Efficient exact enumeration of single-source geodesics on a non-convex polyhedron
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In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point s on a polyhedral surface and a positive real number r, to build a data structure that enables, for any point t on the surface, to enumerate all geodesics from s to t whose length is less than r. First, we present a naive algorithm by removing the trimming process from the MMP algorithm (1987). Next, we present an improved algorithm which is practically more efficient on a non-convex polyhedron, in terms of preprocessing time and memory consumption. Moreover, we introduce a single-pair geodesic graph to succinctly encode a result of geodesic query. Lastly, we compare these naive and improved algorithms by some computer experiments.
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