Finding All Shortest Path Edge Sequences on a convex polyhedron
In this paper, the problems of computing the Euclidean shortest path between two points on the surface of a convex polyhedron and finding all shortest path edge sequences are considered. We propose an O(n6logn) algorithm to find All Shortest Path Edge Sequences, construct n Edge Sequence Trees, and draw out n(n−1)/2 Visibility Relation Diagrams for a given convex polyhedron. According to these data structures, not only can we enumerate all shortest path edge sequences and draw out all maximal ones, but we can also find the shortest path between any two points lying on edges in O(k+logn) time where k is the number of edges crossed by the shortest path.
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- [Mi]J. S. B. Mitchell, Planning Shortest Paths, Ph. D. Thesis, Department of Operations Research, Stanford University, August 1986.Google Scholar
- [Mo85]D. M. Mount, On Finding Shortest Paths on Convex Polyhedra, Technical Report 1495, Computer Science Department, University of Maryland, College Park, 1984.Google Scholar
- [Mo86]D. M. Mount, The Number of Shortest Paths on the Surface of a Polyhedron, Technical Report, Computer Science Department, University of Maryland, College Park, MD, 1986.Google Scholar
- [OSB]J. O'Rourke, S. Suri, and H. Booth, Shortest Paths on Polyhedral Surfaces, Manuscript, Johns Hopkins University, 1984.Google Scholar
- [SO]C. Schevon, J. O'Rourke, The Number of Maximal Edges Sequences on a Convex Polytope, Proceedings of Allerton Conference, 1988.Google Scholar
- [Pa]C. H. Papadimitriou, An Algorithm for Shortest-Path Motion in Three Dimensions, Information Processing Letter, Vol. 20, No. 5, 12 June, 1985.Google Scholar
- [SS]M. Sharir and A. Schorr, On Shortest Paths in Polyhedral Spaces, SIAM J. Comput., Vol. 15, No. 1, Feburary 1986, pp. 193–215.Google Scholar