Multi-Resolution Modeling of Shapes in Contact

We describe an efficient method to model shapes undergoing contact and self-contact. Previous shape modeling methods mostly focused on deformations (without contact), and, if used directly for contact, suffer from excessively long calculation times when new contacts are detected. In our work, we demonstrate fast, output-sensitive shape modeling that does not substantially degrade when new contacts are detected and that degrades gracefully with contact complexity, even for complex geometries. We achieve this by constructing a rotationally invariant linear-precision multi-resolution hierarchy of shape deformation bases. Inspired by the active set method, we propose a new contact model suitable for shape modeling that greatly outperforms prior work in contact quality and smoothness. Our method requires no extensive precomputation and works with triangle meshes embedded in solid tetrahedral meshes. We apply our method to the widely used as-rigid-as-possible energy, enabling modeling of shapes in contact, with arbitrarily large rotations, smoothness and locality.