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-rw-r--r--src/3rdparty/rhill-voronoi-core.js1723
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-rw-r--r--src/index.html23
-rw-r--r--src/main.js42
-rw-r--r--src/modules/Geometry.js229
-rw-r--r--src/modules/Geometry.test.js259
-rw-r--r--src/modules/Mouse.js53
-rw-r--r--src/modules/Terrain.js111
-rw-r--r--src/modules/Util.js13
-rw-r--r--src/modules/Util.test.js23
-rw-r--r--src/modules/test-assert.js21
-rw-r--r--src/package.json3
-rw-r--r--src/test.js22
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diff --git a/src/3rdparty/rhill-voronoi-core.js b/src/3rdparty/rhill-voronoi-core.js
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+++ b/src/3rdparty/rhill-voronoi-core.js
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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;
diff --git a/src/favicon.png b/src/favicon.png
new file mode 100644
index 0000000..181d8ea
--- /dev/null
+++ b/src/favicon.png
Binary files differ
diff --git a/src/index.html b/src/index.html
new file mode 100644
index 0000000..ce0739c
--- /dev/null
+++ b/src/index.html
@@ -0,0 +1,23 @@
+<!doctype html>
+<html>
+ <head>
+ <meta charset="utf-8">
+ <meta name="viewport" content="width=device.width, initial-scale=1">
+ <link rel="shortcut icon" href="favicon.png">
+ <title>bluerose</title>
+ <style>
+ body {
+ font-family: monospace;
+ background-color: #333;
+ color: white;
+ }
+ </style>
+ <script type="module" src="main.js"></script>
+ </head>
+ <body style="margin: 0; padding: 0; overflow: hidden">
+ <div id="root"></div>
+ <noscript>
+ <h1>You need Javascript enabled to use this site</h1>
+ </noscript>
+ </body>
+</html>
diff --git a/src/main.js b/src/main.js
new file mode 100644
index 0000000..ade4e27
--- /dev/null
+++ b/src/main.js
@@ -0,0 +1,42 @@
+import Voronoi from './modules/3rdparty/rhill-voronoi-core.js';
+import Terrain from './modules/Terrain.js';
+import Mouse from './modules/Mouse.js';
+
+const $ = id => document.getElementById(id)
+
+window.onload = () => {
+ let canvas = document.createElement('canvas');
+ const ct = canvas.getContext('2d');
+
+ let render;
+
+ let mouse = new Mouse(ct);
+
+ const setCanvasSize = () => {
+ canvas.setAttribute('width', window.innerWidth);
+ canvas.setAttribute('height', window.innerHeight);
+ const scale = Math.max(canvas.width, canvas.height);
+ ct.scale(scale, scale);
+ render();
+ };
+ window.addEventListener('resize', setCanvasSize);
+
+ const terrain = new Terrain();
+ render = () => {
+ ct.clearRect(0, 0, 1, 1);
+ terrain.renderGrid(ct);
+ mouse.render(ct);
+ };
+ mouse.onMove = () => {
+ terrain.applyBrush(mouse.x, mouse.y, (pt, strength) => {
+ const lerp = (a, b, theta) => ((theta-1)*a) + (theta*b);
+ pt.height = lerp(pt.height, pt.height + 10, strength);
+ }, 1, mouse.radius);
+ render();
+ }
+
+ setCanvasSize();
+
+ const root = $('root');
+ root.appendChild(canvas);
+}
diff --git a/src/modules/Geometry.js b/src/modules/Geometry.js
new file mode 100644
index 0000000..628512b
--- /dev/null
+++ b/src/modules/Geometry.js
@@ -0,0 +1,229 @@
+'use strict';
+
+/* AABB - axis-aligned bounding box */
+class AABB {
+ /* create a new AABB */
+ constructor(x, y, width, height) {
+ this.x = x; this.y = y;
+ this.width = width; this.height = height;
+ }
+
+ /* check if a point is inside the box
+ *
+ * a "point" is any object with an x- and y-coordinate.
+ * any other data in the object is ignored.
+ *
+ * returns true if the point is inside, and false otherwise.
