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Fast exact and approximate geodesics on meshes

Fast exact and approximate geodesics on meshes
Vitaly Surazhsky, Tatiana Surazhsky, Danil Kirsanov, Steven Gortler, Hugues Hoppe.
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.
Hindsights: 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.
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