Computing approximate shortest paths on convex polytopes

The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3 , two points s, t ∈ P, and a parameter ε > 0, it computes a path between s and t on P whose length is at most (1+ε) times the length of the shortest path between those points. It first constructs in time O(n/ √ ε) a graph of size O(1/ε4 ), computes a shortest path on this graph, and projects the path onto the surface in O(n/ε) time, where n is the number of vertices of P. In the postprocessing step we have added a heuristic that considerably improves the quality of the resulting path.

• Type: Conference
• Year: 2000
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Sariel Har-Peled, Meetesh Karia
• Keywords: COMPGEOM 2000, Convex Polyhedral Surface, Discrete Geometry, Polyhedral Surface, Shortest Path