Geodesic computation is very important in various mesh processing techniques such as re-meshing, parameterizing, segmenting, navigating and editing. In this paper we propose a new approach to compute the geodesic paths on triangular meshes. Considering the geodesic path is a local shortest and straightest path between two points on the surface, we first get an initial approximation of the geodesic path using direction tracking method proposed in this paper, and then the approximate path is corrected using an iterative process to get an accurate approximation with bounded error.
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