## 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 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/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 postprocessing step we have added a heuristic that considerably improves the quality of the resulting path.

Original language | English (US) |
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Pages (from-to) | 227-242 |

Number of pages | 16 |

Journal | Algorithmica (New York) |

Volume | 33 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2002 |

## Keywords

- Approximation algorithms
- Covex polytopes
- Path planning

## ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics