Provably Robust and Accurate Methods for Rigid and Deformable Simulation With Contact

Abstract

Contacts are essential to virtually every aspect of life and play a vital role in many physical phenomena. Because of this, the study of contact mechanics has a deep wealth of knowledge. Surprisingly, however, simulating contact is a challenge with many parameters to carefully adjust. Incorrect parameters can result in numerical explosions, intersections, and other failures. Our research seeks to address these problems by developing robust methods that can handle arbitrary scenarios with guaranteed success.

In this thesis, we introduce the Incremental Potential Contact (IPC) method. IPC is the first simulation algorithm for deformable and rigid bodies that is unconditionally robust, requires minimal parameter tuning, and provides a direct way of controlling the trade-off between running time and accuracy. We further back up these claims by providing a large-scale benchmark of continuous collision detection (CCD) algorithms (a core component of the IPC method) based on their efficiency and correctness. As part of this study, we introduce the first efficient CCD algorithm that is provably conservative. For extended accuracy and efficiency, we show how nonlinear geometry and function spaces can be used within the IPC framework. Finally, we introduce the first physically-based adaptive meshing strategy which produces more accurate discretizations depending on elastic, contact, and frictional forces.

This work and our open-source implementations have quickly garnered attention from the computer graphics, mechanical engineering, and biomechanical engineering communities for their robustness and ability to seamlessly handle scenarios that have long been a challenge. This marks a large step towards democratizing simulation tools for design, robotics, biomechanical, and visual effects applications, among others.