PR-Cage consistently produces compact, tightly adhering cages on diverse geometric shapes, including thin plates, tubular structures, and models with high topological complexity.
Cages are fundamental structures in computer graphics, serving as versatile proxies for deformation, simulation, collision handling, neural parameterization, and multiresolution geometry abstraction. A high-quality cage must balance two competing objectives: minimizing face count for simplicity while maximizing tightness to maintain high geometric fidelity to the input mesh.
PR-Cage introduces a nested optimization framework for automated cage generation. The outer control layer uses a thickness parameter τ to define a feasibility region guided by the τ-offset surface, and progressively relaxes this parameter through a staircase schedule. The inner optimization extends the classical Quadric Error Metric framework with rigorous linear inequality constraints that suppress triangle degeneration and prevent normal flips. The algorithm relies only on edge collapses and edge flips, yielding efficient and robust cage generation.
Given a closed, oriented, manifold, self-intersection-free triangle mesh, PR-Cage greedily simplifies it into a lower-complexity bounding cage while maintaining geometric and topological validity.
The method is evaluated on 5,046 Thingi10K models and 5,508 ABC models, covering real-world meshes, CAD-like shapes, thin structures, sharp features, and high topological complexity.
Compared with Nested Cage, Broxy, BPShell, and Robust Cage, PR-Cage targets the simultaneous requirements of low triangle count, strict enclosure, manifoldness, watertightness, absence of self-intersections, and high surface adherence.
Strictly enclosing, tightly fitted cages preserve support at sharp features and reduce contact complexity while maintaining stable cloth interactions.
Cloth simulation: PR-Cage preserves stable contact where other proxies slide or collapse.
High-quality cages provide low-complexity collision proxies for simulations where geometric support and contact normals are critical.
Rigid-body simulation: cages serve as efficient proxies for contact-rich dynamics.
The progressive relaxation strategy can also be extended to high-fidelity constrained simplification by controlling the feasible region around the input surface.
Constrained simplification: the same feasibility relaxation principle enables compact geometry while preserving fidelity.
PR-Cage generates compact, low-poly cage representations that preserve the major geometric structures of the input mesh while significantly reducing triangle count.
Low Poly: PR-Cage produces simplified yet shape-preserving proxy meshes with clean geometric structure.
@article{wen2026prcage,
title = {PR-Cage: Progressive Feasibility Relaxation for Tight Bounding Cage Generation},
author = {Wen, Huibiao and Qin, Kaikai and Su, Xinxin and Mei, Jingcheng and Chen, Shuangmin and Deng, Chongyang and Tu, Changhe and Xin, Shiqing and Wang, Wenping},
journal = {ACM Transactions on Graphics},
volume = {45},
number = {4},
article = {149},
year = {2026},
month = {August},
pages = {16}
}