Real-Time 3D Topological Braiding Simulation with Penetration-Free Guarantee

We present an efficient approach for simulating 3D topological braiding while guaranteeing non-penetration. Our method combines eXtended Position-Based Dynamics (XPBD) with Incremental Potential Contact (IPC), leveraging XPBD's efficiency, robustness, and numerical stability with IPC's non-penetration capabilities. However, incorporating IPC introduces nonlinearity errors that result in instability, numerical issues, and CCD failures in stiff systems. To resolve this, we propose a correction method that ensures non-penetration while retaining XPBD's benefits, resulting in an efficient algorithm for simulating 3D yarn braiding with correct topology. We also propose a parallel implementation of our algorithm on the GPU, achieving real-time simulation of complex braiding. Experimental results show that our method outperforms traditional XPBD in terms of plausibility and non-penetration guarantees while maintaining comparable efficiency and enhanced robustness under extreme collision conditions.