SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Shortest Anisotropic Paths on Terrains
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Shortest path problems on polyhedral surfaces
Shortest path problems on polyhedral surfaces
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Interactive decal compositing with discrete exponential maps
ACM SIGGRAPH 2006 Papers
Computing - Special Issue on Industrial Geometry
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Anisotropic Geodesics for Perceptual Grouping and Domain Meshing
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Curvature-based anisotropic geodesic distance computation for parametric and implicit surfaces
The Visual Computer: International Journal of Computer Graphics - Special Issue SMI'2008
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement
International Journal of Computer Vision
Computer Aided Geometric Design
A hamilton-jacobi-bellman approach to high angular resolution diffusion tractography
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Dual loops meshing: quality quad layouts on manifolds
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
A Triangulation-Invariant Method for Anisotropic Geodesic Map Computation on Surface Meshes
IEEE Transactions on Visualization and Computer Graphics
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The computation of intrinsic, geodesic distances and geodesic paths on surfaces is a fundamental low-level building block in countless Computer Graphics and Geometry Processing applications. This demand led to the development of numerous algorithms -- some for the exact, others for the approximative computation, some focussing on speed, others providing strict guarantees. Most of these methods are designed for computing distances according to the standard Riemannian metric induced by the surface's embedding in Euclidean space. Generalization to other, especially anisotropic, metrics -- which more recently gained interest in several application areas -- is not rarely hampered by fundamental problems. We explore and discuss possibilities for the generalization and extension of well-known methods to the anisotropic case, evaluate their relative performance in terms of accuracy and speed, and propose a novel algorithm, the Short-Term Vector Dijkstra. This algorithm is strikingly simple to implement and proves to provide practical accuracy at a higher speed than generalized previous methods.