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A Survey of Algorithms for Geodesic Paths and Distances

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arxiv 2007.10430 v1 pith:AELSDBQ7 submitted 2020-07-20 cs.GR cs.CG

Keenan Crane , Marco Livesu , Enrico Puppo , Yipeng Qin This is my paper · ORCID
classification cs.GRcs.CG
keywords geodesicpathscomputationcomputerdistancedistancesshortestsurvey
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Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and computer vision. Relative to Euclidean distance computation, these tasks are complicated by the influence of curvature on the behavior of shortest paths, as well as the fact that the representation of the domain may itself be approximate. In spite of the difficulty of this problem, recent literature has developed a wide variety of sophisticated methods that enable rapid queries of geodesic information, even on relatively large models. This survey reviews the major categories of approaches to the computation of geodesic paths and distances, highlighting common themes and opportunities for future improvement.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Differentiable Approximations for Distance Queries

    cs.CG 2026-07 conditional novelty 7.0 of 10

    A (1+ε)-approximate Euclidean distance function that is differentiable and returns gradients, using O(n/ε^(d/2)) space and O(log(n/ε)) query time.

  2. Geodesic distance approximation using a surface finite element method for the $p$-Laplacian

    cs.GR 2025-05 conditional novelty 6.0 of 10

    A surface finite element method for the p-Laplacian approximates intrinsic geodesic distances to features on surfaces, converging numerically to exact distances as p grows.

  3. GEORCE: A Fast New Control Algorithm for Computing Geodesics

    math.DG 2025-05 conditional novelty 6.0 of 10

    A control-based iterative solver computes geodesics on Riemannian and Finsler manifolds with global convergence and empirically fast, accurate performance.

  4. SBAMDT: Bayesian Additive Decision Trees with Adaptive Soft Semi-multivariate Split Rules

    stat.ML 2025-01 conditional novelty 6.0 of 10

    SBAMDT is a Bayesian additive tree model with hard-or-soft and univariate-or-multivariate splits, reporting better spatial predictions than existing tree ensembles.

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