From bcf37e4a66c55d53eeb9263097c6120633baf6aa Mon Sep 17 00:00:00 2001
From: Michael Bostock <mbostock@gmail.com>
Date: Sun, 7 Nov 2010 20:57:25 -0800
Subject: [PATCH] Generate Delaunay from Voronoi.

---
 examples/delaunay/delaunay.html |  11 +--
 examples/delaunay/delaunay.js   | 120 ---------------------------
 examples/index.html             |   3 +
 lib/jit/voronoi.js              | 140 ++++++++++++++++++++------------
 lib/jit/voronoi.min.js          |  17 ++--
 src/externs.js                  |   4 +
 6 files changed, 109 insertions(+), 186 deletions(-)
 delete mode 100644 examples/delaunay/delaunay.js

diff --git a/examples/delaunay/delaunay.html b/examples/delaunay/delaunay.html
index 643260fb..a47b41a1 100644
--- a/examples/delaunay/delaunay.html
+++ b/examples/delaunay/delaunay.html
@@ -4,7 +4,7 @@
     <meta http-equiv="Content-Type" content="text/html;charset=utf-8">
     <title>Delaunay Triangulation</title>
     <script type="text/javascript" src="../../d3.js"></script>
-    <script type="text/javascript" src="delaunay.js"></script>
+    <script type="text/javascript" src="../../lib/jit/voronoi.min.js"></script>
     <style type="text/css">
 
 @import url("../../lib/colorbrewer/colorbrewer.css");
@@ -22,8 +22,8 @@ path {
 var w = 960,
     h = 500;
 
-var vertices = d3.range(500).map(function() {
-  return [~~(w * Math.random()), ~~(h * Math.random())];
+var vertices = d3.range(500).map(function(d) {
+  return [Math.random() * w, Math.random() * h];
 });
 
 var svg = d3.select("body")
@@ -32,11 +32,12 @@ var svg = d3.select("body")
     .attr("height", h)
     .attr("class", "PiYG");
 
-svg.selectAll("path")
+svg.append("svg:g")
+  .selectAll("path")
     .data(delaunay(vertices))
   .enter("svg:path")
     .attr("class", function(d, i) { return "q" + (i % 9) + "-9"; })
-    .attr("d", function(d) { return "M" + d[0] + "L" + d[1] + "L" + d[2] + "Z"; });
+    .attr("d", function(d) { return "M" + d.join("L") + "Z"; });
 
