### Abstract

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 R^{3}, 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/ε^{4}), 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.

Original language | English (US) |
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Pages | 270-279 |

Number of pages | 10 |

DOIs | |

State | Published - Jan 1 2000 |

Externally published | Yes |

Event | 16th Annual Symposium on Computational Geometry - Hong Kong, Hong Kong Duration: Jun 12 2000 → Jun 14 2000 |

### Other

Other | 16th Annual Symposium on Computational Geometry |
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City | Hong Kong, Hong Kong |

Period | 6/12/00 → 6/14/00 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

*Computing approximate shortest paths on convex polytopes*. 270-279. Paper presented at 16th Annual Symposium on Computational Geometry, Hong Kong, Hong Kong, . https://doi.org/10.1145/336154.336213