
+ var halfedges = this.halfedges,
+ iHalfedge = halfedges.length,
+ xmin = Infinity,
+ ymin = Infinity,
+ xmax = -Infinity,
+ ymax = -Infinity,
+ v, vx, vy;
+ while (iHalfedge--) {
+ v = halfedges[iHalfedge].getStartpoint();
+ vx = v.x;
+ vy = v.y;
+ if (vx < xmin) {xmin = vx;}
+ if (vy < ymin) {ymin = vy;}
+ if (vx > xmax) {xmax = vx;}
+ if (vy > ymax) {ymax = vy;}
+ // we dont need to take into account end point,
+ // since each end point matches a start point
+ }
+ return {
+ x: xmin,
+ y: ymin,
+ width: xmax-xmin,
+ height: ymax-ymin
+ };
+ };
+
+// Return whether a point is inside, on, or outside the cell:
+// -1: point is outside the perimeter of the cell
+// 0: point is on the perimeter of the cell
+// 1: point is inside the perimeter of the cell
+//
+Voronoi.prototype.Cell.prototype.pointIntersection = function(x, y) {
+ // Check if point in polygon. Since all polygons of a Voronoi
+ // diagram are convex, then:
+ // http://paulbourke.net/geometry/polygonmesh/
+ // Solution 3 (2D):
+ // "If the polygon is convex then one can consider the polygon
+ // "as a 'path' from the first vertex. A point is on the interior
+ // "of this polygons if it is always on the same side of all the
+ // "line segments making up the path. ...
+ // "(y - y0) (x1 - x0) - (x - x0) (y1 - y0)
+ // "if it is less than 0 then P is to the right of the line segment,
+ // "if greater than 0 it is to the left, if equal to 0 then it lies
+ // "on the line segment"
+ var halfedges = this.halfedges,
+ iHalfedge = halfedges.length,
+ halfedge,
+ p0, p1, r;
+ while (iHalfedge--) {
+ halfedge = halfedges[iHalfedge];
+ p0 = halfedge.getStartpoint();
+ p1 = halfedge.getEndpoint();
+ r = (y-p0.y)*(p1.x-p0.x)-(x-p0.x)*(p1.y-p0.y);
+ if (!r) {
+ return 0;
+ }
+ if (r > 0) {
+ return -1;
+ }
+ }
+ return 1;
+ };
+
+// ---------------------------------------------------------------------------
+// Edge methods
+//
+
+Voronoi.prototype.Vertex = function(x, y) {
+ this.x = x;
+ this.y = y;
+ };
+
+Voronoi.prototype.Edge = function(lSite, rSite) {
+ this.lSite = lSite;
+ this.rSite = rSite;
+ this.va = this.vb = null;
+ };
+
+Voronoi.prototype.Halfedge = function(edge, lSite, rSite) {
+ this.site = lSite;
+ this.edge = edge;
+ // 'angle' is a value to be used for properly sorting the
+ // halfsegments counterclockwise. By convention, we will
+ // use the angle of the line defined by the 'site to the left'
+ // to the 'site to the right'.
+ // However, border edges have no 'site to the right': thus we
+ // use the angle of line perpendicular to the halfsegment (the
+ // edge should have both end points defined in such case.)
+ if (rSite) {
+ this.angle = Math.atan2(rSite.y-lSite.y, rSite.x-lSite.x);
+ }
+ else {
+ var va = edge.va,
+ vb = edge.vb;
+ // rhill 2011-05-31: used to call getStartpoint()/getEndpoint(),
+ // but for performance purpose, these are expanded in place here.
+ this.angle = edge.lSite === lSite ?
+ Math.atan2(vb.x-va.x, va.y-vb.y) :
+ Math.atan2(va.x-vb.x, vb.y-va.y);
+ }
+ };
+
+Voronoi.prototype.createHalfedge = function(edge, lSite, rSite) {
+ return new this.Halfedge(edge, lSite, rSite);
+ };
+
+Voronoi.prototype.Halfedge.prototype.getStartpoint = function() {
+ return this.edge.lSite === this.site ? this.edge.va : this.edge.vb;
+ };
+
+Voronoi.prototype.Halfedge.prototype.getEndpoint = function() {
+ return this.edge.lSite === this.site ? this.edge.vb : this.edge.va;
+ };
+
+
+
+// this create and add a vertex to the internal collection
+
+Voronoi.prototype.createVertex = function(x, y) {
+ var v = this.vertexJunkyard.pop();
+ if ( !v ) {
+ v = new this.Vertex(x, y);
+ }
+ else {
+ v.x = x;
+ v.y = y;
+ }
+ this.vertices.push(v);
+ return v;
+ };
+
+// this create and add an edge to internal collection, and also create
+// two halfedges which are added to each site's counterclockwise array
+// of halfedges.
