Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
Shortest monotone descent path problem in polyhedral terrain
Computational Geometry: Theory and Applications
Finding shortest path on land surface
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
Shortest monotone descent path problem in polyhedral terrain
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Computing highly occluded paths on a terrain
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in ${\mathbb R}^3$ and two points s and t on P, constructs a path on P between s and t whose length is at most ${7(1+{\varepsilon})} dP(s,t), where dP(s,t) is the length of the shortest path between s and t on P, and ${\varepsilon} 0$ is an arbitrarily small positive constant. The algorithm runs in O(n5/3 log5/3 n) time, where n is the number of vertices in P. We also present a slightly faster algorithm that runs in O(n8/5 log8/5 n) time and returns a path whose length is at most ${15(1+{\varepsilon})} d_{P}(s,t)$.