Paper Info
Title
Differentiable surface triangulation
Abstract
AbstractTriangle 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.
Year
DOI
Venue
2021
10.1145/3478513.3480554
ACM Transactions on Graphics
Keywords
DocType
Volume
meshing, geometry processing, surface representation, neural networks
Journal
40
Issue
ISSN
Citations 
6
0730-0301
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Marie-Julie Rakotosaona151.53
Noam Aigerman221512.60
Niloy J. Mitra33813176.15
Maks Ovsjanikov4223584.06
Paul Guerrero59910.97