+
+Voronoi.prototype.createEdge = function(lSite, rSite, va, vb) {
+ var edge = this.edgeJunkyard.pop();
+ if ( !edge ) {
+ edge = new this.Edge(lSite, rSite);
+ }
+ else {
+ edge.lSite = lSite;
+ edge.rSite = rSite;
+ edge.va = edge.vb = null;
+ }
+
+ this.edges.push(edge);
+ if (va) {
+ this.setEdgeStartpoint(edge, lSite, rSite, va);
+ }
+ if (vb) {
+ this.setEdgeEndpoint(edge, lSite, rSite, vb);
+ }
+ this.cells[lSite.voronoiId].halfedges.push(this.createHalfedge(edge, lSite, rSite));
+ this.cells[rSite.voronoiId].halfedges.push(this.createHalfedge(edge, rSite, lSite));
+ return edge;
+ };
+
+Voronoi.prototype.createBorderEdge = function(lSite, va, vb) {
+ var edge = this.edgeJunkyard.pop();
+ if ( !edge ) {
+ edge = new this.Edge(lSite, null);
+ }
+ else {
+ edge.lSite = lSite;
+ edge.rSite = null;
+ }
+ edge.va = va;
+ edge.vb = vb;
+ this.edges.push(edge);
+ return edge;
+ };
+
+Voronoi.prototype.setEdgeStartpoint = function(edge, lSite, rSite, vertex) {
+ if (!edge.va && !edge.vb) {
+ edge.va = vertex;
+ edge.lSite = lSite;
+ edge.rSite = rSite;
+ }
+ else if (edge.lSite === rSite) {
+ edge.vb = vertex;
+ }
+ else {
+ edge.va = vertex;
+ }
+ };
+
+Voronoi.prototype.setEdgeEndpoint = function(edge, lSite, rSite, vertex) {
+ this.setEdgeStartpoint(edge, rSite, lSite, vertex);
+ };
+
+// ---------------------------------------------------------------------------
+// Beachline methods
+
+// rhill 2011-06-07: For some reasons, performance suffers significantly
+// when instanciating a literal object instead of an empty ctor
+Voronoi.prototype.Beachsection = function() {
+ };
+
+// rhill 2011-06-02: A lot of Beachsection instanciations
+// occur during the computation of the Voronoi diagram,
+// somewhere between the number of sites and twice the
+// number of sites, while the number of Beachsections on the
+// beachline at any given time is comparatively low. For this
+// reason, we reuse already created Beachsections, in order
+// to avoid new memory allocation. This resulted in a measurable
+// performance gain.
+
+Voronoi.prototype.createBeachsection = function(site) {
+ var beachsection = this.beachsectionJunkyard.pop();
+ if (!beachsection) {
+ beachsection = new this.Beachsection();
+ }
+ beachsection.site = site;
+ return beachsection;
+ };
+
+// calculate the left break point of a particular beach section,
+// given a particular sweep line
+Voronoi.prototype.leftBreakPoint = function(arc, directrix) {
+ // http://en.wikipedia.org/wiki/Parabola
+ // http://en.wikipedia.org/wiki/Quadratic_equation
+ // h1 = x1,
+ // k1 = (y1+directrix)/2,
+ // h2 = x2,
+ // k2 = (y2+directrix)/2,
+ // p1 = k1-directrix,
+ // a1 = 1/(4*p1),
+ // b1 = -h1/(2*p1),
+ // c1 = h1*h1/(4*p1)+k1,
+ // p2 = k2-directrix,
+ // a2 = 1/(4*p2),
+ // b2 = -h2/(2*p2),
+ // c2 = h2*h2/(4*p2)+k2,
+ // x = (-(b2-b1) + Math.sqrt((b2-b1)*(b2-b1) - 4*(a2-a1)*(c2-c1))) / (2*(a2-a1))
+ // When x1 become the x-origin:
+ // h1 = 0,
+ // k1 = (y1+directrix)/2,
+ // h2 = x2-x1,
+ // k2 = (y2+directrix)/2,
+ // p1 = k1-directrix,
+ // a1 = 1/(4*p1),
+ // b1 = 0,
+ // c1 = k1,
+ // p2 = k2-directrix,
+ // a2 = 1/(4*p2),
+ // b2 = -h2/(2*p2),
+ // c2 = h2*h2/(4*p2)+k2,
+ // x = (-b2 + Math.sqrt(b2*b2 - 4*(a2-a1)*(c2-k1))) / (2*(a2-a1)) + x1
+
+ // change code below at your own risk: care has been taken to
+ // reduce errors due to computers' finite arithmetic precision.
+ // Maybe can still be improved, will see if any more of this
+ // kind of errors pop up again.
