# 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 ε 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 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.

### Full Text

### Duke Authors

### Cited Authors

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

### Published Date

- January 1, 2002

### Published In

### Volume / Issue

- 33 / 2

### Start / End Page

- 227 - 242

### International Standard Serial Number (ISSN)

- 0178-4617

### Digital Object Identifier (DOI)

- 10.1007/s00453-001-0111-x

### Citation Source

- Scopus