Smooth-surface reconstruction in near-linear time
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal-Time Algorithm for Shortest Paths on Realistic Polyhedra
Discrete & Computational Geometry
Algorithms for Approximate Shortest Path Queries on Weighted Polyhedral Surfaces
Discrete & Computational Geometry
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
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We present an algorithm for approximating geodesic distances on 2-manifolds in R^3. Our algorithm works on an @e-sample of the underlying manifold and computes approximate geodesic distances between all pairs of points in this sample. The approximation error is multiplicative and depends on the density of the sample. For an @e-sample S, the algorithm has a near-optimal running time of O(|S|^2log|S|), an optimal space requirement of O(|S|^2), and approximates the geodesic distances up to a factor of 1-O(@e) and (1-O(@e))^-^1.