This paper presents volumetric homogenization, a spatially varying homogenization scheme for knitwear simulation. We are motivated by the observation that macro-scale fabric dynamics is strongly correlated with its underlying knitting patterns. Therefore, homogenization towards a single material is less effective when the knitting is complex and non-repetitive. Our method tackles this challenge by homogenizing the yarn-level material locally at volumetric elements. Assigning a virtual volume of a knitting structure enables us to model bending and twisting effects via a simple volume-preserving penalty and thus effectively alleviates the material nonlinearity. We employ an adjoint Gauss-Newton formulation[Zehnder et al. 2021] to battle the dimensionality challenge of such per-element material optimization. This intuitive material model makes the forward simulation GPU-friendly. To this end, our pipeline also equips a novel domain-decomposed subspace solver crafted for GPU projective dynamics, which makes our simulator hundreds of times faster than the yarn-level simulator. Experiments validate the capability and effectiveness of volumetric homogenization. Our method produces realistic animations of knitwear matching the quality of full-scale yarn-level simulations. It is also orders of magnitude faster than existing homogenization techniques in both the training and simulation stages.

中文翻译：

---

用于针织品模拟的体积均质化


本文介绍了体积均质化，这是一种用于针织品模拟的空间变化均质化方案。我们的动机是观察到宏观尺度的织物动态与其潜在的针织图案密切相关。因此，当针织复杂且不重复时，对单一材料的均质化效果较差。我们的方法通过在体积元件处局部均质纱线级材料来应对这一挑战。分配针织结构的虚拟体积使我们能够通过简单的体积守恒惩罚来模拟弯曲和扭曲效应，从而有效地减轻材料的非线性。我们采用伴随高斯-牛顿公式 [Zehnder et al. 2021] 来应对这种逐元素材料优化的维度挑战。这种直观的材料模型使正向模拟对 GPU 友好。为此，我们的管道还配备了一个为 GPU 投影动力学设计的新型域分解子空间求解器，这使得我们的模拟器比纱线级模拟器快数百倍。实验验证了容量均质化的能力和有效性。我们的方法生成了逼真的针织品动画，与全尺寸纱线级模拟的质量相匹配。在训练和模拟阶段，它也比现有的同质化技术快几个数量级。