发表机构
Kyoto University; The University of Tokyo（京都大学; 东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出CCFR碰撞处理方法，显式构建顶点独立的凸无碰撞区域，兼顾多类碰撞与接触，兼容XPBD框架，在多类模拟场景中展现高效通用的碰撞处理效果。
AI 中文摘要
凸无碰撞区域（Convex Collision-Free Regions，CCFR）是一种碰撞处理方法，它显式表示局部凸可行区域以确保不穿透。每个可行区域由周围的网格基元构型构建，包括边-边和顶点-面相互作用，所得凸区域表示当前构型下可接受的无穿透顶点位移。现有用于可变形体模拟的碰撞处理方法大多依赖可行性的隐式表示，导致要么在二次碰撞和余维接触上鲁棒性受损，要么与特定非线性优化方案紧密耦合。我们的方法在穿透发生前为每个顶点独立构建可行区域，不仅固有地考虑了主碰撞，还兼顾了二次碰撞和余维接触，实现了高度可扩展且可并行化的碰撞处理。这些可行区域独立于物理接触响应模型编码几何无穿透约束，CCFR不依赖非线性优化，且与扩展位置动力学（Extended Position-Based Dynamics，XPBD）等模拟框架兼容，这些框架在迭代更新期间不会显式维护内部可行性。CCFR的有效性在布料、头发、金属丝、粒子系统及余维接触场景中得到验证，展现出通用且高效的碰撞处理能力。
英文摘要
Convex Collision-Free Regions (CCFR) is a collision handling method that explicitly represents local convex feasible regions to enforce non-penetration. Each feasible region is constructed from surrounding mesh primitive configurations, including edge-edge and vertex-face interactions. The resulting convex region represents admissible non-penetrating vertex displacements at the current configuration. Existing collision handling methods for deformable body simulation have largely relied on implicit representations of feasibility, resulting in either compromised robustness for secondary collisions and codimensional contacts or tight coupling with specific nonlinear optimization schemes. Our formulation constructs feasible regions independently for each vertex, defined prior to penetration, inherently accounts not only for primary collisions but also for secondary collisions and codimensional contacts, enabling highly scalable and parallelizable collision handling. These feasible regions encode geometric non-penetration constraints independently of physical contact response models. CCFR does not rely on nonlinear optimization and is compatible with simulation frameworks such as Extended Position-Based Dynamics (XPBD) that do not explicitly maintain interior feasibility during iterative updates. The effectiveness of CCFR is demonstrated across cloth, hair, wire, particle systems, and codimensional contact scenarios, showing versatile and efficient collision handling.
