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+/* d3.geom.js - Data Driven Documents
+ * Version: 2.6.1
+ * Homepage: http://mbostock.github.com/d3/
+ * Copyright: 2010, Michael Bostock
+ * Licence: 3-Clause BSD
+ *
+ * Copyright (c) 2010, Michael Bostock
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * * Redistributions of source code must retain the above copyright notice, this
+ * list of conditions and the following disclaimer.
+ *
+ * * Redistributions in binary form must reproduce the above copyright notice,
+ * this list of conditions and the following disclaimer in the documentation
+ * and/or other materials provided with the distribution.
+ *
+ * * The name Michael Bostock may not be used to endorse or promote products
+ * derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+ * DISCLAIMED. IN NO EVENT SHALL MICHAEL BOSTOCK BE LIABLE FOR ANY DIRECT,
+ * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+ * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
+ * EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+(function(){d3.geom = {};
+/**
+ * Computes a contour for a given input grid function using the <a
+ * href="http://en.wikipedia.org/wiki/Marching_squares">marching
+ * squares</a> algorithm. Returns the contour polygon as an array of points.
+ *
+ * @param grid a two-input function(x, y) that returns true for values
+ * inside the contour and false for values outside the contour.
+ * @param start an optional starting point [x, y] on the grid.
+ * @returns polygon [[x1, y1], [x2, y2], …]
+ */
+d3.geom.contour = function(grid, start) {
+ var s = start || d3_geom_contourStart(grid), // starting point
+ c = [], // contour polygon
+ x = s[0], // current x position
+ y = s[1], // current y position
+ dx = 0, // next x direction
+ dy = 0, // next y direction
+ pdx = NaN, // previous x direction
+ pdy = NaN, // previous y direction
+ i = 0;
+
+ do {
+ // determine marching squares index
+ i = 0;
+ if (grid(x-1, y-1)) i += 1;
+ if (grid(x, y-1)) i += 2;
+ if (grid(x-1, y )) i += 4;
+ if (grid(x, y )) i += 8;
+
+ // determine next direction
+ if (i === 6) {
+ dx = pdy === -1 ? -1 : 1;
+ dy = 0;
+ } else if (i === 9) {
+ dx = 0;
+ dy = pdx === 1 ? -1 : 1;
+ } else {
+ dx = d3_geom_contourDx[i];
+ dy = d3_geom_contourDy[i];
+ }
+
+ // update contour polygon
+ if (dx != pdx && dy != pdy) {
+ c.push([x, y]);
+ pdx = dx;
+ pdy = dy;
+ }
+
+ x += dx;
+ y += dy;
+ } while (s[0] != x || s[1] != y);
+
+ return c;
+};
+
+// lookup tables for marching directions
+var d3_geom_contourDx = [1, 0, 1, 1,-1, 0,-1, 1,0, 0,0,0,-1, 0,-1,NaN],
+ d3_geom_contourDy = [0,-1, 0, 0, 0,-1, 0, 0,1,-1,1,1, 0,-1, 0,NaN];
+
+function d3_geom_contourStart(grid) {
+ var x = 0,
+ y = 0;
+
+ // search for a starting point; begin at origin
+ // and proceed along outward-expanding diagonals
+ while (true) {
+ if (grid(x,y)) {
+ return [x,y];
+ }
+ if (x === 0) {
+ x = y + 1;
+ y = 0;
+ } else {
+ x = x - 1;
+ y = y + 1;
+ }
+ }
+}
+/**
+ * Computes the 2D convex hull of a set of points using Graham's scanning
+ * algorithm. The algorithm has been implemented as described in Cormen,
+ * Leiserson, and Rivest's Introduction to Algorithms. The running time of
+ * this algorithm is O(n log n), where n is the number of input points.