+ var site = arc.site,
+ rfocx = site.x,
+ rfocy = site.y,
+ pby2 = rfocy-directrix;
+ // parabola in degenerate case where focus is on directrix
+ if (!pby2) {
+ return rfocx;
+ }
+ var lArc = arc.rbPrevious;
+ if (!lArc) {
+ return -Infinity;
+ }
+ site = lArc.site;
+ var lfocx = site.x,
+ lfocy = site.y,
+ plby2 = lfocy-directrix;
+ // parabola in degenerate case where focus is on directrix
+ if (!plby2) {
+ return lfocx;
+ }
+ var hl = lfocx-rfocx,
+ aby2 = 1/pby2-1/plby2,
+ b = hl/plby2;
+ if (aby2) {
+ return (-b+this.sqrt(b*b-2*aby2*(hl*hl/(-2*plby2)-lfocy+plby2/2+rfocy-pby2/2)))/aby2+rfocx;
+ }
+ // both parabolas have same distance to directrix, thus break point is midway
+ return (rfocx+lfocx)/2;
+ };
+
+// calculate the right break point of a particular beach section,
+// given a particular directrix
+Voronoi.prototype.rightBreakPoint = function(arc, directrix) {
+ var rArc = arc.rbNext;
+ if (rArc) {
+ return this.leftBreakPoint(rArc, directrix);
+ }
+ var site = arc.site;
+ return site.y === directrix ? site.x : Infinity;
+ };
+
+Voronoi.prototype.detachBeachsection = function(beachsection) {
+ this.detachCircleEvent(beachsection); // detach potentially attached circle event
+ this.beachline.rbRemoveNode(beachsection); // remove from RB-tree
+ this.beachsectionJunkyard.push(beachsection); // mark for reuse
+ };
+
+Voronoi.prototype.removeBeachsection = function(beachsection) {
+ var circle = beachsection.circleEvent,
+ x = circle.x,
+ y = circle.ycenter,
+ vertex = this.createVertex(x, y),
+ previous = beachsection.rbPrevious,
+ next = beachsection.rbNext,
+ disappearingTransitions = [beachsection],
+ abs_fn = Math.abs;
+
+ // remove collapsed beachsection from beachline
+ this.detachBeachsection(beachsection);
+
+ // there could be more than one empty arc at the deletion point, this
+ // happens when more than two edges are linked by the same vertex,
+ // so we will collect all those edges by looking up both sides of
+ // the deletion point.
+ // by the way, there is *always* a predecessor/successor to any collapsed
+ // beach section, it's just impossible to have a collapsing first/last
+ // beach sections on the beachline, since they obviously are unconstrained
+ // on their left/right side.
+
+ // look left
+ var lArc = previous;
+ while (lArc.circleEvent && abs_fn(x-lArc.circleEvent.x)<1e-9 && abs_fn(y-lArc.circleEvent.ycenter)<1e-9) {
+ previous = lArc.rbPrevious;
+ disappearingTransitions.unshift(lArc);
+ this.detachBeachsection(lArc); // mark for reuse
+ lArc = previous;
+ }
+ // even though it is not disappearing, I will also add the beach section
+ // immediately to the left of the left-most collapsed beach section, for
+ // convenience, since we need to refer to it later as this beach section
+ // is the 'left' site of an edge for which a start point is set.
+ disappearingTransitions.unshift(lArc);
+ this.detachCircleEvent(lArc);
+
+ // look right
+ var rArc = next;
+ while (rArc.circleEvent && abs_fn(x-rArc.circleEvent.x)<1e-9 && abs_fn(y-rArc.circleEvent.ycenter)<1e-9) {
+ next = rArc.rbNext;
+ disappearingTransitions.push(rArc);
+ this.detachBeachsection(rArc); // mark for reuse
+ rArc = next;
+ }
+ // we also have to add the beach section immediately to the right of the
+ // right-most collapsed beach section, since there is also a disappearing
+ // transition representing an edge's start point on its left.
+ disappearingTransitions.push(rArc);
+ this.detachCircleEvent(rArc);
+
+ // walk through all the disappearing transitions between beach sections and
+ // set the start point of their (implied) edge.
+ var nArcs = disappearingTransitions.length,
+ iArc;
+ for (iArc=1; iArc<nArcs; iArc++) {
+ rArc = disappearingTransitions[iArc];
+ lArc = disappearingTransitions[iArc-1];
+ this.setEdgeStartpoint(rArc.edge, lArc.site, rArc.site, vertex);
+ }
+
+ // create a new edge as we have now a new transition between
+ // two beach sections which were previously not adjacent.
