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Geodesic distances between pairs of points on a 3D mesh surface are a crucial ingredient of many geometry processing tasks, but are notoriously difficult to compute efficiently on demand. We propose a novel method for the compact storage of geodesic distance information, which enables answering point-to-point geodesic distance queries very efficiently. We achieve this by computing a nested bisection of the mesh surface using separator curves and storing compactly-described functions approximating the distances between each mesh vertex and a small relevant subset of these curves. Using this database, the geodesic distance between two mesh vertices can then be approximated well by solving a small number of simple univariate minimization problems.

Our method provides an excellent tradeoff between the size of the database, query runtime, and accuracy of the result. It can be used to compress exact or approximate geodesic distances, for example, those obtained by VTP (exact), fast DGG, fast marching, or the heat method (approximate).

Short Bio:

Kai Hormann is a full professor in the Faculty of Informatics at the Università della Svizzera italiana (USI) in Lugano, Switzerland.

His research interests are focussed on the mathematical foundations of geometry processing algorithms as well as their applications in computer graphics and related fields. In particular, he is working on generalized barycentric coordinates, subdivision of curves and surfaces, barycentric rational interpolation, and dynamic geometry processing. Professor Hormann has published over 100 papers in the professional literature and is an associate editor of the journals Computer Aided Geometric Design and Dolomites Research Notes on Approximation. He served as chair of the SIAM Activity Group on Geometric Design in 2017/2018 and is entrusted with the chairmanship of the steering board of the international conference Geometric Modeling and Processing (GMP) since 2017.