S4R: Scaling for Rigid-Body Interpenetration Resolution

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 ( S caling for Rigid-Body Interpenetration R esolution), 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 [Greff et al. 2022], HY3D-Bench [Team Hunyuan3D et al. 2026], and Thingi10K [Zhou and Jacobson 2016] 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: https://frank-zy-dou.github.io/projects/S4R/index.html.