2005/07/01 by Vitaly Surazhsky, Tatiana Surazhsky, Danil Kirsanov +2
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation
paper · doi:10.1145/1073204.1073228
openalex publication_date 2005/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact "single source, all destination" algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lower-bound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm. thereby obtaining an exact solution even more quickly.