     </script>
   </body>
diff --git a/examples/delaunay/delaunay.js b/examples/delaunay/delaunay.js
deleted file mode 100644
index 2326d8d7..00000000
--- a/examples/delaunay/delaunay.js
+++ /dev/null
@@ -1,120 +0,0 @@
-// Based on work by:
-// Mike Migurski - mike.teczno.com/notes/canvas-warp.html
-// Joshua Bell - travellermap.com/tmp/delaunay.htm
-// Sjaak Priester - codeguru.com/cpp/data/mfc_database/misc/article.php/c8901
-// Joseph O'Rourke - exaflop.org/docs/cgafaq/cga1.html
-
-function delaunay(vertices) {
-  var bounds = delaunay_bounds(vertices),
-      boundsMap = {},
-      circumcircles = [delaunay_circumcircle(bounds)],
-      triangles = [bounds];
-  boundsMap[bounds[0]] = 1;
-  boundsMap[bounds[1]] = 1;
-  boundsMap[bounds[2]] = 1;
-
-  // For each vertex…
-  vertices.forEach(function(vertex) {
-    var edgesMap = {},
-        edges = [];
-
-    // Remove triangles whose circumcircle contains the vertex.
-    for (var i in triangles) {
-      if (circumcircles[i](vertex)) {
-        var triangle = triangles[i];
-        addEdge(triangle[0], triangle[1]);
-        addEdge(triangle[1], triangle[2]);
-        addEdge(triangle[2], triangle[0]);
-        delete circumcircles[i];
-        delete triangles[i];
-      }
-    }
-
-    // Add the specified edge. If it's already present, delete it!
-    function addEdge(v0, v1) {
-      var edge = (v0[0] > v1[0]) || (v0[0] == v1[0] && v0[1] > v1[1])
-          ? [v1, v0]
-          : [v0, v1];
-      if (edge in edgesMap) delete edges[edgesMap[edge]];
-      else edgesMap[edge] = edges.push(edge) - 1;
-    }
-
-    // Add triangles for each remaining edge and the new vertex.
-    for (var i in edges) {
-      var edge = edges[i],
-          triangle = [edge[0], edge[1], vertex];
-      circumcircles.push(delaunay_circumcircle(triangle));
-      triangles.push(triangle);
-    }
-  });
-
-  // Remove triangles that share a vertex with the bounds.
-  // The filter also removes any triangles we deleted previously.
-  return triangles.filter(function(triangle) {
-    return !triangle.some(function(vertex) {
-      return vertex in boundsMap;
-    });
-  });
-}
-
-function delaunay_bounds(vertices) {
-  var minX = Infinity,
-      minY = Infinity,
-      maxX = -Infinity,
-      maxY = -Infinity,
-      dx,
-      dy;
-  for (var i = 0, n = vertices.length; i < n; i++) {
-    var vertex = vertices[i];
-    if (vertex[0] < minX) minX = vertex[0];
-    if (vertex[0] > maxX) maxX = vertex[0];
-    if (vertex[1] < minY) minY = vertex[1];
-    if (vertex[1] > maxY) maxY = vertex[1];
-  }
-  dx = (maxX - minX) * 10;
-  dy = (maxY - minX) * 10;
-  return [
-    [minX - dx, minY - dy * 3],
-    [minX - dx, maxY + dy],
-    [maxX + dx * 3, maxY + dy]
-  ];
-}
-
-function delaunay_circumcircle(triangle) {
-  var v0 = triangle[0],
-      v1 = triangle[1],
-      v2 = triangle[2],
-      A = v1[0] - v0[0],
-      B = v1[1] - v0[1],
-      C = v2[0] - v0[0],
-      D = v2[1] - v0[1],
-      E = A * (v0[0] + v1[0]) + B * (v0[1] + v1[1]),
-      F = C * (v0[0] + v2[0]) + D * (v0[1] + v2[1]),
-      G = 2 * (A * (v2[1] - v1[1]) - B * (v2[0] - v1[0])),
-      cx,
-      cy,
-      dx,
-      dy,
-      r2;
-
-  // If collinear, find extremes and use the midpoint.
-  if (Math.abs(G) < 1e-6) {
-    var minX = Math.min(v0[0], v1[0], v2[0]),
-        minY = Math.min(v0[1], v1[1], v2[1]),
-        maxX = Math.max(v0[0], v1[0], v2[0]),
-        maxY = Math.max(v0[1], v1[1], v2[1]);
-    dx = (cx = (minX + maxX) / 2) - minX;
-    dy = (cy = (minY + maxY) / 2) - minY;
-  } else {
-    dx = (cx = (D * E - B * F) / G) - v0[0];
-    dy = (cy = (A * F - C * E) / G) - v0[1];
-  }
-  r2 = dx * dx + dy * dy;
-
-  return function(vertex) {
-    var dx = cx - vertex[0],
-        dy = cy - vertex[1],
-        d2 = dx * dx + dy * dy;
-    return d2 <= r2;
-  };
-}
diff --git a/examples/index.html b/examples/index.html
index 05721f62..c3b9695e 100644
--- a/examples/index.html
+++ b/examples/index.html
@@ -12,6 +12,7 @@
       <li><a href="calendar/dji.html">calendar-dji</a></li>
       <li><a href="calendar/vix.html">calendar-vix</a></li>
       <li><a href="choropleth/choropleth.html">choropleth</a></li>
+      <li><a href="delaunay/delaunay.html">delaunay</a></li>
       <li><a href="donut/donut.html">donut</a></li>
       <li><a href="dot/dot.html">dot</a></li>
       <li><a href="force/force.html">force</a></li>
@@ -19,9 +20,11 @@
       <li><a href="line/line.html">line</a></li>
       <li><a href="pie/pie.html">pie</a></li>
       <li><a href="pie/pie-transition.html">pie-transition</a></li>
+      <li><a href="splom/splom.html">splom</a></li>
       <li><a href="stream/stream.html">stream</a></li>
       <li><a href="stream/stack.html">stack</a></li>
       <li><a href="symbol-map/symbol-map.html">symbol-map</a></li>
+      <li><a href="voronoi/voronoi.html">voronoi</a></li>
       <li><a href="zoom/zoom.html">zoom</a></li>
     </ul>
   </body>
diff --git a/lib/jit/voronoi.js b/lib/jit/voronoi.js
index ccda0e7c..de031004 100644
--- a/lib/jit/voronoi.js
+++ b/lib/jit/voronoi.js
@@ -7,42 +7,90 @@
  * @returns polygons [[[x1, y1], [x2, y2], …], …]
  */
 voronoi = function(vertices) {
-  var polygons = vertices.map(function() { return []; }),
-      opposite = {"l": "r", "r": "l"};
+  var polygons = vertices.map(function() { return []; });
 