+ *
+ * @param vertices [[x1, y1], [x2, y2], …]
+ * @returns polygon [[x1, y1], [x2, y2], …]
+ */
+d3.geom.hull = function(vertices) {
+ if (vertices.length < 3) return [];
+
+ var len = vertices.length,
+ plen = len - 1,
+ points = [],
+ stack = [],
+ i, j, h = 0, x1, y1, x2, y2, u, v, a, sp;
+
+ // find the starting ref point: leftmost point with the minimum y coord
+ for (i=1; i<len; ++i) {
+ if (vertices[i][1] < vertices[h][1]) {
+ h = i;
+ } else if (vertices[i][1] == vertices[h][1]) {
+ h = (vertices[i][0] < vertices[h][0] ? i : h);
+ }
+ }
+
+ // calculate polar angles from ref point and sort
+ for (i=0; i<len; ++i) {
+ if (i === h) continue;
+ y1 = vertices[i][1] - vertices[h][1];
+ x1 = vertices[i][0] - vertices[h][0];
+ points.push({angle: Math.atan2(y1, x1), index: i});
+ }
+ points.sort(function(a, b) { return a.angle - b.angle; });
+
+ // toss out duplicate angles
+ a = points[0].angle;
+ v = points[0].index;
+ u = 0;
+ for (i=1; i<plen; ++i) {
+ j = points[i].index;
+ if (a == points[i].angle) {
+ // keep angle for point most distant from the reference
+ x1 = vertices[v][0] - vertices[h][0];
+ y1 = vertices[v][1] - vertices[h][1];
+ x2 = vertices[j][0] - vertices[h][0];
+ y2 = vertices[j][1] - vertices[h][1];
+ if ((x1*x1 + y1*y1) >= (x2*x2 + y2*y2)) {
+ points[i].index = -1;
+ } else {
+ points[u].index = -1;
+ a = points[i].angle;
+ u = i;
+ v = j;
+ }
+ } else {
+ a = points[i].angle;
+ u = i;
+ v = j;
+ }
+ }
+
+ // initialize the stack
+ stack.push(h);
+ for (i=0, j=0; i<2; ++j) {
+ if (points[j].index !== -1) {
+ stack.push(points[j].index);
+ i++;
+ }
+ }
+ sp = stack.length;
+
+ // do graham's scan
+ for (; j<plen; ++j) {
+ if (points[j].index === -1) continue; // skip tossed out points
+ while (!d3_geom_hullCCW(stack[sp-2], stack[sp-1], points[j].index, vertices)) {
+ --sp;
+ }
+ stack[sp++] = points[j].index;
+ }
+
+ // construct the hull
+ var poly = [];
+ for (i=0; i<sp; ++i) {
+ poly.push(vertices[stack[i]]);
+ }
+ return poly;
+}
+
+// are three points in counter-clockwise order?
+function d3_geom_hullCCW(i1, i2, i3, v) {
+ var t, a, b, c, d, e, f;
+ t = v[i1]; a = t[0]; b = t[1];
+ t = v[i2]; c = t[0]; d = t[1];
+ t = v[i3]; e = t[0]; f = t[1];
+ return ((f-b)*(c-a) - (d-b)*(e-a)) > 0;
+}
+// Note: requires coordinates to be counterclockwise and convex!
+d3.geom.polygon = function(coordinates) {
+
+ coordinates.area = function() {
+ var i = 0,
+ n = coordinates.length,
+ a = coordinates[n - 1][0] * coordinates[0][1],
+ b = coordinates[n - 1][1] * coordinates[0][0];
+ while (++i < n) {
+ a += coordinates[i - 1][0] * coordinates[i][1];
+ b += coordinates[i - 1][1] * coordinates[i][0];
+ }
+ return (b - a) * .5;
+ };
+
+ coordinates.centroid = function(k) {
+ var i = -1,
+ n = coordinates.length - 1,
+ x = 0,
+ y = 0,
+ a,
+ b,
+ c;
+ if (!arguments.length) k = -1 / (6 * coordinates.area());
+ while (++i < n) {
+ a = coordinates[i];
+ b = coordinates[i + 1];
+ c = a[0] * b[1] - b[0] * a[1];
+ x += (a[0] + b[0]) * c;
+ y += (a[1] + b[1]) * c;
+ }
+ return [x * k, y * k];
+ };
+
+ // The Sutherland-Hodgman clipping algorithm.