+ // since this edge appears as a new vertex is defined, the vertex
+ // actually define an end point of the edge (relative to the site
+ // on the left)
+ lArc = disappearingTransitions[0];
+ rArc = disappearingTransitions[nArcs-1];
+ rArc.edge = this.createEdge(lArc.site, rArc.site, undefined, vertex);
+
+ // create circle events if any for beach sections left in the beachline
+ // adjacent to collapsed sections
+ this.attachCircleEvent(lArc);
+ this.attachCircleEvent(rArc);
+ };
+
+Voronoi.prototype.addBeachsection = function(site) {
+ var x = site.x,
+ directrix = site.y;
+
+ // find the left and right beach sections which will surround the newly
+ // created beach section.
+ // rhill 2011-06-01: This loop is one of the most often executed,
+ // hence we expand in-place the comparison-against-epsilon calls.
+ var lArc, rArc,
+ dxl, dxr,
+ node = this.beachline.root;
+
+ while (node) {
+ dxl = this.leftBreakPoint(node,directrix)-x;
+ // x lessThanWithEpsilon xl => falls somewhere before the left edge of the beachsection
+ if (dxl > 1e-9) {
+ // this case should never happen
+ // if (!node.rbLeft) {
+ // rArc = node.rbLeft;
+ // break;
+ // }
+ node = node.rbLeft;
+ }
+ else {
+ dxr = x-this.rightBreakPoint(node,directrix);
+ // x greaterThanWithEpsilon xr => falls somewhere after the right edge of the beachsection
+ if (dxr > 1e-9) {
+ if (!node.rbRight) {
+ lArc = node;
+ break;
+ }
+ node = node.rbRight;
+ }
+ else {
+ // x equalWithEpsilon xl => falls exactly on the left edge of the beachsection
+ if (dxl > -1e-9) {
+ lArc = node.rbPrevious;
+ rArc = node;
+ }
+ // x equalWithEpsilon xr => falls exactly on the right edge of the beachsection
+ else if (dxr > -1e-9) {
+ lArc = node;
+ rArc = node.rbNext;
+ }
+ // falls exactly somewhere in the middle of the beachsection
+ else {
+ lArc = rArc = node;
+ }
+ break;
+ }
+ }
+ }
+ // at this point, keep in mind that lArc and/or rArc could be
+ // undefined or null.
+
+ // create a new beach section object for the site and add it to RB-tree
+ var newArc = this.createBeachsection(site);
+ this.beachline.rbInsertSuccessor(lArc, newArc);
+
+ // cases:
+ //
+
+ // [null,null]
+ // least likely case: new beach section is the first beach section on the
+ // beachline.
+ // This case means:
+ // no new transition appears
+ // no collapsing beach section
+ // new beachsection become root of the RB-tree
+ if (!lArc && !rArc) {
+ return;
+ }
+
+ // [lArc,rArc] where lArc == rArc
+ // most likely case: new beach section split an existing beach
+ // section.
+ // This case means:
+ // one new transition appears
+ // the left and right beach section might be collapsing as a result
+ // two new nodes added to the RB-tree
+ if (lArc === rArc) {
+ // invalidate circle event of split beach section
+ this.detachCircleEvent(lArc);
+
+ // split the beach section into two separate beach sections
+ rArc = this.createBeachsection(lArc.site);
+ this.beachline.rbInsertSuccessor(newArc, rArc);
+
+ // since we have a new transition between two beach sections,
+ // a new edge is born
+ newArc.edge = rArc.edge = this.createEdge(lArc.site, newArc.site);
+
+ // check whether the left and right beach sections are collapsing
+ // and if so create circle events, to be notified when the point of
+ // collapse is reached.
+ this.attachCircleEvent(lArc);
+ this.attachCircleEvent(rArc);
+ return;
+ }
+
+ // [lArc,null]
+ // even less likely case: new beach section is the *last* beach section
+ // on the beachline -- this can happen *only* if *all* the previous beach
+ // sections currently on the beachline share the same y value as
+ // the new beach section.
+ // This case means:
+ // one new transition appears
+ // no collapsing beach section as a result
+ // new beach section become right-most node of the RB-tree
+ if (lArc && !rArc) {
+ newArc.edge = this.createEdge(lArc.site,newArc.site);
+ return;
+ }
+
+ // [null,rArc]
+ // impossible case: because sites are strictly processed from top to bottom,
+ // and left to right, which guarantees that there will always be a beach section
+ // on the left -- except of course when there are no beach section at all on
+ // the beach line, which case was handled above.
