# A Survey of Algorithms for Geodesic Paths and Distances

arXiv: https://arxiv.org/abs/2007.10430 · HTML: https://mlsanity.com/paper/2007.10430/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 12 of 12)

- [GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation](https://mlsanity.com/paper/2205.15217/) (2022)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [Monitoring of Pigmented Skin Lesions Using 3D Whole Body Imaging](https://mlsanity.com/paper/2205.07085/) (2022)
- [Using the Path of Least Resistance to Explain Deep Networks](https://mlsanity.com/paper/2502.12108/) (2025)
- [Leveraging Point Transformers for Detecting Anatomical Landmarks in Digital Dentistry](https://mlsanity.com/paper/2504.11418/) (2025)
- [Parallelised Differentiable Straightest Geodesics for 3D Meshes](https://mlsanity.com/paper/2603.15780/) (2026)
- [Registration-Free Monitoring of Unstructured Point Cloud Data via Intrinsic Geometrical Properties](https://mlsanity.com/paper/2511.05623/) (2025)
- [From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data](https://mlsanity.com/paper/2606.02268/) (2026)
- [A Spectral Framework for Evaluating Geodesic Distances Between Graphs](https://mlsanity.com/paper/2406.10500/) (2024)
- [Manifold-Preserving Superpixel Hierarchies and Embeddings for the Exploration of High-Dimensional Images](https://mlsanity.com/paper/2602.24160/) (2026)
- [Curve Skeletonization in Continuous domain for Meshes and Point Clouds](https://mlsanity.com/paper/2605.25921/) (2026)
- [Manifold Navigation Learning Using Recurrent Networks: Efficient Training Techniques](https://mlsanity.com/paper/2610.14325/) (2026)

## Abstract (arXiv)

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.