+ coordinates.clip = function(subject) {
+ var input,
+ i = -1,
+ n = coordinates.length,
+ j,
+ m,
+ a = coordinates[n - 1],
+ b,
+ c,
+ d;
+ while (++i < n) {
+ input = subject.slice();
+ subject.length = 0;
+ b = coordinates[i];
+ c = input[(m = input.length) - 1];
+ j = -1;
+ while (++j < m) {
+ d = input[j];
+ if (d3_geom_polygonInside(d, a, b)) {
+ if (!d3_geom_polygonInside(c, a, b)) {
+ subject.push(d3_geom_polygonIntersect(c, d, a, b));
+ }
+ subject.push(d);
+ } else if (d3_geom_polygonInside(c, a, b)) {
+ subject.push(d3_geom_polygonIntersect(c, d, a, b));
+ }
+ c = d;
+ }
+ a = b;
+ }
+ return subject;
+ };
+
+ return coordinates;
+};
+
+function d3_geom_polygonInside(p, a, b) {
+ return (b[0] - a[0]) * (p[1] - a[1]) < (b[1] - a[1]) * (p[0] - a[0]);
+}
+
+// Intersect two infinite lines cd and ab.
+function d3_geom_polygonIntersect(c, d, a, b) {
+ var x1 = c[0], x2 = d[0], x3 = a[0], x4 = b[0],
+ y1 = c[1], y2 = d[1], y3 = a[1], y4 = b[1],
+ x13 = x1 - x3,
+ x21 = x2 - x1,
+ x43 = x4 - x3,
+ y13 = y1 - y3,
+ y21 = y2 - y1,
+ y43 = y4 - y3,
+ ua = (x43 * y13 - y43 * x13) / (y43 * x21 - x43 * y21);
+ return [x1 + ua * x21, y1 + ua * y21];
+}
+// Adapted from Nicolas Garcia Belmonte's JIT implementation:
+// http://blog.thejit.org/2010/02/12/voronoi-tessellation/
+// http://blog.thejit.org/assets/voronoijs/voronoi.js
+// See lib/jit/LICENSE for details.
+
+// Notes:
+//
+// This implementation does not clip the returned polygons, so if you want to
+// clip them to a particular shape you will need to do that either in SVG or by
+// post-processing with d3.geom.polygon's clip method.
+//
+// If any vertices are coincident or have NaN positions, the behavior of this
+// method is undefined. Most likely invalid polygons will be returned. You
+// should filter invalid points, and consolidate coincident points, before
+// computing the tessellation.
+
+/**
+ * @param vertices [[x1, y1], [x2, y2], …]
+ * @returns polygons [[[x1, y1], [x2, y2], …], …]
+ */
+d3.geom.voronoi = function(vertices) {
+ var polygons = vertices.map(function() { return []; });
+
+ d3_voronoi_tessellate(vertices, function(e) {
+ var s1,
+ s2,
+ x1,
+ x2,
+ y1,
+ y2;
+ if (e.a === 1 && e.b >= 0) {
+ s1 = e.ep.r;
+ s2 = e.ep.l;
+ } else {
+ s1 = e.ep.l;
+ s2 = e.ep.r;
+ }
+ if (e.a === 1) {
+ y1 = s1 ? s1.y : -1e6;
+ x1 = e.c - e.b * y1;
+ y2 = s2 ? s2.y : 1e6;
+ x2 = e.c - e.b * y2;
+ } else {
+ x1 = s1 ? s1.x : -1e6;
+ y1 = e.c - e.a * x1;
+ x2 = s2 ? s2.x : 1e6;
+ y2 = e.c - e.a * x2;
+ }
+ var v1 = [x1, y1],
+ v2 = [x2, y2];
+ polygons[e.region.l.index].push(v1, v2);
+ polygons[e.region.r.index].push(v1, v2);
+ });
+
+ // Reconnect the polygon segments into counterclockwise loops.
