// Source from https://github.com/ironwallaby/delaunay
 
 window.delaunay = function() {};
 
 window.delaunay.Triangle = function (a, b, c) {
        this.a = a
        this.b = b
        this.c = c

        var A = b.x - a.x,
            B = b.y - a.y,
            C = c.x - a.x,
            D = c.y - a.y,
            E = A * (a.x + b.x) + B * (a.y + b.y),
            F = C * (a.x + c.x) + D * (a.y + c.y),
            G = 2 * (A * (c.y - b.y) - B * (c.x - b.x)),
            minx, miny, dx, dy
  
        /* If the points of the triangle are collinear, then just find the
         * extremes and use the midpoint as the center of the circumcircle. */
        if(Math.abs(G) < 0.000001) {
          minx = Math.min(a.x, b.x, c.x)
          miny = Math.min(a.y, b.y, c.y)
          dx   = (Math.max(a.x, b.x, c.x) - minx) * 0.5
          dy   = (Math.max(a.y, b.y, c.y) - miny) * 0.5

          this.x = minx + dx
          this.y = miny + dy
          this.r = dx * dx + dy * dy
        }

        else {
          this.x = (D*E - B*F) / G
          this.y = (A*F - C*E) / G
          dx = this.x - a.x
          dy = this.y - a.y
          this.r = dx * dx + dy * dy
        }
      }

      function byX(a, b) {
        return b.x - a.x
      }

      function dedup(edges) {
        var j = edges.length,
            a, b, i, m, n

        outer: while(j) {
          b = edges[--j]
          a = edges[--j]
          i = j
          while(i) {
            n = edges[--i]
            m = edges[--i]
            if((a === m && b === n) || (a === n && b === m)) {
              edges.splice(j, 2)
              edges.splice(i, 2)
              j -= 2
              continue outer
            }
          }
        }
      }

  window.delaunay.triangulate = function (vertices) {
        /* Bail if there aren't enough vertices to form any triangles. */
        if(vertices.length < 3)
          return []

        /* Ensure the vertex array is in order of descending X coordinate
         * (which is needed to ensure a subquadratic runtime), and then find
         * the bounding box around the points. */
        vertices.sort(byX)

        var i    = vertices.length - 1,
            xmin = vertices[i].x,
            xmax = vertices[0].x,
            ymin = vertices[i].y,
            ymax = ymin

        while(i--) {
          if(vertices[i].y < ymin) ymin = vertices[i].y
          if(vertices[i].y > ymax) ymax = vertices[i].y
        }

        /* Find a supertriangle, which is a triangle that surrounds all the
         * vertices. This is used like something of a sentinel value to remove
         * cases in the main algorithm, and is removed before we return any
         * results.
         * 
         * Once found, put it in the "open" list. (The "open" list is for
         * triangles who may still need to be considered; the "closed" list is
         * for triangles which do not.) */
        var dx     = xmax - xmin,
            dy     = ymax - ymin,
            dmax   = (dx > dy) ? dx : dy,
            xmid   = (xmax + xmin) * 0.5,
            ymid   = (ymax + ymin) * 0.5,
            open   = [
              new window.delaunay.Triangle(
                {x: xmid - 20 * dmax, y: ymid -      dmax, __sentinel: true},
                {x: xmid            , y: ymid + 20 * dmax, __sentinel: true},
                {x: xmid + 20 * dmax, y: ymid -      dmax, __sentinel: true}
              )
            ],
            closed = [],
            edges = [],
            j, a, b

        /* Incrementally add each vertex to the mesh. */
        i = vertices.length
        while(i--) {
          /* For each open triangle, check to see if the current point is
           * inside it's circumcircle. If it is, remove the triangle and add
           * it's edges to an edge list. */
          edges.length = 0
          j = open.length
          while(j--) {
            /* If this point is to the right of this triangle's circumcircle,
             * then this triangle should never get checked again. Remove it
             * from the open list, add it to the closed list, and skip. */
            dx = vertices[i].x - open[j].x
            if(dx > 0 && dx * dx > open[j].r) {
              closed.push(open[j])
              open.splice(j, 1)
              continue
            }

            /* If not, skip this triangle. */
            dy = vertices[i].y - open[j].y
            if(dx * dx + dy * dy > open[j].r)
              continue

            /* Remove the triangle and add it's edges to the edge list. */
            edges.push(
              open[j].a, open[j].b,
              open[j].b, open[j].c,
              open[j].c, open[j].a
            )
            open.splice(j, 1)
          }

          /* Remove any doubled edges. */
          dedup(edges)

          /* Add a new triangle for each edge. */
          j = edges.length
          while(j) {
            b = edges[--j]
            a = edges[--j]
            open.push(new window.delaunay.Triangle(a, b, vertices[i]))
          }
        }

        /* Copy any remaining open triangles to the closed list, and then
         * remove any triangles that share a vertex with the supertriangle. */
        Array.prototype.push.apply(closed, open)

        i = closed.length
        while(i--)
          if(closed[i].a.__sentinel ||
             closed[i].b.__sentinel ||
             closed[i].c.__sentinel)
            closed.splice(i, 1)

        /* Yay, we're done! */
        return closed
      }