+ */
+ contains(point) {
+ if (point.x >= this.x && point.y >= this.y
+ && point.x < this.x + this.width
+ && point.y < this.y + this.height)
+ return true;
+ return false;
+ }
+
+ /* check if two AABBs overlap */
+ intersects(aabb) {
+ const overlap = (ax, arange, bx, brange) => {
+ const range = ax < bx ? arange : brange;
+ if (Math.abs(bx - ax) < range)
+ return true;
+ return false;
+ };
+
+ if (overlap(this.x, this.width, aabb.x, aabb.width) &&
+ overlap(this.y, this.height, aabb.y, aabb.height))
+ return true;
+ return false;
+ }
+}
+
+
+/* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ *
+ * QUADTREE
+ *
+ * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ */
+
+/* lil enum class for QTNode types */
+class QTNodeType {
+ constructor(name) { this.name = name; }
+ toString() { return `QTNode.${this.name}`; }
+}
+
+
+/* nodes in a quadtree
+ *
+ * they can be either "Empty" (no point),
+ * "Leaf" (they contain a point and no sub-nodes),
+ * or "Branch" (they contain no point and have sub-nodes).
+ * There are no QTNodes with children and point data.
+ */
+class QTNode {
+ static Empty = new QTNodeType('Empty');
+ static Leaf = new QTNodeType('Leaf');
+ static Branch = new QTNodeType('Branch');
+
+ constructor(x, y, width, height) {
+ this.aabb = new AABB(x, y, width, height);
+ /* all QTNodes start empty */
+ this.type = QTNode.Empty;
+ }
+
+ /* insert a point into the tree, starting with this node
+ *
+ * as above, points are just objects with 'x' and 'y' values.
+ * other data in the point is not examined and is incorporated into the
+ * tree.
+ *
+ * this function returns false if the point was not contained in the bounding box,
+ * and true otherwise. inserting a point may cause the node's type to change
+ * (e.g. a Leaf node would become a Branch node and its point data would be
+ * moved lower in the tree).
+ */
+ insert(point) {
+ if (this.aabb.contains(point)) {
+ if (this.type == QTNode.Empty) {
+ /* empty nodes are easy -- just switch to Leaf and add the point */
+ this.type = QTNode.Leaf;
+ this.point = point;
+ return true;
+ }
+ else if (this.type == QTNode.Leaf) {
+ /* Leaf must become a Branch */
+ this.type = QTNode.Branch;
+ this.subdivide();
+
+ /* move current point into a child */
+ let result = this.insert(this.point);
+ if (!result) return false;
+ this.point = undefined;
+
+ /* add new point */
+ return this.insert(point);
+ }
+ else {
+ /* This is a Branch, and we should insert into a child node */
+ /* just try them all until we find one where the point can go */
+ if (this.subnode[0].insert(point)) return true;
+ if (this.subnode[1].insert(point)) return true;
+ if (this.subnode[2].insert(point)) return true;
+ if (this.subnode[3].insert(point)) return true;
+ return false; // something strange has happened!!
+ }
+ }
+ /* point not in this node, return false */
+ return false;
+ }
+
+ /* subdivide the node into four child nodes
+ *
+ * under normal circumstances, the user should not call this function --
+ * it's just meant to be used during insertion.
+ */
+ subdivide() {
+ /* some useful constants */
+ const x = this.aabb.x; const y = this.aabb.y;
+ const w = this.aabb.width/2; const h = this.aabb.height/2;
+
+ /* generate sub-nodes */
+ this.subnode = [
+ new QTNode(x, y, w, h),
+ new QTNode(x+w, y, w, h),
+ new QTNode(x, y+h, w, h),
+ new QTNode(x+w, y+h, w, h),
+ ];
+ }
+
+ /* query the tree for all points contained within a region recursively
+ *
+ * returns an array containing any points in the tree beneath this node
+ * that are inside the supplied AABB.
