Volumetric Homogenization for Knitwear Simulation

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.

Figures (19)

• Figure 1: Volumetric homogenization pipeline. Given an input rod-based yarn model, our pipeline generates a volume mesh encapsulating the entire yarn structure. We lump the yarn-level mass to the mesh's nodal points so that the inertia effect(\ref{['eq:g']}) can be isolated. The yarn-to-mesh and mesh-to-yarn shape fitting facilitates us to define the loss function for homogenization. Per-element material parameters are obtained via an adjoint Gauss-Newton procedure, in a sample-by-sample manner. With a domain-decomposed PD solver, our method not only produces high-quality animation of knitwear garments that is visually similar to the full-scale YLS result but also achieves these results two orders of magnitude faster.
• Figure 2: Mass lumping. We estimate lumped mass at each mesh node via the line integral of the shape function over the embedded yarn segment.
• Figure 3: Harmonic initialization. We design a progressive initialization strategy based on Harmonic bases of the volume mesh. By projecting the material vector into the Harmonic subspaces of different ranks, volumetric homogenization always finds a reliable initial value for the two-stage elasticity fitting procedure.
• Figure 4: Harmonic material bases. We leverage mesh Harmonics to explore a good initial material variation from low frequency to high frequency. This figure visualizes the first ten basis vectors.
• Figure 5: DOF types with domain decomposition. The fabric is decomposed into two domains corresponding to two different knitting patterns. It is required that duplicated boundary DOFs at domains must always be equal to each other.