   // Note: we expect the caller to clip the polygons, if needed.
-  var Canvas = {
-    plotEdge: 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);
+  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);
+    });
+  });
+};
+
+/**
+* @param vertices [[x1, y1], [x2, y2], …]
+* @returns triangles [[[x1, y1], [x2, y2], [x3, y3]], …]
+ */
+delaunay = function(vertices) {
+  var edges = vertices.map(function() { return []; }),
+      triangles = [];
+
+  // Use the Voronoi tessellation to determine Delaunay edges.
+  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;
+};
+
+var voronoi_opposite = {"l": "r", "r": "l"};
+
+function voronoi_tessellate(vertices, callback) {
 
   var Sites = {
     list: vertices
@@ -125,7 +173,7 @@ voronoi = function(vertices) {
     rightRegion: function(he) {
       return he.edge == null
           ? Sites.bottomSite
-          : he.edge.region[opposite[he.side]];
+          : he.edge.region[voronoi_opposite[he.side]];
     }
   };
 
@@ -244,8 +292,8 @@ voronoi = function(vertices) {
 
     endPoint: function(edge, side, site) {
       edge.ep[side] = site;
-      if (!edge.ep[opposite[side]]) return;
-      Canvas.plotEdge(edge);
+      if (!edge.ep[voronoi_opposite[side]]) return;
+      callback(edge);
     },
 