+ // rhill 2011-06-02: No point testing in non-debug version
+ //if (!lArc && rArc) {
+ // throw "Voronoi.addBeachsection(): What is this I don't even";
+ // }
+
+ // [lArc,rArc] where lArc != rArc
+ // somewhat less likely case: new beach section falls *exactly* in between two
+ // existing beach sections
+ // This case means:
+ // one transition disappears
+ // two new transitions appear
+ // the left and right beach section might be collapsing as a result
+ // only one new node added to the RB-tree
+ if (lArc !== rArc) {
+ // invalidate circle events of left and right sites
+ this.detachCircleEvent(lArc);
+ this.detachCircleEvent(rArc);
+
+ // an existing transition disappears, meaning a vertex is defined at
+ // the disappearance point.
+ // since the disappearance is caused by the new beachsection, the
+ // vertex is at the center of the circumscribed circle of the left,
+ // new and right beachsections.
+ // http://mathforum.org/library/drmath/view/55002.html
+ // Except that I bring the origin at A to simplify
+ // calculation
+ var lSite = lArc.site,
+ ax = lSite.x,
+ ay = lSite.y,
+ bx=site.x-ax,
+ by=site.y-ay,
+ rSite = rArc.site,
+ cx=rSite.x-ax,
+ cy=rSite.y-ay,
+ d=2*(bx*cy-by*cx),
+ hb=bx*bx+by*by,
+ hc=cx*cx+cy*cy,
+ vertex = this.createVertex((cy*hb-by*hc)/d+ax, (bx*hc-cx*hb)/d+ay);
+
+ // one transition disappear
+ this.setEdgeStartpoint(rArc.edge, lSite, rSite, vertex);
+
+ // two new transitions appear at the new vertex location
+ newArc.edge = this.createEdge(lSite, site, undefined, vertex);
+ rArc.edge = this.createEdge(site, rSite, undefined, vertex);
+
+ // check whether the left and right beach sections are collapsing
+ // and if so create circle events, to handle the point of collapse.
+ this.attachCircleEvent(lArc);
+ this.attachCircleEvent(rArc);
+ return;
+ }
+ };
+
+// ---------------------------------------------------------------------------
+// Circle event methods
+
+// rhill 2011-06-07: For some reasons, performance suffers significantly
+// when instanciating a literal object instead of an empty ctor
+Voronoi.prototype.CircleEvent = function() {
+ // rhill 2013-10-12: it helps to state exactly what we are at ctor time.
+ this.arc = null;
+ this.rbLeft = null;
+ this.rbNext = null;
+ this.rbParent = null;
+ this.rbPrevious = null;
+ this.rbRed = false;
+ this.rbRight = null;
+ this.site = null;
+ this.x = this.y = this.ycenter = 0;
+ };
+
+Voronoi.prototype.attachCircleEvent = function(arc) {
+ var lArc = arc.rbPrevious,
+ rArc = arc.rbNext;
+ if (!lArc || !rArc) {return;} // does that ever happen?
+ var lSite = lArc.site,
+ cSite = arc.site,
+ rSite = rArc.site;
+
+ // If site of left beachsection is same as site of
+ // right beachsection, there can't be convergence
+ if (lSite===rSite) {return;}
+
+ // Find the circumscribed circle for the three sites associated
+ // with the beachsection triplet.
+ // rhill 2011-05-26: It is more efficient to calculate in-place
+ // rather than getting the resulting circumscribed circle from an
+ // object returned by calling Voronoi.circumcircle()
+ // http://mathforum.org/library/drmath/view/55002.html
+ // Except that I bring the origin at cSite to simplify calculations.
+ // The bottom-most part of the circumcircle is our Fortune 'circle
+ // event', and its center is a vertex potentially part of the final
+ // Voronoi diagram.
+ var bx = cSite.x,
+ by = cSite.y,
+ ax = lSite.x-bx,
+ ay = lSite.y-by,
+ cx = rSite.x-bx,
+ cy = rSite.y-by;
+
+ // If points l->c->r are clockwise, then center beach section does not
+ // collapse, hence it can't end up as a vertex (we reuse 'd' here, which
+ // sign is reverse of the orientation, hence we reverse the test.
+ // http://en.wikipedia.org/wiki/Curve_orientation#Orientation_of_a_simple_polygon
+ // rhill 2011-05-21: Nasty finite precision error which caused circumcircle() to
+ // return infinites: 1e-12 seems to fix the problem.
+ var d = 2*(ax*cy-ay*cx);
+ if (d >= -2e-12){return;}
+
+ var ha = ax*ax+ay*ay,
+ hc = cx*cx+cy*cy,
+ x = (cy*ha-ay*hc)/d,
+ y = (ax*hc-cx*ha)/d,
+ ycenter = y+by;
+
+ // Important: ybottom should always be under or at sweep, so no need
+ // to waste CPU cycles by checking
+
+ // recycle circle event object if possible
+ var circleEvent = this.circleEventJunkyard.pop();
+ if (!circleEvent) {
+ circleEvent = new this.CircleEvent();
+ }
+ circleEvent.arc = arc;
+ circleEvent.site = cSite;
+ circleEvent.x = x+bx;
+ circleEvent.y = ycenter+this.sqrt(x*x+y*y); // y bottom
+ circleEvent.ycenter = ycenter;
+ arc.circleEvent = circleEvent;
+
+ // find insertion point in RB-tree: circle events are ordered from
+ // smallest to largest
+ var predecessor = null,
+ node = this.circleEvents.root;
+ while (node) {
+ if (circleEvent.y < node.y || (circleEvent.y === node.y && circleEvent.x <= node.x)) {
+ if (node.rbLeft) {
+ node = node.rbLeft;
+ }
+ else {
+ predecessor = node.rbPrevious;
+ break;
+ }
+ }
+ else {
+ if (node.rbRight) {
+ node = node.rbRight;
+ }
+ else {
+ predecessor = node;
+ break;
+ }
+ }
+ }
+ this.circleEvents.rbInsertSuccessor(predecessor, circleEvent);
+ if (!predecessor) {
+ this.firstCircleEvent = circleEvent;
+ }
+ };
+
+Voronoi.prototype.detachCircleEvent = function(arc) {
+ var circleEvent = arc.circleEvent;
+ if (circleEvent) {
+ if (!circleEvent.rbPrevious) {
+ this.firstCircleEvent = circleEvent.rbNext;
+ }
+ this.circleEvents.rbRemoveNode(circleEvent); // remove from RB-tree
+ this.circleEventJunkyard.push(circleEvent);
+ arc.circleEvent = null;
+ }
+ };
+
+// ---------------------------------------------------------------------------
+// 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 endpoint couldn't be connected
+// true: the dangling endpoint could be connected
+Voronoi.prototype.connectEdge = function(edge, bbox) {
+ // skip if end point already connected
+ var vb = edge.vb;
+ if (!!vb) {return true;}
+
+ // make local copy for performance purpose
+ var va = edge.va,
+ xl = bbox.xl,
+ xr = bbox.xr,
+ yt = bbox.yt,
+ yb = bbox.yb,
+ lSite = edge.lSite,
+ rSite = edge.rSite,
+ lx = lSite.x,
+ ly = lSite.y,
+ rx = rSite.x,
+ ry = rSite.y,
+ fx = (lx+rx)/2,
+ fy = (ly+ry)/2,
+ fm, fb;
+
+ // 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.voronoiId].closeMe = true;
+ this.cells[rSite.voronoiId].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 (fm === undefined) {
+ // doesn't intersect with viewport
+ if (fx < xl || fx >= xr) {return false;}
+ // downward
+ if (lx > rx) {
+ if (!va || va.y < yt) {
+ va = this.createVertex(fx, yt);
+ }
+ else if (va.y >= yb) {
+ return false;
+ }
+ vb = this.createVertex(fx, yb);
+ }
+ // upward
+ else {
+ if (!va || va.y > yb) {
+ va = this.createVertex(fx, yb);
+ }
+ else if (va.y < yt) {
+ return false;
+ }
+ vb = this.createVertex(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) {
+ va = this.createVertex((yt-fb)/fm, yt);
+ }
+ else if (va.y >= yb) {
+ return false;
+ }
+ vb = this.createVertex((yb-fb)/fm, yb);
+ }
+ // upward
+ else {
+ if (!va || va.y > yb) {
+ va = this.createVertex((yb-fb)/fm, yb);
+ }
+ else if (va.y < yt) {
+ return false;
+ }
+ vb = this.createVertex((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) {
+ va = this.createVertex(xl, fm*xl+fb);
+ }
+ else if (va.x >= xr) {
+ return false;
+ }
+ vb = this.createVertex(xr, fm*xr+fb);
+ }
+ // leftward
+ else {
+ if (!va || va.x > xr) {
+ va = this.createVertex(xr, fm*xr+fb);
+ }
+ else if (va.x < xl) {
+ return false;
+ }
+ vb = this.createVertex(xl, fm*xl+fb);
+ }
+ }
+ edge.va = va;
+ edge.vb = vb;
+
+ return true;
+ };
+
+// 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
+Voronoi.prototype.clipEdge = function(edge, bbox) {
+ var ax = edge.va.x,
+ ay = edge.va.y,
+ bx = edge.vb.x,
+ by = edge.vb.y,
+ t0 = 0,
+ t1 = 1,
+ dx = bx-ax,
+ dy = by-ay;
+ // left
+ var q = ax-bbox.xl;
+ if (dx===0 && q<0) {return false;}
+ var 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.xr-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.yt;
+ 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.yb-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 = this.createVertex(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 = this.createVertex(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.voronoiId].closeMe = true;
+ this.cells[edge.rSite.voronoiId].closeMe = true;
+ }
+
+ return true;
+ };
+
+// Connect/cut edges at bounding box
+Voronoi.prototype.clipEdges = function(bbox) {
+ // connect all dangling edges to bounding box
+ // or get rid of them if it can't be done
+ var edges = this.edges,
+ iEdge = edges.length,
+ edge,
+ abs_fn = Math.abs;
+
+ // iterate backward so we can splice safely
+ while (iEdge--) {
+ edge = edges[iEdge];
+ // edge is removed if:
+ // it is wholly outside the bounding box
+ // it is looking more like a point than a line
+ if (!this.connectEdge(edge, bbox) ||
+ !this.clipEdge(edge, bbox) ||
+ (abs_fn(edge.va.x-edge.vb.x)<1e-9 && abs_fn(edge.va.y-edge.vb.y)<1e-9)) {
+ edge.va = edge.vb = null;
+ edges.splice(iEdge,1);
+ }
+ }
+ };
+
+// 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.
