ACM Trans. Graphics (SIGGRAPH), 24(3), 2005.
Efficient computation of shortest paths and distances on triangle meshes.
Abstract: 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.
Hindsight: This computation of geodesic distances is used to improve the texture atlas parameterizations produced by the DirectX UVAtlas tool. See Bommes and Kobbelt 2007 for an interesting extension to compute geodesics from more general (non-point) sources.
ACM Copyright Notice
Copyright by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or firstname.lastname@example.org. The definitive version of this paper can be found at ACM's Digital Library http://www.acm.org/dl/.