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COMPGEOM

2006

ACM

2006

ACM

We present an optimal-time algorithm for computing (an implicit representation of) the shortest-path map from a ﬁxed source s on the surface of a convex polytope P in three dimensions. Our algorithm runs in O(n log n) time and requires O(n log n) space, where n is the number of edges of P. The algorithm is based on the O(n log n) algorithm of Hershberger and Suri for shortest paths in the plane [22], and similarly follows the continuous Dijkstra paradigm, which propagates a “wavefront” from s along ∂P. This is eﬀected by generalizing the concept of conforming subdivision of the free space used in [22], and by adapting it for the case of a convex polytope in R3, allowing the algorithm to accomplish the propagation in discrete steps, between the “transparent” edges of the subdivision. The algorithm constructs a dynamic version of Mount’s data structure [32] that implicitly encodes the shortest paths from s to all other points of the surface. This structure allows us to a...

Related Content

Added |
13 Jun 2010 |

Updated |
13 Jun 2010 |

Type |
Conference |

Year |
2006 |

Where |
COMPGEOM |

Authors |
Yevgeny Schreiber, Micha Sharir |

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