+Voronoi.prototype.closeCells = function(bbox) {
+ var xl = bbox.xl,
+ xr = bbox.xr,
+ yt = bbox.yt,
+ yb = bbox.yb,
+ cells = this.cells,
+ iCell = cells.length,
+ cell,
+ iLeft,
+ halfedges, nHalfedges,
+ edge,
+ va, vb, vz,
+ lastBorderSegment,
+ abs_fn = Math.abs;
+
+ while (iCell--) {
+ cell = cells[iCell];
+ // prune, order halfedges counterclockwise, then add missing ones
+ // required to close cells
+ if (!cell.prepareHalfedges()) {
+ continue;
+ }
+ if (!cell.closeMe) {
+ continue;
+ }
+ // find first 'unclosed' point.
+ // an 'unclosed' point will be the end point of a halfedge which
+ // does not match the start point of the following halfedge
+ halfedges = cell.halfedges;
+ nHalfedges = halfedges.length;
+ // special case: only one site, in which case, the viewport is the cell
+ // ...
+
+ // all other cases
+ iLeft = 0;
+ while (iLeft < nHalfedges) {
+ va = halfedges[iLeft].getEndpoint();
+ vz = halfedges[(iLeft+1) % nHalfedges].getStartpoint();
+ // if end point is not equal to start point, we need to add the missing
+ // halfedge(s) up to vz
+ if (abs_fn(va.x-vz.x)>=1e-9 || abs_fn(va.y-vz.y)>=1e-9) {
+
+ // rhill 2013-12-02:
+ // "Holes" in the halfedges are not necessarily always adjacent.
+ // https://github.com/gorhill/Javascript-Voronoi/issues/16
+
+ // find entry point:
+ switch (true) {
+
+ // walk downward along left side
+ case this.equalWithEpsilon(va.x,xl) && this.lessThanWithEpsilon(va.y,yb):
+ lastBorderSegment = this.equalWithEpsilon(vz.x,xl);
+ vb = this.createVertex(xl, lastBorderSegment ? vz.y : yb);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk rightward along bottom side
+ case this.equalWithEpsilon(va.y,yb) && this.lessThanWithEpsilon(va.x,xr):
+ lastBorderSegment = this.equalWithEpsilon(vz.y,yb);
+ vb = this.createVertex(lastBorderSegment ? vz.x : xr, yb);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk upward along right side
+ case this.equalWithEpsilon(va.x,xr) && this.greaterThanWithEpsilon(va.y,yt):
+ lastBorderSegment = this.equalWithEpsilon(vz.x,xr);
+ vb = this.createVertex(xr, lastBorderSegment ? vz.y : yt);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk leftward along top side
+ case this.equalWithEpsilon(va.y,yt) && this.greaterThanWithEpsilon(va.x,xl):
+ lastBorderSegment = this.equalWithEpsilon(vz.y,yt);
+ vb = this.createVertex(lastBorderSegment ? vz.x : xl, yt);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk downward along left side
+ lastBorderSegment = this.equalWithEpsilon(vz.x,xl);
+ vb = this.createVertex(xl, lastBorderSegment ? vz.y : yb);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk rightward along bottom side
+ lastBorderSegment = this.equalWithEpsilon(vz.y,yb);
+ vb = this.createVertex(lastBorderSegment ? vz.x : xr, yb);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ va = vb;
+ // fall through
+
+ // walk upward along right side
+ lastBorderSegment = this.equalWithEpsilon(vz.x,xr);
+ vb = this.createVertex(xr, lastBorderSegment ? vz.y : yt);
+ edge = this.createBorderEdge(cell.site, va, vb);
+ iLeft++;
+ halfedges.splice(iLeft, 0, this.createHalfedge(edge, cell.site, null));
+ nHalfedges++;
+ if ( lastBorderSegment ) { break; }
+ // fall through
+
+ default:
+ throw "Voronoi.closeCells() > this makes no sense!";
+ }
+ }
+ iLeft++;
+ }
+ cell.closeMe = false;
+ }
+ };
+
+// ---------------------------------------------------------------------------
+// Debugging helper
+/*
+Voronoi.prototype.dumpBeachline = function(y) {
+ console.log('Voronoi.dumpBeachline(%f) > Beachsections, from left to right:', y);
+ if ( !this.beachline ) {
+ console.log(' None');
+ }
+ else {
+ var bs = this.beachline.getFirst(this.beachline.root);
+ while ( bs ) {
+ console.log(' site %d: xl: %f, xr: %f', bs.site.voronoiId, this.leftBreakPoint(bs, y), this.rightBreakPoint(bs, y));
+ bs = bs.rbNext;
+ }
+ }
+ };
+*/
+
+// ---------------------------------------------------------------------------
+// Helper: Quantize sites
+
+// rhill 2013-10-12:
+// This is to solve https://github.com/gorhill/Javascript-Voronoi/issues/15
+// Since not all users will end up using the kind of coord values which would
+// cause the issue to arise, I chose to let the user decide whether or not
+// he should sanitize his coord values through this helper. This way, for
+// those users who uses coord values which are known to be fine, no overhead is
+// added.
