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-/*!
-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 2024-11-15 04:44:01 +0000