/// <summary>
 /// This function can be overridden if the original chains are needed.
 /// </summary>
 /// <param name="mc1"></param>
 /// <param name="start1">The index of the start of the overlapping segment from mc1.</param>
 /// <param name="mc2"></param>
 /// <param name="start2">The index of the start of the overlapping segment from mc2.</param>
 public virtual void Overlap(MonotoneChain mc1, int start1, MonotoneChain mc2, int start2)
 {
     mc1.GetLineSegment(start1, ref overlapSeg1);
     mc2.GetLineSegment(start2, ref overlapSeg2);
     Overlap(overlapSeg1, overlapSeg2);
 }
 /// <summary>
 /// This function can be overridden if the original chains are needed.
 /// </summary>
 /// <param name="mc1"></param>
 /// <param name="start1">The index of the start of the overlapping segment from mc1.</param>
 /// <param name="mc2"></param>
 /// <param name="start2">The index of the start of the overlapping segment from mc2.</param>
 public virtual void Overlap(MonotoneChain mc1, int start1, MonotoneChain mc2, int start2)
 {
     mc1.GetLineSegment(start1, ref overlapSeg1);
     mc2.GetLineSegment(start2, ref overlapSeg2);
     Overlap(overlapSeg1, overlapSeg2);
 }
 /// <summary>
 /// This method is overridden to process a segment
 /// in the context of the parent chain.
 /// </summary>
 /// <param name="mc">The parent chain</param>
 /// <param name="startIndex">The index of the start vertex of the segment being processed</param>
 public virtual void Select(MonotoneChain mc, int startIndex)
 {
     mc.GetLineSegment(startIndex, ref SelectedSegment);
     // call this routine in case select(segment) was overridden
     Select(SelectedSegment);
 }
 /// <summary> 
 /// This method is overridden to process a segment 
 /// in the context of the parent chain.
 /// </summary>
 /// <param name="mc">The parent chain</param>
 /// <param name="startIndex">The index of the start vertex of the segment being processed</param>
 public virtual void Select(MonotoneChain mc, int startIndex)
 {
     mc.GetLineSegment(startIndex, ref SelectedSegment);
     // call this routine in case select(segmenet) was overridden
     Select(SelectedSegment);
 }