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 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.

翻译：本文提出体积均质化方法，一种用于针织品仿真的空间变化均质化方案。我们的研究动机源于观察到宏观织物动力学与其底层编织图案存在强相关性。当编织结构复杂且非重复时，向单一材料的均质化效果会显著降低。本方法通过在体积单元局部对纱线级材料进行均质化来应对这一挑战。通过为编织结构分配虚拟体积，我们能够通过简单的体积保持惩罚项来模拟弯曲和扭转效应，从而有效缓解材料非线性问题。我们采用伴随高斯-牛顿公式化方法来解决这种逐单元材料优化的维度挑战。这种直观的材料模型使得正向仿真适合GPU加速。为此，我们的流程还配备了专为GPU投影动力学设计的新型域分解子空间求解器，这使得我们的仿真器比纱线级仿真器快数百倍。实验验证了体积均质化的能力与有效性。我们的方法能够生成与全尺度纱线级仿真质量相当的逼真针织品动画，且在训练和仿真阶段都比现有均质化技术快数个数量级。