Differentiable Geodesic Distance for Intrinsic Minimization on Triangle Meshes

Author:

Li Yue1ORCID,Numerow Logan1ORCID,Thomaszewski Bernhard1ORCID,Coros Stelian1ORCID

Affiliation:

1. ETH Zürich, Zurich, Switzerland

Abstract

Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along with their derivatives. We present a novel approach for intrinsic minimization of distance-based objectives defined on triangle meshes. Using a variational formulation of shortest-path geodesics, we compute first and second-order distance derivatives based on the implicit function theorem, thus opening the door to efficient Newton-type minimization solvers. We demonstrate our differentiable geodesic distance framework on a wide range of examples, including geodesic networks and membranes on surfaces of arbitrary genus, two-way coupling between hosting surface and embedded system, differentiable geodesic Voronoi diagrams, and efficient computation of Karcher means on complex shapes. Our analysis shows that second-order descent methods based on our differentiable geodesics outperform existing first-order and quasi-Newton methods by large margins.

Funder

Swiss National Science Foundation

European Research Council

Publisher

Association for Computing Machinery (ACM)

Reference57 articles.

1. An ADMM-based scheme for distance function approximation

2. Alexander G Belyaev and Pierre-Alain Fayolle. 2015. On variational and PDE-based distance function approximations. In Computer Graphics Forum, Vol. 34. Wiley Online Library, 104--118.

3. A survey of geodesic paths on 3D surfaces

4. Shortest paths on a polyhedron

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