+ */
+ getPointsInRegion(aabb) {
+ if (this.type == QTNode.Empty) return [];
+ if (!this.aabb.intersects(aabb)) return [];
+ if (this.type == QTNode.Leaf) return [this.point];
+
+ /* Branch - recusively query children */
+ return [
+ ...this.subnode[0].getPointsInRegion(aabb),
+ ...this.subnode[1].getPointsInRegion(aabb),
+ ...this.subnode[2].getPointsInRegion(aabb),
+ ...this.subnode[3].getPointsInRegion(aabb),
+ ];
+ }
+}
+
+
+/* full-blown quadtree! */
+class QuadTree {
+ /* create a new quadtree */
+ constructor(width, height) {
+ this.root = new QTNode(0, 0, width, height);
+ }
+
+ /* insert a point into the tree */
+ insert(point) {
+ return this.root.insert(point);
+ }
+
+ /* get the closest tree point to the given point */
+ closest(point) {
+ /* the algorithm goes like this:
+ * 1. find the smallest node containing the point
+ * 2. the closest point is within a box at most 4x the
+ * size of that lowest node, so query all points within
+ * such a region.
+ * 3. brute-force within the list of points.
+ */
+
+ /* recursively find the node containing a point */
+ const getLeaf = (point, node) => {
+ /* is point in bounding box? */
+ if (!node.aabb.contains(point)) return null;
+ /* is this a Leaf or Empty node? */
+ if (node.type == QTNode.Empty ||
+ node.type == QTNode.Leaf) return node;
+
+ /* this is a branch node, so recurse */
+ for (let subnode of node.subnode) {
+ const leaf = getLeaf(point, subnode);
+ if (leaf !== null) return leaf;
+ }
+
+ /* should never get here */
+ return null;
+ }
+
+ /* find the node, starting at the tree root */
+ const leaf = getLeaf(point, this.root);
+ if (leaf === null) return leaf;
+
+ /* construct the 4x AABB, centered on the query point */
+ const dim = 2*Math.max(leaf.aabb.width, leaf.aabb.height);
+ const region = new AABB(point.x - dim, point.y - dim, 2*dim, 2*dim);
+
+ /* get all points */
+ const points = this.root.getPointsInRegion(region);
+
+ /* brute force search within the small list */
+ let closest = null;
+ let min_dist = 100 * this.root.aabb.width * this.root.aabb.height;
+ const dist = (a, b) => (a.x - b.x)**2 + (a.y - b.y)**2;
+ for (let pt of points) {
+ const d = dist(point, pt);
+ if (d < min_dist) {
+ closest = pt;
+ min_dist = d;
+ }
+ }
+
+ /* done! */
+ return closest;
+ }
+}
+
+export { AABB, QTNode, QuadTree };
diff --git a/src/modules/Geometry.test.js b/src/modules/Geometry.test.js
new file mode 100644
index 0000000..925a53d
--- /dev/null
+++ b/src/modules/Geometry.test.js
@@ -0,0 +1,259 @@
+import { test, assert } from './test-assert.js';
+import { AABB, QTNode, QuadTree } from './Geometry.js';
+
+const RUN_BENCHMARKS = false;
+
+
+test('AABB correctly contains/excludes points', () => {
+ const box = new AABB(0, 0, 1, 1);
+
+ // interior
+ assert.ok(box.contains({ x: 0.5, y: 0.5 }));
+
+ // upper left
+ assert.ok(!box.contains({ x: -1, y: -1 }));
+
+ // above
+ assert.ok(!box.contains({ x: 0.5, y: -1}));
+
+ // upper right
+ assert.ok(!box.contains({ x: 2, y: -1 }));
+
+ // left
+ assert.ok(!box.contains({ x: -1, y: 0.5 }));
+
+ // right
+ assert.ok(!box.contains({ x: 2, y: 0.5}));
+
+ // lower left
+ assert.ok(!box.contains({ x: -1, y: 2 }));
