# Computing approximate shortest paths on convex polytopes

Published

Journal Article

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 post-processing we have added a heuristic that considerably improves the quality of the resulting path.

### Duke Authors

### Cited Authors

- Agarwal, PK; Har-Peled, S; Karia, M

### Published Date

- January 1, 2000

### Published In

- Proceedings of the Annual Symposium on Computational Geometry

### Start / End Page

- 270 - 279

### Citation Source

- Scopus