Geodesic Paths On 3D Surfaces: Survey and Open Problems

TL;DR

This survey reviews algorithms for computing geodesic paths and distances on 3D polyhedral surfaces, highlighting theoretical foundations, practical methods, and open problems in the field.

Contribution

It provides a comprehensive overview of existing algorithms and identifies open challenges in computing geodesics on 3D surfaces.

Findings

Summary of key algorithms for geodesic computation

Identification of open problems in the field

Comparison of theoretical and practical approaches

Abstract

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.