+
+Voronoi.prototype.quantizeSites = function(sites) {
+ var ε = this.ε,
+ n = sites.length,
+ site;
+ while ( n-- ) {
+ site = sites[n];
+ site.x = Math.floor(site.x / ε) * ε;
+ site.y = Math.floor(site.y / ε) * ε;
+ }
+ };
+
+// ---------------------------------------------------------------------------
+// Helper: Recycle diagram: all vertex, edge and cell objects are
+// "surrendered" to the Voronoi object for reuse.
+// TODO: rhill-voronoi-core v2: more performance to be gained
+// when I change the semantic of what is returned.
+
+Voronoi.prototype.recycle = function(diagram) {
+ if ( diagram ) {
+ if ( diagram instanceof this.Diagram ) {
+ this.toRecycle = diagram;
+ }
+ else {
+ throw 'Voronoi.recycleDiagram() > Need a Diagram object.';
+ }
+ }
+ };
+
+// ---------------------------------------------------------------------------
+// Top-level Fortune loop
+
+// rhill 2011-05-19:
+// Voronoi sites are kept client-side now, to allow
+// user to freely modify content. At compute time,
+// *references* to sites are copied locally.
+
+Voronoi.prototype.compute = function(sites, bbox) {
+ // to measure execution time
+ var startTime = new Date();
+
+ // init internal state
+ this.reset();
+
+ // any diagram data available for recycling?
+ // I do that here so that this is included in execution time
+ if ( this.toRecycle ) {
+ this.vertexJunkyard = this.vertexJunkyard.concat(this.toRecycle.vertices);
+ this.edgeJunkyard = this.edgeJunkyard.concat(this.toRecycle.edges);
+ this.cellJunkyard = this.cellJunkyard.concat(this.toRecycle.cells);
+ this.toRecycle = null;
+ }
+
+ // Initialize site event queue
+ var siteEvents = sites.slice(0);
+ siteEvents.sort(function(a,b){
+ var r = b.y - a.y;
+ if (r) {return r;}
+ return b.x - a.x;
+ });
+
+ // process queue
+ var site = siteEvents.pop(),
+ siteid = 0,
+ xsitex, // to avoid duplicate sites
+ xsitey,
+ cells = this.cells,
+ circle;
+
+ // 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
+ 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
+ cells[siteid] = this.createCell(site);
+ site.voronoiId = 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.pop();
+ }
+
+ // remove beach section
+ else if (circle) {
+ this.removeBeachsection(circle.arc);
+ }
+
+ // all done, quit
+ else {
+ break;
+ }
+ }
+
+ // wrapping-up:
+ // connect dangling edges to bounding box
+ // cut edges as per bounding box
+ // discard edges completely outside bounding box
+ // discard edges which are point-like
+ this.clipEdges(bbox);
+
+ // add missing edges in order to close opened cells
+ this.closeCells(bbox);
+
+ // to measure execution time
+ var stopTime = new Date();
+
+ // prepare return values
+ var diagram = new this.Diagram();
+ diagram.cells = this.cells;
+ diagram.edges = this.edges;
+ diagram.vertices = this.vertices;
+ diagram.execTime = stopTime.getTime()-startTime.getTime();
+
+ // clean up
+ this.reset();
+
+ return diagram;
+ };
+
+/******************************************************************************/
+
+// stuff below here was modified by sanine
+export default Voronoi;
generated by cgit v1.2.1 (git 2.18.0) at 2024-12-22 20:07:21 +0000