+ return polygons.map(function(polygon, i) {
+ var cx = vertices[i][0],
+ cy = vertices[i][1];
+ polygon.forEach(function(v) {
+ v.angle = Math.atan2(v[0] - cx, v[1] - cy);
+ });
+ return polygon.sort(function(a, b) {
+ return a.angle - b.angle;
+ }).filter(function(d, i) {
+ return !i || (d.angle - polygon[i - 1].angle > 1e-10);
+ });
+ });
+};
+
+var d3_voronoi_opposite = {"l": "r", "r": "l"};
+
+function d3_voronoi_tessellate(vertices, callback) {
+
+ var Sites = {
+ list: vertices
+ .map(function(v, i) {
+ return {
+ index: i,
+ x: v[0],
+ y: v[1]
+ };
+ })
+ .sort(function(a, b) {
+ return a.y < b.y ? -1
+ : a.y > b.y ? 1
+ : a.x < b.x ? -1
+ : a.x > b.x ? 1
+ : 0;
+ }),
+ bottomSite: null
+ };
+
+ var EdgeList = {
+ list: [],
+ leftEnd: null,
+ rightEnd: null,
+
+ init: function() {
+ EdgeList.leftEnd = EdgeList.createHalfEdge(null, "l");
+ EdgeList.rightEnd = EdgeList.createHalfEdge(null, "l");
+ EdgeList.leftEnd.r = EdgeList.rightEnd;
+ EdgeList.rightEnd.l = EdgeList.leftEnd;
+ EdgeList.list.unshift(EdgeList.leftEnd, EdgeList.rightEnd);
+ },
+
+ createHalfEdge: function(edge, side) {
+ return {
+ edge: edge,
+ side: side,
+ vertex: null,
+ "l": null,
+ "r": null
+ };
+ },
+
+ insert: function(lb, he) {
+ he.l = lb;
+ he.r = lb.r;
+ lb.r.l = he;
+ lb.r = he;
+ },
+
+ leftBound: function(p) {
+ var he = EdgeList.leftEnd;
+ do {
+ he = he.r;
+ } while (he != EdgeList.rightEnd && Geom.rightOf(he, p));
+ he = he.l;
+ return he;
+ },
+
+ del: function(he) {
+ he.l.r = he.r;
+ he.r.l = he.l;
+ he.edge = null;
+ },
+
+ right: function(he) {
+ return he.r;
+ },
+
+ left: function(he) {
+ return he.l;
+ },
+
+ leftRegion: function(he) {
+ return he.edge == null
+ ? Sites.bottomSite
+ : he.edge.region[he.side];
+ },
+
+ rightRegion: function(he) {
+ return he.edge == null
+ ? Sites.bottomSite
+ : he.edge.region[d3_voronoi_opposite[he.side]];
+ }
+ };
+
+ var Geom = {
+
+ bisect: function(s1, s2) {
+ var newEdge = {
+ region: {"l": s1, "r": s2},
+ ep: {"l": null, "r": null}
+ };
+
+ var dx = s2.x - s1.x,
+ dy = s2.y - s1.y,
+ adx = dx > 0 ? dx : -dx,
+ ady = dy > 0 ? dy : -dy;
+
+ newEdge.c = s1.x * dx + s1.y * dy
+ + (dx * dx + dy * dy) * .5;
+
+ if (adx > ady) {
+ newEdge.a = 1;
+ newEdge.b = dy / dx;
+ newEdge.c /= dx;
+ } else {
+ newEdge.b = 1;
+ newEdge.a = dx / dy;
+ newEdge.c /= dy;
+ }
+
+ return newEdge;
+ },
+
+ intersect: function(el1, el2) {
+ var e1 = el1.edge,
+ e2 = el2.edge;
+ if (!e1 || !e2 || (e1.region.r == e2.region.r)) {
+ return null;
+ }
+ var d = (e1.a * e2.b) - (e1.b * e2.a);
+ if (Math.abs(d) < 1e-10) {
+ return null;
+ }
+ var xint = (e1.c * e2.b - e2.c * e1.b) / d,
+ yint = (e2.c * e1.a - e1.c * e2.a) / d,
+ e1r = e1.region.r,
+ e2r = e2.region.r,
+ el,
+ e;
+ if ((e1r.y < e2r.y) ||
+ (e1r.y == e2r.y && e1r.x < e2r.x)) {
+ el = el1;
+ e = e1;
+ } else {
+ el = el2;
+ e = e2;
+ }
+ var rightOfSite = (xint >= e.region.r.x);
+ if ((rightOfSite && (el.side === "l")) ||
+ (!rightOfSite && (el.side === "r"))) {
