Rakotosaona, Marie-Julie;
Aigerman, Noam;
Mitra, Niloy J;
Ovsjanikov, Maks;
Guerrero, Paul;
(2021)
Differentiable Surface Triangulation.
ACM Transactions on Graphics
, 40
(6)
, Article 267. 10.1145/3478513.3480554.
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Abstract
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable surface triangulation that enables optimization for any per-vertex or per-face differentiable objective function over the space of underlying surface triangulations. Our method builds on the result that any 2D triangulation can be achieved by a suitably perturbed weighted Delaunay triangulation. We translate this result into a computational algorithm by proposing a soft relaxation of the classical weighted Delaunay triangulation and optimizing over vertex weights and vertex locations. We extend the algorithm to 3D by decomposing shapes into developable sets and differentiably meshing each set with suitable boundary constraints. We demonstrate the efficacy of our method on various planar and surface meshes on a range of difficult-to-optimize objective functions. Our code can be found online: https://github.com/mrakotosaon/diff-surface-triangulation.
| Type: | Article |
|---|---|
| Title: | Differentiable Surface Triangulation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1145/3478513.3480554 |
| Publisher version: | https://doi.org/10.1145/3478513.3480554 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Technology, Computer Science, Software Engineering, Computer Science, meshing, geometry processing, surface representation, neural networks, VORONOI, COMPUTATION, MESHES |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10159072 |
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