diff options
Diffstat (limited to 'web/pw-visualizer/src/voronoi/voronoi-core.js')
| -rw-r--r-- | web/pw-visualizer/src/voronoi/voronoi-core.js | 1726 |
1 files changed, 1726 insertions, 0 deletions
diff --git a/web/pw-visualizer/src/voronoi/voronoi-core.js b/web/pw-visualizer/src/voronoi/voronoi-core.js new file mode 100644 index 0000000..9dcc5b3 --- /dev/null +++ b/web/pw-visualizer/src/voronoi/voronoi-core.js @@ -0,0 +1,1726 @@ +/*! +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; + }; + +/******************************************************************************/ + +if ( typeof module !== 'undefined' ) { + module.exports = Voronoi; +} + +export default Voronoi; |