+ return null;
+ }
+ return {
+ x: xint,
+ y: yint
+ };
+ },
+
+ rightOf: function(he, p) {
+ var e = he.edge,
+ topsite = e.region.r,
+ rightOfSite = (p.x > topsite.x);
+
+ if (rightOfSite && (he.side === "l")) {
+ return 1;
+ }
+ if (!rightOfSite && (he.side === "r")) {
+ return 0;
+ }
+ if (e.a === 1) {
+ var dyp = p.y - topsite.y,
+ dxp = p.x - topsite.x,
+ fast = 0,
+ above = 0;
+
+ if ((!rightOfSite && (e.b < 0)) ||
+ (rightOfSite && (e.b >= 0))) {
+ above = fast = (dyp >= e.b * dxp);
+ } else {
+ above = ((p.x + p.y * e.b) > e.c);
+ if (e.b < 0) {
+ above = !above;
+ }
+ if (!above) {
+ fast = 1;
+ }
+ }
+ if (!fast) {
+ var dxs = topsite.x - e.region.l.x;
+ above = (e.b * (dxp * dxp - dyp * dyp)) <
+ (dxs * dyp * (1 + 2 * dxp / dxs + e.b * e.b));
+
+ if (e.b < 0) {
+ above = !above;
+ }
+ }
+ } else /* e.b == 1 */ {
+ var yl = e.c - e.a * p.x,
+ t1 = p.y - yl,
+ t2 = p.x - topsite.x,
+ t3 = yl - topsite.y;
+
+ above = (t1 * t1) > (t2 * t2 + t3 * t3);
+ }
+ return he.side === "l" ? above : !above;
+ },
+
+ endPoint: function(edge, side, site) {
+ edge.ep[side] = site;
+ if (!edge.ep[d3_voronoi_opposite[side]]) return;
+ callback(edge);
+ },
+
+ distance: function(s, t) {
+ var dx = s.x - t.x,
+ dy = s.y - t.y;
+ return Math.sqrt(dx * dx + dy * dy);
+ }
+ };
+
+ var EventQueue = {
+ list: [],
+
+ insert: function(he, site, offset) {
+ he.vertex = site;
+ he.ystar = site.y + offset;
+ for (var i=0, list=EventQueue.list, l=list.length; i<l; i++) {
+ var next = list[i];
+ if (he.ystar > next.ystar ||
+ (he.ystar == next.ystar &&
+ site.x > next.vertex.x)) {
+ continue;
+ } else {
+ break;
+ }
+ }
+ list.splice(i, 0, he);
+ },
+
+ del: function(he) {
+ for (var i=0, ls=EventQueue.list, l=ls.length; i<l && (ls[i] != he); ++i) {}
+ ls.splice(i, 1);
+ },
+
+ empty: function() { return EventQueue.list.length === 0; },
+
+ nextEvent: function(he) {
+ for (var i=0, ls=EventQueue.list, l=ls.length; i<l; ++i) {
+ if (ls[i] == he) return ls[i+1];
+ }
+ return null;
+ },
+
+ min: function() {
+ var elem = EventQueue.list[0];
+ return {
+ x: elem.vertex.x,
+ y: elem.ystar
+ };
+ },
+
+ extractMin: function() {
+ return EventQueue.list.shift();
+ }
+ };
+
+ EdgeList.init();
+ Sites.bottomSite = Sites.list.shift();
+
+ var newSite = Sites.list.shift(), newIntStar;
+ var lbnd, rbnd, llbnd, rrbnd, bisector;
+ var bot, top, temp, p, v;
+ var e, pm;
+
+ while (true) {
+ if (!EventQueue.empty()) {
+ newIntStar = EventQueue.min();
+ }
+ if (newSite && (EventQueue.empty()
+ || newSite.y < newIntStar.y
+ || (newSite.y == newIntStar.y
+ && newSite.x < newIntStar.x))) { //new site is smallest
+ lbnd = EdgeList.leftBound(newSite);
+ rbnd = EdgeList.right(lbnd);
+ bot = EdgeList.rightRegion(lbnd);
+ e = Geom.bisect(bot, newSite);
+ bisector = EdgeList.createHalfEdge(e, "l");
+ EdgeList.insert(lbnd, bisector);
+ p = Geom.intersect(lbnd, bisector);
+ if (p) {
+ EventQueue.del(lbnd);
+ EventQueue.insert(lbnd, p, Geom.distance(p, newSite));
+ }
+ lbnd = bisector;
