The Polynomial That Fixed 30 Years of Cloth Simulation
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ZOZO, Japan's largest fashion e-commerce platform, published a physics solver in ACM Transactions on Graphics that addresses a 30-year-old cloth simulation bug. The core fix replaces the logarithmic barrier function used in Incremental Potential Contact (IPC) with a cubic polynomial. The log barrier's second derivative grows unboundedly near contact, causing Newton system ill-conditioning and solver instability under tight strain limits. The cubic barrier's curvature is bounded at 6κ/d̂², keeping the Newton system well-conditioned. A second innovation dynamically couples barrier stiffness to local elastic properties per element, preventing the barrier and elasticity from fighting each other. The result handles 184 million simultaneous contact pairs without interpenetration. The post includes Python code demonstrating the condition number difference between the two approaches on a 2D cloth drape test.
