SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Saddle vertex graph (SVG): a novel solution to the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Parallel chen-han (PCH) algorithm for discrete geodesics
ACM Transactions on Graphics (TOG)
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Computing geodesic distance on surfaces plays a critical role in digital geometry processing. However, due to its locally shortest nature, geodesic distance is highly sensitive to local geometrical and topological changes, diminishing its applications to real-world models which may contain various types of defects. This paper presents a new algorithm to compute defect-tolerant geodesic distance on broken meshes. In contrast to the existing approaches which compute the distance from source to destinations in a single Dijkstra-like sweep, our method proceeds in an iterative and global manner. Thanks to its global nature, the resulting distance is tolerant to some defects (e.g. holes, gaps, shortcuts), insensitive to mesh tessellation/resolution, and robust to noise, which provides a meaningful approximation of geodesics on broken meshes.