+ bisector = EdgeList.createHalfEdge(e, "r");
+ EdgeList.insert(lbnd, bisector);
+ p = Geom.intersect(bisector, rbnd);
+ if (p) {
+ EventQueue.insert(bisector, p, Geom.distance(p, newSite));
+ }
+ newSite = Sites.list.shift();
+ } else if (!EventQueue.empty()) { //intersection is smallest
+ lbnd = EventQueue.extractMin();
+ llbnd = EdgeList.left(lbnd);
+ rbnd = EdgeList.right(lbnd);
+ rrbnd = EdgeList.right(rbnd);
+ bot = EdgeList.leftRegion(lbnd);
+ top = EdgeList.rightRegion(rbnd);
+ v = lbnd.vertex;
+ Geom.endPoint(lbnd.edge, lbnd.side, v);
+ Geom.endPoint(rbnd.edge, rbnd.side, v);
+ EdgeList.del(lbnd);
+ EventQueue.del(rbnd);
+ EdgeList.del(rbnd);
+ pm = "l";
+ if (bot.y > top.y) {
+ temp = bot;
+ bot = top;
+ top = temp;
+ pm = "r";
+ }
+ e = Geom.bisect(bot, top);
+ bisector = EdgeList.createHalfEdge(e, pm);
+ EdgeList.insert(llbnd, bisector);
+ Geom.endPoint(e, d3_voronoi_opposite[pm], v);
+ p = Geom.intersect(llbnd, bisector);
+ if (p) {
+ EventQueue.del(llbnd);
+ EventQueue.insert(llbnd, p, Geom.distance(p, bot));
+ }
+ p = Geom.intersect(bisector, rrbnd);
+ if (p) {
+ EventQueue.insert(bisector, p, Geom.distance(p, bot));
+ }
+ } else {
+ break;
+ }
+ }//end while
+
+ for (lbnd = EdgeList.right(EdgeList.leftEnd);
+ lbnd != EdgeList.rightEnd;
+ lbnd = EdgeList.right(lbnd)) {
+ callback(lbnd.edge);
+ }
+}
+/**
+* @param vertices [[x1, y1], [x2, y2], …]
+* @returns triangles [[[x1, y1], [x2, y2], [x3, y3]], …]
+ */
+d3.geom.delaunay = function(vertices) {
+ var edges = vertices.map(function() { return []; }),
+ triangles = [];
+
+ // Use the Voronoi tessellation to determine Delaunay edges.
+ d3_voronoi_tessellate(vertices, function(e) {
+ edges[e.region.l.index].push(vertices[e.region.r.index]);
+ });
+
+ // Reconnect the edges into counterclockwise triangles.
+ edges.forEach(function(edge, i) {
+ var v = vertices[i],
+ cx = v[0],
+ cy = v[1];
+ edge.forEach(function(v) {
+ v.angle = Math.atan2(v[0] - cx, v[1] - cy);
+ });
+ edge.sort(function(a, b) {
+ return a.angle - b.angle;
+ });
+ for (var j = 0, m = edge.length - 1; j < m; j++) {
+ triangles.push([v, edge[j], edge[j + 1]]);
+ }
+ });
+
+ return triangles;
+};
+// Constructs a new quadtree for the specified array of points. A quadtree is a
+// two-dimensional recursive spatial subdivision. This implementation uses
+// square partitions, dividing each square into four equally-sized squares. Each
+// point exists in a unique node; if multiple points are in the same position,
+// some points may be stored on internal nodes rather than leaf nodes. Quadtrees
+// can be used to accelerate various spatial operations, such as the Barnes-Hut
+// approximation for computing n-body forces, or collision detection.
+d3.geom.quadtree = function(points, x1, y1, x2, y2) {
+ var p,
+ i = -1,
+ n = points.length;
+
+ // Type conversion for deprecated API.
+ if (n && isNaN(points[0].x)) points = points.map(d3_geom_quadtreePoint);
+
+ // Allow bounds to be specified explicitly.
