Multi-Resolution Modeling of Shapes in Contact

Abstract

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.

A time-independent deformer for elastic contacts

“…This method is independent of the deformation model, but involves a computationally extensive numerical constrained optimization and lacks artistic controls of the deformation. The method of Li and Barbič [2019] showed improved results for the specific case of handle-based As-Rigid-As-Possible (ARAP) deformation [Sorkine and Alexa 2007], but otherwise suffers from similar limitations.…”

“…For character animation with contacts, quasi-static simulations (e.g., [McAdams et al 2011]) and specific skinning techniques (e.g., [Vaillant et al 2013]) partially lift this limitation, but they cannot be trivially extended to arbitrary elastic objects. Geometric modelling approaches handling collisions (e.g., [Li and Barbič 2019]) can be applied in this context, but they require expensive optimization and lack artistic controls of the deformation. Recently, Brunel et al [2020] have presented a geometric, timeindependent approach to resolve local contacts between an elastic and a rigid object, producing plausible and art-directable bulge deformations.…”

A Time-independent Deformer for Elastic-rigid Contacts

“…The geometric framework of Harmon et al [2011] numerical constrained optimization and lacks artistic controls of the deformation. The concurrent method of Li and Barbič [2019] showed improved results for the specific case of handle-based As-Rigid-As-Possible (ARAP) deformation [Wang et al 2015], but otherwise suffers from similar limitations.…”