     distance: function(s, t) {
@@ -359,7 +407,7 @@ voronoi = function(vertices) {
       e = Geom.bisect(bot, top);
       bisector = EdgeList.createHalfEdge(e, pm);
       EdgeList.insert(llbnd, bisector);
-      Geom.endPoint(e, opposite[pm], v);
+      Geom.endPoint(e, voronoi_opposite[pm], v);
       p = Geom.intersect(llbnd, bisector);
       if (p) {
         EventQueue.del(llbnd);
@@ -377,20 +425,6 @@ voronoi = function(vertices) {
   for (lbnd = EdgeList.right(EdgeList.leftEnd);
       lbnd != EdgeList.rightEnd;
       lbnd = EdgeList.right(lbnd)) {
-    Canvas.plotEdge(lbnd.edge);
+    callback(lbnd.edge);
   }
-
-  // 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);
-    });
-  });
-};
+}
diff --git a/lib/jit/voronoi.min.js b/lib/jit/voronoi.min.js
index 9677bdd3..20c88f5d 100644
--- a/lib/jit/voronoi.min.js
+++ b/lib/jit/voronoi.min.js
@@ -1,8 +1,9 @@
-(function(){var k=null;
-voronoi=function(w){var y=w.map(function(){return[]}),z={l:"r",r:"l"},A={A:function(a){var c,b,d,e;if(a.d==1&&a.a>=0){c=a.k.r;b=a.k.l}else{c=a.k.l;b=a.k.r}if(a.d==1){d=c?c.y:-1E6;c=a.b-a.a*d;e=b?b.y:1E6;b=a.b-a.a*e}else{c=c?c.x:-1E6;d=a.b-a.d*c;b=b?b.x:1E6;e=a.b-a.d*b}c=[c,d];b=[b,e];y[a.region.l.index].push(c,b);y[a.region.r.index].push(c,b)}},t={c:w.map(function(a,c){return{index:c,x:a[0],y:a[1]}}).sort(function(a,c){return a.y<c.y?-1:a.y>c.y?1:a.x<c.x?-1:a.x>c.x?1:0}),v:k},f={c:[],m:k,n:k,D:function(){f.m=
-f.o(k,"l");f.n=f.o(k,"l");f.m.r=f.n;f.n.l=f.m;f.c.unshift(f.m,f.n)},o:function(a,c){return{g:a,h:c,u:k,l:k,r:k}},i:function(a,c){c.l=a;c.r=a.r;a.r.l=c;a.r=c},F:function(a){var c=f.m;do c=c.r;while(c!=f.n&&n.H(c,a));return c=c.l},j:function(a){a.l.r=a.r;a.r.l=a.l;a.g=k},right:function(a){return a.r},left:function(a){return a.l},G:function(a){return a.g==k?t.v:a.g.region[a.h]},B:function(a){return a.g==k?t.v:a.g.region[z[a.h]]}},n={z:function(a,c){var b={region:{l:a,r:c},k:{l:k,r:k}},d=c.x-a.x,e=c.y-
-a.y,h=d>0?d:-d,l=e>0?e:-e;b.b=a.x*d+a.y*e+(d*d+e*e)*0.5;if(h>l){b.d=1;b.a=e/d;b.b/=d}else{b.a=1;b.d=d/e;b.b/=e}return b},t:function(a,c){var b=a.g,d=c.g;if(!b||!d||b.region.r==d.region.r)return k;var e=b.d*d.a-b.a*d.d;if(Math.abs(e)<1.0E-10)return k;var h=(b.b*d.a-d.b*b.a)/e;e=(d.b*b.d-b.b*d.d)/e;var l=b.region.r,s=d.region.r;if(l.y<s.y||l.y==s.y&&l.x<s.x){l=a;b=b}else{l=c;b=d}if((b=h>=b.region.r.x)&&l.h=="l"||!b&&l.h=="r")return k;return{x:h,y:e}},H:function(a,c){var b=a.g,d=b.region.r,e=c.x>d.x;
-if(e&&a.h=="l")return 1;if(!e&&a.h=="r")return 0;if(b.d==1){var h=c.y-d.y,l=c.x-d.x,s=0,o=0;if(!e&&b.a<0||e&&b.a>=0)o=s=h>=b.a*l;else{o=c.x+c.y*b.a>b.b;if(b.a<0)o=!o;o||(s=1)}if(!s){d=d.x-b.region.l.x;o=b.a*(l*l-h*h)<d*h*(1+2*l/d+b.a*b.a);if(b.a<0)o=!o}}else{l=b.b-b.d*c.x;b=c.y-l;h=c.x-d.x;d=l-d.y;o=b*b>h*h+d*d}return a.h=="l"?o:!o},w:function(a,c,b){a.k[c]=b;a.k[z[c]]&&A.A(a)},s:function(a,c){var b=a.x-c.x,d=a.y-c.y;return Math.sqrt(b*b+d*d)}},i={c:[],i:function(a,c,b){a.u=c;a.p=c.y+b;b=0;for(var d=
