/// <summary>
 ///
 /// </summary>
 /// <param name="chainIndex0"></param>
 /// <param name="mce"></param>
 /// <param name="chainIndex1"></param>
 /// <param name="si"></param>
 public void ComputeIntersectsForChain(int chainIndex0, MonotoneChainEdge mce, int chainIndex1, SegmentIntersector si)
 {
     ComputeIntersectsForChain(startIndex[chainIndex0], startIndex[chainIndex0 + 1], mce,
                               mce.startIndex[chainIndex1], mce.startIndex[chainIndex1 + 1], si);
 }
 /// <summary>
 ///
 /// </summary>
 /// <param name="edges0"></param>
 /// <param name="edges1"></param>
 /// <param name="si"></param>
 public override void ComputeIntersections(IList <Edge> edges0, IList <Edge> edges1, SegmentIntersector si)
 {
     foreach (var edge0 in edges0)
     {
         foreach (var edge1 in edges1)
         {
             ComputeIntersects(edge0, edge1, si);
         }
     }
 }
        /// <summary>
        ///
        /// </summary>
        /// <param name="start0"></param>
        /// <param name="end0"></param>
        /// <param name="mce"></param>
        /// <param name="start1"></param>
        /// <param name="end1"></param>
        /// <param name="ei"></param>
        private void ComputeIntersectsForChain(int start0, int end0, MonotoneChainEdge mce, int start1, int end1, SegmentIntersector ei)
        {
            // terminating condition for the recursion
            if (end0 - start0 == 1 && end1 - start1 == 1)
            {
                ei.AddIntersections(e, start0, mce.e, start1);
                return;
            }

            // nothing to do if the envelopes of these chains don't overlap
            if (!Overlaps(start0, end0, mce, start1, end1))
            {
                return;
            }

            // the chains overlap, so split each in half and iterate  (binary search)
            int mid0 = (start0 + end0) / 2;
            int mid1 = (start1 + end1) / 2;

            // check terminating conditions before recursing
            if (start0 < mid0)
            {
                if (start1 < mid1)
                {
                    ComputeIntersectsForChain(start0, mid0, mce, start1, mid1, ei);
                }
                if (mid1 < end1)
                {
                    ComputeIntersectsForChain(start0, mid0, mce, mid1, end1, ei);
                }
            }
            if (mid0 < end0)
            {
                if (start1 < mid1)
                {
                    ComputeIntersectsForChain(mid0, end0, mce, start1, mid1, ei);
                }
                if (mid1 < end1)
                {
                    ComputeIntersectsForChain(mid0, end0, mce, mid1, end1, ei);
                }
            }
        }