+
+ // below
+ assert.ok(!box.contains({ x: 0.5, y: 2}));
+
+ // lower right
+ assert.ok(!box.contains({ x: 2, y: 2 }));
+});
+
+
+test('AABB correctly intersects other AABBs', () => {
+ const box = new AABB(1, 1, 4, 4);
+
+ // interior
+ assert.ok(box.intersects(new AABB(2, 2, 2, 2,)));
+
+ // upper left
+ assert.ok(box.intersects(new AABB(0, 0, 4, 4)));
+ assert.ok(!box.intersects(new AABB(0, 0, 0.5, 0.5)));
+
+ // above
+ assert.ok(box.intersects(new AABB(2, 0, 2, 2)));
+ assert.ok(!box.intersects(new AABB(2, 0, 2, 0.5)));
+
+ // upper right
+ assert.ok(box.intersects(new AABB(2, 0, 4, 2)));
+ assert.ok(!box.intersects(new AABB(6, 0, 4, 2)));
+
+ // left
+ assert.ok(box.intersects(new AABB(0, 2, 2, 2)));
+ assert.ok(!box.intersects(new AABB(0, 2, 0.5, 2)));
+
+ // right
+ assert.ok(box.intersects(new AABB(4, 2, 2, 2)));
+ assert.ok(!box.intersects(new AABB(6, 2, 2, 2)));
+
+ // lower left
+ assert.ok(box.intersects(new AABB(0, 4, 4, 4)));
+ assert.ok(!box.intersects(new AABB(0, 6, 0.5, 0.5)));
+
+ // below
+ assert.ok(box.intersects(new AABB(2, 4, 2, 2)));
+ assert.ok(!box.intersects(new AABB(2, 6, 2, 0.5)));
+
+ // lower right
+ assert.ok(box.intersects(new AABB(2, 4, 4, 2)));
+ assert.ok(!box.intersects(new AABB(6, 6, 4, 2)));
+});
+
+
+test('AABB correctly handles points at the edges', () => {
+ const box = new AABB(0, 0, 1, 1);
+
+ assert.ok(box.contains({ x: 0, y: 0 }));
+ assert.ok(box.contains({ x: 0.5, y: 0 }));
+ assert.ok(box.contains({ x: 0, y: 0.5 }));
+
+ // bad corners
+ assert.ok(!box.contains({ x: 1, y: 0 }));
+ assert.ok(!box.contains({ x: 0, y: 1 }));
+ assert.ok(!box.contains({ x: 1, y: 1 }));
+
+ // bad edges
+ assert.ok(!box.contains({ x: 1, y: 0.5 }));
+ assert.ok(!box.contains({ x: 0.5, y: 1 }));
+});
+
+
+test('QTNode correctly inserts points', () => {
+ const node = new QTNode(0, 0, 1, 1);
+ assert.equal(node.type.toString(), 'QTNode.Empty');
+
+ let result = node.insert({ x: -1, y: -1 }); // out of range, should not insert
+ assert.ok(!result);
+ assert.equal(node.type.toString(), 'QTNode.Empty');
+
+ result = node.insert({ x: 0.5, y: 0.5 }); // in range
+ assert.ok(result);
+ assert.equal(node.type.toString(), 'QTNode.Leaf');
+ assert.deepEqual(node.point, { x: 0.5, y: 0.5 });
+});
+
+
+test('QTNode correctly subdivides', () => {
+ const node = new QTNode(0, 0, 2, 2);
+ assert.ok(!node.subnode);
+ node.subdivide();
+ assert.equal(node.subnode.length, 4);
+
+ assert.deepEqual(node.subnode[0], new QTNode(0, 0, 1, 1));
+ assert.deepEqual(node.subnode[1], new QTNode(1, 0, 1, 1));
+ assert.deepEqual(node.subnode[2], new QTNode(0, 1, 1, 1));
+ assert.deepEqual(node.subnode[3], new QTNode(1, 1, 1, 1));
+});
+
+
+test('QTNode correctly inserts multiple points', () => {
+ const node = new QTNode(0, 0, 2, 2);
+
+ const p0 = { x: 1, y: 1 };
+ const p1 = { x: 0.5, y: 0.5 };
+ const oob = { x: 10, y: 15 };
+
+ assert.ok(node.insert(p0));
+ assert.ok(node.insert(p1));
+ assert.ok(!node.insert(oob));
+
+ assert.equal(node.type.toString(), 'QTNode.Branch');
+
+ assert.equal(node.subnode[0].type.toString(), 'QTNode.Leaf');
+ assert.deepEqual(node.subnode[0].point, p1);