+ if (arguments.length < 5) {
+ if (arguments.length === 3) {
+ y2 = x2 = y1;
+ y1 = x1;
+ } else {
+ x1 = y1 = Infinity;
+ x2 = y2 = -Infinity;
+
+ // Compute bounds.
+ while (++i < n) {
+ p = points[i];
+ if (p.x < x1) x1 = p.x;
+ if (p.y < y1) y1 = p.y;
+ if (p.x > x2) x2 = p.x;
+ if (p.y > y2) y2 = p.y;
+ }
+
+ // Squarify the bounds.
+ var dx = x2 - x1,
+ dy = y2 - y1;
+ if (dx > dy) y2 = y1 + dx;
+ else x2 = x1 + dy;
+ }
+ }
+
+ // Recursively inserts the specified point p at the node n or one of its
+ // descendants. The bounds are defined by [x1, x2] and [y1, y2].
+ function insert(n, p, x1, y1, x2, y2) {
+ if (isNaN(p.x) || isNaN(p.y)) return; // ignore invalid points
+ if (n.leaf) {
+ var v = n.point;
+ if (v) {
+ // If the point at this leaf node is at the same position as the new
+ // point we are adding, we leave the point associated with the
+ // internal node while adding the new point to a child node. This
+ // avoids infinite recursion.
+ if ((Math.abs(v.x - p.x) + Math.abs(v.y - p.y)) < .01) {
+ insertChild(n, p, x1, y1, x2, y2);
+ } else {
+ n.point = null;
+ insertChild(n, v, x1, y1, x2, y2);
+ insertChild(n, p, x1, y1, x2, y2);
+ }
+ } else {
+ n.point = p;
+ }
+ } else {
+ insertChild(n, p, x1, y1, x2, y2);
+ }
+ }
+
+ // Recursively inserts the specified point p into a descendant of node n. The
+ // bounds are defined by [x1, x2] and [y1, y2].
+ function insertChild(n, p, x1, y1, x2, y2) {
+ // Compute the split point, and the quadrant in which to insert p.
+ var sx = (x1 + x2) * .5,
+ sy = (y1 + y2) * .5,
+ right = p.x >= sx,
+ bottom = p.y >= sy,
+ i = (bottom << 1) + right;
+
+ // Recursively insert into the child node.
+ n.leaf = false;
+ n = n.nodes[i] || (n.nodes[i] = d3_geom_quadtreeNode());
+
+ // Update the bounds as we recurse.
+ if (right) x1 = sx; else x2 = sx;
+ if (bottom) y1 = sy; else y2 = sy;
+ insert(n, p, x1, y1, x2, y2);
+ }
+
+ // Create the root node.
+ var root = d3_geom_quadtreeNode();
+
+ root.add = function(p) {
+ insert(root, p, x1, y1, x2, y2);
+ };
+
+ root.visit = function(f) {
+ d3_geom_quadtreeVisit(f, root, x1, y1, x2, y2);
+ };
+
+ // Insert all points.
+ points.forEach(root.add);
+ return root;
+};
+
+function d3_geom_quadtreeNode() {
+ return {
+ leaf: true,
+ nodes: [],
+ point: null
+ };
+}
+
+function d3_geom_quadtreeVisit(f, node, x1, y1, x2, y2) {
+ if (!f(node, x1, y1, x2, y2)) {
+ var sx = (x1 + x2) * .5,
+ sy = (y1 + y2) * .5,
+ children = node.nodes;
+ if (children[0]) d3_geom_quadtreeVisit(f, children[0], x1, y1, sx, sy);
+ if (children[1]) d3_geom_quadtreeVisit(f, children[1], sx, y1, x2, sy);
+ if (children[2]) d3_geom_quadtreeVisit(f, children[2], x1, sy, sx, y2);
+ if (children[3]) d3_geom_quadtreeVisit(f, children[3], sx, sy, x2, y2);
+ }
+}
+
+function d3_geom_quadtreePoint(p) {
+ return {
+ x: p[0],
+ y: p[1]
+ };
+}
+})();
generated by cgit v1.2.3-54-g00ecf (git 2.45.2) at 2024-11-18 07:39:46 +0000