Efficient Exact Enumeration of Single-Source Geodesics on a Non-Convex Polyhedron

Kazuma Tateiri

doi:10.1142/s0218195923500048

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arXiv · 2306.02559

Efficient Exact Enumeration of Single-Source Geodesics on a Non-Convex Polyhedron

Kazuma Tateiri

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Abstract

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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BibTeX RIS

Kazuma Tateiri. 2023-06-05. Efficient Exact Enumeration of Single-Source Geodesics on a Non-Convex Polyhedron. https://doi.org/10.1142/s0218195923500048

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