+
+ assert.equal(node.subnode[1].type.toString(), 'QTNode.Empty');
+ assert.equal(node.subnode[2].type.toString(), 'QTNode.Empty');
+
+ assert.equal(node.subnode[3].type.toString(), 'QTNode.Leaf');
+assert.deepEqual(node.subnode[3].point, p0);
+});
+
+
+const randomPoint = () => ({ x: Math.random(), y: Math.random() });
+
+
+test('QTNode correctly returns points in region', () => {
+ const node = new QTNode(0, 0, 1, 1);
+ let points = [];
+ for (let i=0; i<100; i++) {
+ const pt = randomPoint();
+ node.insert(pt);
+ points.push(pt);
+ }
+
+ const pointsInRegion = aabb => {
+ let pts = [];
+ for (let pt of points) {
+ if (aabb.contains(pt)) pts.push(pt);
+ }
+ return pts;
+ };
+
+ const region = new AABB(0.25, 0.25, 0.5, 0.5);
+ let bf_points = pointsInRegion(region);
+ let qt_points = node.getPointsInRegion(region);
+ const compare = (a, b) => {
+ if (a.x == b.x)
+ return b.y - a.y;
+ return b.x - a.x;
+ };
+ bf_points.sort(compare);
+ qt_points.sort(compare);
+ assert.deepEqual(bf_points, qt_points);});
+
+
+test('QuadTree correctly finds closest point for 10,000 random points', () => {
+ const tree = new QuadTree(1, 1);
+
+ let points = [];
+ for (let i=0; i<10000; i++) {
+ const pt = randomPoint();
+ tree.insert(pt);
+ points.push(pt);
+ }
+
+ const distance = (a, b) => Math.sqrt((a.x - b.x)**2 + (a.y - b.y)**2);
+ const bf_closest = a => {
+ let closest = null;
+ let min_dist = 1000;
+ for (let b of points) {
+ let d = distance(a, b);
+ if (d < min_dist) {
+ min_dist = d;
+ closest = b;
+ }
+ }
+ return closest;
+ }
+
+ for (let i=0; i<10000; i++) {
+ const pt = randomPoint();
+ assert.deepEqual(bf_closest(pt), tree.closest(pt));
+ }
+});
+
+
+function benchmark(desc, f, iterations) {
+ process.stdout.write(`${desc}: `);
+ const start = process.uptime();
+ for (let i=0; i<iterations; i++) f();
+ const elapsed = process.uptime() - start;
+ console.log(`${elapsed} seconds`);
+}
+
+const closest_benchmark = () => {
+ const n_points = 1e5;
+ const iterations = 1e4;
+ console.log(`> benchmark get closest of ${n_points} random points ${iterations} times`);
+
+ const tree = new QuadTree(1, 1);
+ let points = [];
+ for (let i=0; i<n_points; i++) {
+ const pt = randomPoint();
+ tree.insert(pt);
+ points.push(pt);
+ }
+
+ const distance = (a, b) => Math.sqrt((a.x - b.x)**2 + (a.y - b.y)**2);
+ const bf_closest = a => {
+ let closest = null;
+ let min_dist = 1000;
+ for (let b of points) {
+ let d = distance(a, b);
+ if (d < min_dist) {
+ min_dist = d;
+ closest = b;
+ }
+ }
+ return closest;
+ }
+
+ benchmark('\tbrute force', () => {
+ const pt = randomPoint();
+ bf_closest(pt);
+ }, iterations);
+
+ benchmark('\tquadtree', () => {
+ const pt = randomPoint();
+ tree.closest(pt);
+ }, iterations);
+}
+if (RUN_BENCHMARKS)
+ closest_benchmark();
diff --git a/src/modules/Mouse.js b/src/modules/Mouse.js
new file mode 100644
index 0000000..0b8f922
--- /dev/null
+++ b/src/modules/Mouse.js
@@ -0,0 +1,53 @@
+class Mouse {
+ constructor(ct) {
+ this.ct = ct;
+ this.x = 0;
+ this.y = 0;
+ this.radius = 0.005;
+ this.show = false;
+ this.pressed = false;
+ this.onMove = null;
+
+ window.addEventListener('mousemove', e => {