-i.c,e=d.length;b<e;b++){var h=d[b];if(!(a.p>h.p||a.p==h.p&&c.x>h.u.x))break}d.splice(b,0,a)},j:function(a){for(var c=0,b=i.c,d=b.length;c<d&&b[c]!=a;++c);b.splice(c,1)},empty:function(){return i.c.length==0},I:function(a){for(var c=0,b=i.c,d=b.length;c<d;++c)if(b[c]==a)return b[c+1];return k},min:function(){var a=i.c[0];return{x:a.u.x,y:a.p}},C:function(){return i.c.shift()}};f.D();t.v=t.c.shift();for(var p=t.c.shift(),x,g,q,v,B,j,r,m,u;;){i.empty()||(x=i.min());if(p&&(i.empty()||p.y<x.y||p.y==x.y&&
-p.x<x.x)){g=f.F(p);q=f.right(g);r=f.B(g);u=n.z(r,p);j=f.o(u,"l");f.i(g,j);if(m=n.t(g,j)){i.j(g);i.i(g,m,n.s(m,p))}g=j;j=f.o(u,"r");f.i(g,j);(m=n.t(j,q))&&i.i(j,m,n.s(m,p));p=t.c.shift()}else if(i.empty())break;else{g=i.C();v=f.left(g);q=f.right(g);B=f.right(q);r=f.G(g);j=f.B(q);m=g.u;n.w(g.g,g.h,m);n.w(q.g,q.h,m);f.j(g);i.j(q);f.j(q);g="l";if(r.y>j.y){g=r;r=j;j=g;g="r"}u=n.z(r,j);j=f.o(u,g);f.i(v,j);n.w(u,z[g],m);if(m=n.t(v,j)){i.j(v);i.i(v,m,n.s(m,r))}(m=n.t(j,B))&&i.i(j,m,n.s(m,r))}}for(g=f.right(f.m);g!=
-f.n;g=f.right(g))A.A(g.g);return y.map(function(a,c){var b=w[c][0],d=w[c][1];a.forEach(function(e){e.q=Math.atan2(e[0]-b,e[1]-d)});return a.sort(function(e,h){return e.q-h.q}).filter(function(e,h){return!h||e.q-a[h-1].q>1.0E-10})})};})()
+(function(){var m=null;
+voronoi=function(q){var v=q.map(function(){return[]});A(q,function(h){var c,g,i,j;if(h.d==1&&h.a>=0){c=h.m.r;g=h.m.l}else{c=h.m.l;g=h.m.r}if(h.d==1){i=c?c.y:-1E6;c=h.b-h.a*i;j=g?g.y:1E6;g=h.b-h.a*j}else{c=c?c.x:-1E6;i=h.b-h.d*c;g=g?g.x:1E6;j=h.b-h.d*g}c=[c,i];g=[g,j];v[h.region.l.index].push(c,g);v[h.region.r.index].push(c,g)});return v.map(function(h,c){var g=q[c][0],i=q[c][1];h.forEach(function(j){j.j=Math.atan2(j[0]-g,j[1]-i)});return h.sort(function(j,r){return j.j-r.j}).filter(function(j,r){return!r||
+j.j-h[r-1].j>1.0E-10})})};delaunay=function(q){var v=q.map(function(){return[]}),h=[];A(q,function(c){v[c.region.l.index].push(q[c.region.r.index])});v.forEach(function(c,g){var i=q[g],j=i[0],r=i[1];c.forEach(function(s){s.j=Math.atan2(s[0]-j,s[1]-r)});c.sort(function(s,z){return s.j-z.j});for(var f=0,t=c.length-1;f<t;f++)h.push([i,c[f],c[f+1]])});return h};var B={l:"r",r:"l"};
+function A(q,v){var h={c:q.map(function(a,d){return{index:d,x:a[0],y:a[1]}}).sort(function(a,d){return a.y<d.y?-1:a.y>d.y?1:a.x<d.x?-1:a.x>d.x?1:0}),v:m},c={c:[],n:m,o:m,C:function(){c.n=c.p(m,"l");c.o=c.p(m,"l");c.n.r=c.o;c.o.l=c.n;c.c.unshift(c.n,c.o)},p:function(a,d){return{g:a,h:d,u:m,l:m,r:m}},i:function(a,d){d.l=a;d.r=a.r;a.r.l=d;a.r=d},D:function(a){var d=c.n;do d=d.r;while(d!=c.o&&g.G(d,a));return d=d.l},k:function(a){a.l.r=a.r;a.r.l=a.l;a.g=m},right:function(a){return a.r},left:function(a){return a.l},
