Merge commit 'ffdaac4' from archweb: Add D3 geometry package

1 files changed, 868 insertions, 0 deletions

diff --git a/media/d3.geom.js b/media/d3.geom.js
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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]
+  };
+}
+})();