Volumetric Homogenization for Knitwear Simulation

TL;DR

This paper introduces a volumetric homogenization method for knitwear simulation that models yarn-level effects locally, enabling realistic, fast animations that match yarn-level accuracy while significantly improving computational efficiency.

Contribution

The paper presents a novel volumetric homogenization scheme with a GPU-friendly model and a domain-decomposed solver, achieving high-fidelity knitwear simulation at much faster speeds.

Findings

Realistic knitwear animations matching yarn-level quality.

Simulation speed is hundreds of times faster than yarn-level methods.

Effective modeling of bending and twisting effects through local homogenization.

Abstract

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.