A global algorithm to compute defect-tolerant geodesic distance

Abstract

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.