Robust and Artefact-Free Deformable Contact with Smooth Surface Representations

Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on C⁰-discretizations—piece-wise linear or polynomial surfaces—suffer from discontinuities and irregularities in tangential contact forces, which can significantly affect simulation outcomes and even prevent convergence. In this work, we show that these limitations can be overcome with a smooth surface representation based on Implicit Moving Least Squares (IMLS). In particular, we propose a self collision detection scheme tailored to IMLS surfaces that enables robust and efficient handling of challenging self contacts. Through a series of test cases, we show that our approach offers advantages over existing methods in terms of accuracy and robustness for both forward and inverse problems.