S4R: Scaling for Rigid-Body Interpenetration Resolution

Abstract:Rigid-body interpenetration frequently occurs in procedurally assembled and generated scenes and must be removed before downstream applications such as physical simulation. We present S4R (Scaling for Rigid-Body Interpenetration Resolution), a scale-continuation method for static interpenetration repair. S4R first uniformly shrinks each body about a fixed reference center to a small initial scale, at which the layout is penetration-free, and then restores full scale through a sequence of minimum-norm convex contact quadratic programs (QPs) that target the linearized separation margin during continuation. Resolution thereby replaces one deep correction with a sequence of shallow-contact subproblems. A conservative scale-event bound and frozen-witness gap predictions cut the number of exact mesh queries; the continuation then ends with a full-scale evaluator check and bounded tail refinement. We evaluate S4R on Kubric, HY3D-Bench, and Thingi10K using a shared mesh-level evaluator and a unified per-scene timing protocol. In the main comparisons on all three benchmarks, up to N=5000 bodies, S4R reaches zero reported penetration with displacement that stays small and nearly independent of scene size, and at the lowest wall time within each hardware tier among the compared methods. A GPU implementation extends these results to large-scale scenes. Our code and data can be found on our project page: this https URL.

ACM Transactions on Graphics 45(6), Article 197 (SIGGRAPH Asia 2026). Project page: this https URL

Graphics (cs.GR); Computational Geometry (cs.CG); Robotics (cs.RO)

I.3.5; I.3.7; I.6.8

arXiv:2609.20524 [cs.GR]

(or arXiv:2609.20524v1 [cs.GR] for this version)

https://doi.org/10.48550/arXiv.2609.20524 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

https://doi.org/10.1145/3842510 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.