A Unified Analysis of Penalty-Based Collision Energies
Alvin Shi and T. Kim (Yale University)
We analyze a wide class of penalty energies used for contact response through the lens of a reduced frame. Applying our analysis to both spring-based and barrier-based energies, we show that we can obtain closed-form, analytic eigensystems that can be used to guarantee positive semidefiniteness in implicit solvers. Our approach is both faster than direct numerical methods, and more robust than approximate methods such as Gauss-Newton. Over the course of our analysis, we investigate physical interpretations for two separate notions of length. Finally, we showcase the stability of our analysis on challenging strand, cloth, and volume scenarios with large timesteps on the order of 1/40 s.
We thank the reviewers for their comments. This work was supported by Adobe, the Bungie Foundation, Teng and Han Family Fund, and National Science Foundation (IIS-2132280). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.