+F:function(a){return a.g==m?h.v:a.g.region[a.h]},A:function(a){return a.g==m?h.v:a.g.region[B[a.h]]}},g={z:function(a,d){var b={region:{l:a,r:d},m:{l:m,r:m}},e=d.x-a.x,k=d.y-a.y,o=e>0?e:-e,n=k>0?k:-k;b.b=a.x*e+a.y*k+(e*e+k*k)*0.5;if(o>n){b.d=1;b.a=k/e;b.b/=e}else{b.a=1;b.d=e/k;b.b/=k}return b},t:function(a,d){var b=a.g,e=d.g;if(!b||!e||b.region.r==e.region.r)return m;var k=b.d*e.a-b.a*e.d;if(Math.abs(k)<1.0E-10)return m;var o=(b.b*e.a-e.b*b.a)/k;k=(e.b*b.d-b.b*e.d)/k;var n=b.region.r,x=e.region.r;
+if(n.y<x.y||n.y==x.y&&n.x<x.x){n=a;b=b}else{n=d;b=e}if((b=o>=b.region.r.x)&&n.h=="l"||!b&&n.h=="r")return m;return{x:o,y:k}},G:function(a,d){var b=a.g,e=b.region.r,k=d.x>e.x;if(k&&a.h=="l")return 1;if(!k&&a.h=="r")return 0;if(b.d==1){var o=d.y-e.y,n=d.x-e.x,x=0,u=0;if(!k&&b.a<0||k&&b.a>=0)u=x=o>=b.a*n;else{u=d.x+d.y*b.a>b.b;if(b.a<0)u=!u;u||(x=1)}if(!x){e=e.x-b.region.l.x;u=b.a*(n*n-o*o)<e*o*(1+2*n/e+b.a*b.a);if(b.a<0)u=!u}}else{n=b.b-b.d*d.x;b=d.y-n;o=d.x-e.x;e=n-e.y;u=b*b>o*o+e*e}return a.h=="l"?
+u:!u},w:function(a,d,b){a.m[d]=b;a.m[B[d]]&&v(a)},s:function(a,d){var b=a.x-d.x,e=a.y-d.y;return Math.sqrt(b*b+e*e)}},i={c:[],i:function(a,d,b){a.u=d;a.q=d.y+b;b=0;for(var e=i.c,k=e.length;b<k;b++){var o=e[b];if(!(a.q>o.q||a.q==o.q&&d.x>o.u.x))break}e.splice(b,0,a)},k:function(a){for(var d=0,b=i.c,e=b.length;d<e&&b[d]!=a;++d);b.splice(d,1)},empty:function(){return i.c.length==0},H:function(a){for(var d=0,b=i.c,e=b.length;d<e;++d)if(b[d]==a)return b[d+1];return m},min:function(){var a=i.c[0];return{x:a.u.x,
+y:a.q}},B:function(){return i.c.shift()}};c.C();h.v=h.c.shift();for(var j=h.c.shift(),r,f,t,s,z,l,w,p,y;;){i.empty()||(r=i.min());if(j&&(i.empty()||j.y<r.y||j.y==r.y&&j.x<r.x)){f=c.D(j);t=c.right(f);w=c.A(f);y=g.z(w,j);l=c.p(y,"l");c.i(f,l);if(p=g.t(f,l)){i.k(f);i.i(f,p,g.s(p,j))}f=l;l=c.p(y,"r");c.i(f,l);(p=g.t(l,t))&&i.i(l,p,g.s(p,j));j=h.c.shift()}else if(i.empty())break;else{f=i.B();s=c.left(f);t=c.right(f);z=c.right(t);w=c.F(f);l=c.A(t);p=f.u;g.w(f.g,f.h,p);g.w(t.g,t.h,p);c.k(f);i.k(t);c.k(t);
+f="l";if(w.y>l.y){f=w;w=l;l=f;f="r"}y=g.z(w,l);l=c.p(y,f);c.i(s,l);g.w(y,B[f],p);if(p=g.t(s,l)){i.k(s);i.i(s,p,g.s(p,w))}(p=g.t(l,z))&&i.i(l,p,g.s(p,w))}}for(f=c.right(c.n);f!=c.o;f=c.right(f))v(f.g)};})()
diff --git a/src/externs.js b/src/externs.js
index b0e650a8..3c7f5df7 100644
--- a/src/externs.js
+++ b/src/externs.js
@@ -168,3 +168,7 @@ d3.time = {
   format: 1,
   parse: 1
 };
+
+// jit
+var voronoi,
+    delaunay;