TCE Guest Lecture: A New Approach to Computing Geodesic Distance Based on Heat Flow

Max Wardetzky (University of Gottingen)
Tuesday, 4.2.2014, 11:30
Room 337-8 Taub Bld.

In this talk, I discuss the heat method for computing the geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard linear elliptic problems. The resulting systems can be prefactored once and subsequently solved in near-linear time. In practice, distance is updated an order of magnitude faster than with state-of-the-art methods, while maintaining a comparable level of accuracy. The method requires only standard differential operators and can hence be applied on a wide variety of domains (grids, triangle meshes, point clouds, etc.). Numerical evidence shows that the method converges to the exact distance in the limit of refinement; yet, a proof of convergence is still missing, and I will touch upon some of the attendant difficulties.

Prof. Max Wardetzky is the head of the Discrete Differential Geometry Lab at the University of Gottingen. Discrete differential geometry (DDG) explores discrete counterparts of classical differential geometry, such that the classical smooth theory arises in the limit of refinement of the discrete one. The tools of DDG offer a variety of exciting applications—ranging from geometry processing and computational geometry over computer graphics to physical simulations.

His main research interests are Discrete Differential Geometry, Geometry Processing, Computational Topology, Physical Simulation, Computer Graphics

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