TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization

We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh - a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation.

PhysGraph: Physics-Based Integration Using Graph Neural Networks

Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential energy in order to compute velocities or displacements. Recently, learning based method for physics-based simulation have sparked interest with graph based approaches being a promising research direction. One of the challenges for these methods is to generate models that are mesh independent and generalize to different material properties. Moreover, the model should also be able to react to unforeseen external forces like ubiquitous collisions. Our contribution is based on a simple observation: evaluating forces is computationally relatively cheap for traditional simulation methods and can be computed in parallel in contrast to their integration. If we learn how a system reacts to forces in general, irrespective of their origin, we can learn an integrator that can predict state changes due to the total forces with high generalization power. We effectively factor out the physical model behind resulting forces by relying on an opaque force module. We demonstrate that this idea leads to a learnable module that can be trained on basic internal forces of small mesh patches and generalizes to different mesh typologies, resolutions, material parameters and unseen forces like collisions at inference time. Our proposed paradigm is general and can be used to model a variety of physical phenomena. We focus our exposition on the detail enhancement of coarse clothing geometry which has many applications including computer games, virtual reality and virtual try-on.