A Survey of Algorithms for Geodesic Paths and Distances

TL;DR

This survey reviews various algorithms for computing geodesic paths and distances on curved domains, emphasizing their importance across multiple fields and discussing recent advances and future opportunities.

Contribution

It provides a comprehensive overview of major approaches to geodesic computation, highlighting common themes and identifying areas for future research.

Findings

Various algorithms enable rapid geodesic queries on large models

Curvature significantly influences shortest path behavior

Recent methods improve computational efficiency and accuracy

Abstract

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.