+ /* get current transform matrix */
+ const matrix = this.ct.getTransform();
+ matrix.invertSelf();
+
+ const x = e.offsetX; const y = e.offsetY;
+ this.x = matrix.a*x + matrix.b*y;
+ this.y = matrix.c*x + matrix.d*y;
+
+ if (this.onMove) this.onMove();
+ });
+
+ const root = document.getElementById('root');
+
+ root.addEventListener('mouseover', e => {
+ e = e ? e : window.event;
+ this.show = true;
+ });
+
+ root.addEventListener('mouseout', e => {
+ e = e ? e: window.event;
+ this.show = false;
+ });
+ }
+
+ render(ct) {
+ if (!this.show) return;
+ console.log(this.radius);
+ ct.save();
+
+ ct.strokeStyle = '#fff';
+
+ ct.beginPath();
+ ct.arc(this.x, this.y, this.radius, 0, 2*Math.PI);
+ ct.closePath();
+ ct.stroke();
+
+ ct.restore();
+ }
+}
+
+
+export default Mouse;
diff --git a/src/modules/Terrain.js b/src/modules/Terrain.js
new file mode 100644
index 0000000..21908ac
--- /dev/null
+++ b/src/modules/Terrain.js
@@ -0,0 +1,111 @@
+'use strict';
+
+import Voronoi from './3rdparty/rhill-voronoi-core.js';
+
+import { useAverage } from './Util.js';
+import { AABB, QuadTree } from './Geometry.js';
+
+
+/* from here on up, we always assume that points live in the range [(0,0), (1,1)) */
+
+function lloydRelax(point_set, density) {
+ /* setup quadtree and averages */
+ let tree = new QuadTree(1,1);
+ let averages = {};
+ for (let i=0; i<point_set.length; i++) {
+ const point = point_set[i];
+ point.index = i;
+ tree.insert(point);
+
+ let [avg, append] = useAverage();
+ const cent_x = { avg, append };
+ [avg, append] = useAverage();
+ const cent_y = { avg, append };
+ averages[i] = { cent_x, cent_y };
+ }
+
+ /* compute average centroids */
+ for (let x=0; x<1; x += 1/density) {
+ for (let y=0; y<1; y += 1/density) {
+ const point = { x, y };
+ const closest = tree.closest(point);
+ const { cent_x, cent_y } = averages[closest.index];
+ cent_x.append(point.x);
+ cent_y.append(point.y);
+ }
+ }
+
+ /* return centroid points */
+ const result = [];
+ for (let i=0; i<point_set.length; i++) {
+ const point = { x: averages[i].cent_x.avg(), y: averages[i].cent_y.avg() };
+ result.push(point);
+ }
+ return result;
+}
+
+
+class Terrain {
+ constructor() {
+ const N_SEED_POINTS = 2**12;
+ const N_RELAX_ITERATIONS = 1;
+ const RELAX_DENSITY = 400;
+ const randomPoint = () => ({x: Math.random(), y: Math.random()});
+
+ this.min_height = 0;
+ this.max_height = 0;
+
+ let seed_points = [];
+ for (let i=0; i<N_SEED_POINTS; i++) seed_points.push(randomPoint());
+
+ for (let i=0; i<N_RELAX_ITERATIONS; i++)
+ lloydRelax(seed_points, RELAX_DENSITY);
+
+ const v = new Voronoi();
+ this.graph = v.compute(seed_points, {xl: 0, xr: 1, yt: 0, yb: 1});
+
+ this.tree = new QuadTree(1,1);
+ for (let v of this.graph.vertices) {
+ v.height = 0;
+ this.tree.insert(v);
+ }
+ }
+
+
+ applyBrush(x, y, f, strength, radius) {
+ const region = new AABB(x-radius, y-radius, 2*radius, 2*radius);
+ const points = this.tree.root.getPointsInRegion(region);
+
+ const dist2 = (a, b) => (a.x - b.x)**2 + (a.y - b.y)**2;
+
+ const sigma = radius/3;
+ const beta = 1/(2*sigma*sigma);
+ const center = { x, y };
