Shortest Descending Paths through Given Faces

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. No efficient algorithm is known to find a shortest descending path from s to t in a polyhedral terrain. We give some properties of such paths. In the case where the face sequence is specified, we show that the shortest descending path is unique, and give an -approximation algorithm that computes the path in O(n3.5 log(1 )) time.

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Mustaq Ahmed, Anna Lubiw
• Keywords: CCCG 2006, CCCG 2007, Efficient Algorithm, Polyhedral Terrain, Shortest Descending Path