The discrete geodesic problem
The authors present an algorithm for determining the shortest path between a source and a destination on an arbitrary (possibly nonconvex) polyhedral surface. The path is constrained to lie on the surface, and distances are measured according to the Euclidean metric. The algorithm runs in time O(n/sup 2/ log n) and requires O(n/sup 2/) space, where n is the number of edges of the surface. After running the algorithm, the distance from the source to any other destination may be determined using standard techniques in time O(log n) by locating the destination in the subdivision created by the algorithm. The actual shortest path from the source to a destination can be reported in time O(kappa+log n), where kappa is the number of faces crossed by the path. The algorithm generalizes to the case of multiple source points to build the Voronoi diagram on the surface, where n is now the maximum of the number of vertices and the number of sources.
- Research Organization:
- Dept. of Operations Research, Stanford Univ. and Hughes Artificial Intelligence Center, Stanford, CA 94305
- OSTI ID:
- 5838443
- Journal Information:
- SIAM J. Comput.; (United States), Journal Name: SIAM J. Comput.; (United States) Vol. 16:4; ISSN SMJCA
- Country of Publication:
- United States
- Language:
- English
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