/**

* @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;

};