Differentiable surface triangulation

Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous is essentially a hybrid one that decouples continuous vertex locations from discrete topological triangulation. Unfortunately, combinatorial nature of triangulation prevents taking derivatives over space possible meshings any given surface. As result, to date, mesh processing and optimization techniques have been unable truly take advantage modular gradient descent components modern frameworks. In this work, we present differentiable enables per-vertex or per-face objective function underlying triangulations. Our method builds on result 2D can be achieved by suitably perturbed weighted Delaunay We translate into computational algorithm proposing soft relaxation classical optimizing weights locations. extend 3D decomposing shapes developable sets differentiably meshing each set with suitable boundary constraints. demonstrate efficacy our various planar range difficult-to-optimize functions. code found online: https://github.com/mrakotosaon/diff-surface-triangulation.