In this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any decoupling. Self-collisions are modeled in a natural way that allows considering the thickness of cloth without introducing unwanted oscillations. The discretization of the equations of motion leads naturally to a sequence of quadratic problems with inequality and equality constraints. In order to solve these problems efficiently, we develop a novel active-set algorithm that takes into account past active constraints to accelerate the resolution of unresolved contacts. We put to a test the developed collision procedure with diverse scenarios involving static and dynamic friction, sharp objects, and complex-topology folding sequences. Finally, we perform an experimental validation of the collision model by comparing simulations with recordings of real textiles as given by a $\textit{Motion Capture System}$. The results are very accurate, having errors around 1 cm for DIN A2 textiles (42 x 59.4 cm) even in difficult scenarios involving fast and strong hits with a rigid object.

翻译：本文提出了一种专门用于模拟不可延展纺织品的碰撞模型。该模型同时考虑摩擦、接触和不可延展性约束，无需进行解耦处理。自碰撞以自然方式建模，既能考虑织物的厚度，又不会引入不必要的振荡。运动方程的离散化自然导出一系列带不等式和等式约束的二次规划问题。为高效求解这些问题，我们开发了一种新型有效集算法，该算法利用历史有效约束来加速未解决接触的收敛。我们通过涉及静态/动态摩擦、尖锐物体以及复杂拓扑折叠序列的多种场景对开发的碰撞流程进行了测试。最后，我们通过将模拟结果与真实纺织品在$\textit{运动捕捉系统}$下的记录进行对比，完成了碰撞模型的实验验证。结果显示出极高的精度，即使面对刚性物体快速强力撞击等困难场景，对DIN A2尺寸纺织品（42 × 59.4厘米）的误差也仅约1厘米。