+ const power = pt => Math.exp(-beta * dist2(pt, center));
+
+ for (let pt of points) f(pt, strength * power(pt));
+ }
+
+
+ renderGrid(ct) {
+ ct.save();
+ ct.lineWidth = 0.001;
+ for (let edge of this.graph.edges) {
+ ct.fillStyle = `hsl(${edge.va.height}, 100%, 50%)`;
+ ct.beginPath();
+ ct.arc(edge.va.x, edge.va.y, 0.005, 0, 2*Math.PI);
+ ct.closePath();
+ ct.fill();
+
+ ct.beginPath();
+ ct.moveTo(edge.va.x, edge.va.y);
+ ct.lineTo(edge.vb.x, edge.vb.y);
+ ct.closePath();
+ ct.stroke();
+ }
+ ct.restore();
+ }
+}
+
+export { lloydRelax };
+export default Terrain;
diff --git a/src/modules/Util.js b/src/modules/Util.js
new file mode 100644
index 0000000..cbe466d
--- /dev/null
+++ b/src/modules/Util.js
@@ -0,0 +1,13 @@
+function useAverage() {
+ var avg = 0;
+ let weight = 0;
+ const append = value => {
+ avg = (weight * avg) + value;
+ weight += 1;
+ avg = avg/weight;
+ }
+
+ return [() => avg, append];
+}
+
+export { useAverage };
diff --git a/src/modules/Util.test.js b/src/modules/Util.test.js
new file mode 100644
index 0000000..000d54e
--- /dev/null
+++ b/src/modules/Util.test.js
@@ -0,0 +1,23 @@
+import { test, assert} from './test-assert.js';
+import { useAverage } from './Util.js';
+
+
+test('Average correctly accumulates an average', () => {
+ let [avg, avg_append] = useAverage();
+ let data = [];
+ for (let i=0; i<5000; i++) {
+ let d = Math.random();
+ data.push(d);
+ avg_append(d);
+ }
+
+ let manual_average = 0;
+ for (let d of data) manual_average += d;
+ manual_average /= data.length;
+
+ const precision = (decimalPlaces, num) => {
+ const theta = 10**decimalPlaces;
+ return Math.floor(num * theta) / theta;
+ };
+ assert.equal(precision(5, avg()), precision(5, manual_average));
+});
diff --git a/src/modules/test-assert.js b/src/modules/test-assert.js
new file mode 100644
index 0000000..7be2989
--- /dev/null
+++ b/src/modules/test-assert.js
@@ -0,0 +1,21 @@
+import { strict as assert } from 'node:assert';
+
+function test(description, func)
+{
+ process.stdout.write(description);
+ let error = null;
+ try {
+ func();
+ }
+ catch(err) {
+ error = err;
+ }
+
+ if (error) {
+ console.log(' - FAIL');
+ console.log(error);
+ }
+ else console.log(' - OK');
+}
+
+export { test, assert };
diff --git a/src/package.json b/src/package.json
new file mode 100644
index 0000000..bedb411
--- /dev/null
+++ b/src/package.json
@@ -0,0 +1,3 @@
+{
+ "type": "module"
+}
diff --git a/src/test.js b/src/test.js
new file mode 100644
index 0000000..6a92978
--- /dev/null
+++ b/src/test.js
@@ -0,0 +1,22 @@
+import fs from 'node:fs';
+import { execSync } from 'node:child_process';
+
+function recursiveScanDir(path, f)
+{
+ let dirs = [];
+ for (let dirent of fs.readdirSync(path, { withFileTypes: true })) {
+ if (dirent.isDirectory()) dirs.push(`${path}/${dirent.name}`);
+ else f(`${path}/${dirent.name}`);
+ }
+ for (let dir of dirs) {
+ recursiveScanDir(dir, f);
+ }
+}
+
+recursiveScanDir('.', fname => {
+ if (fname.endsWith('.test.js')) {
+ console.log(`======== ${fname} ========`);
+ execSync(`node ${fname}`, { stdio: 'inherit' });
+ console.log('');
+ }
+});
generated by cgit v1.2.1 (git 2.18.0) at 2024-12-23 01:29:20 +0000