Efficient GPU Cloth Simulation with Non-distance Barriers and Subspace Reuse

TL;DR

This paper proposes a major overhaul of this modality within the projective dynamics framework by leveraging an adaptive weighting mechanism inspired by barrier formulation, which does not depend on the distance between mesh primitives, but on the virtual life span of a collision event and thus keeps all the vertices within feasible region.

Abstract

This paper pushes the performance of cloth simulation, making the simulation interactive even for high-resolution garment models while keeping every triangle untangled. The penetration-free guarantee is inspired by the interior point method, which converts the inequality constraints to barrier potentials. We propose a major overhaul of this modality within the projective dynamics framework by leveraging an adaptive weighting mechanism inspired by barrier formulation. This approach does not depend on the distance between mesh primitives, but on the virtual life span of a collision event and thus keeps all the vertices within feasible region. Such a non-distance barrier model allows a new way to integrate collision resolution into the simulation pipeline. Another contributor to the performance boost comes from the subspace reuse strategy. This is based on the observation that low-frequency strain propagation is near orthogonal to the deformation induced by collisions or self-collisions, often of high frequency. Subspace reuse then takes care of low-frequency residuals, while high-frequency residuals can also be effectively smoothed by GPU-based iterative solvers. We show that our method outperforms existing fast cloth simulators by at least one order while producing high-quality animations of high-resolution models.

Figures (21)

• Figure 1: Fashion show. We present a new GPU-based cloth simulation framework with projective dynamics. Our method is able to simulate high-resolution cloth meshes at an interactive rate. With a non-distance-based barrier formulation, we can replace a large portion of traditional CCDs with the partial CCD procedure, which is much less expensive. The subspace reuse strategy relaxes the low-frequency errors effectively at the cost of single-digit milliseconds. Our method also features a residual forwarding trick to alleviate the damping issues generated by early termination and small-step line search filtering. In the teaser, we show an animated scene of the virtual fashion show. The model, dressed in a soft and light midi skirt, walks to the front and then turns around. These series of movements cause complex fabric dynamics, vividly showcasing the design concept of the garment. The garment is of high resolution and has $340$K vertices. The corresponding simulation involves over one million unknowns, and detailed local wrinkles can be well perceived. With a time step of $\Delta t = 1/200$ sec, the simulation runs at $4.8$ FPS. Please refer to the supplementary video for the corresponding animations.
• Figure 2: Bending strips w. and w/o subspace. We simulate a collision-free scene where a cloth strip bends under gravity. The model consists of $30$K DOFs. The resulting deformation is of low frequency, which is challenging for Jacobi-like methods. A subspace solve effectively resolves this issue: only $20$ A-Jacobi iterations are needed to fully converge the simulation, which otherwise takes over one thousand iterations. Because the bending stiffness is quite strong in this example, we need to assign a big SOR-like weight ($\omega = 0.9$) to dampen each A-Jacobi iteration. Our method runs over $300$ FPS for this example, while PD-IPC lan2022penetration is less than 0.5 FPS due to the large number of A-Jacobi iterations.
• Figure 3: Spectral distribution of residual errors (w/o collision). We plot the distribution of residual error over the first 100 modal bases of the strip test (Fig. \ref{['fig:beam']}). As shown at the top, the dominant deformation is low-frequency, which is efficiently solved within the subspace (bottom). On the other hand, A-Jacobi iterations are not effective in dealing with low-frequency residuals. 100 A-Jacobi iterations barely lower the low-frequency errors, while the high-frequency strains are well relaxed (middle).
• Figure 4: Subspace reuse. A piece of tablecloth (66K DOFs) drops on a wooden Armadillo. Over $30\%$ of vertices are involved in collision constraints.
• Figure 5: Spectral distribution of residual errors (w. collision). We visualize the distribution of residual errors over the first 100 modal bases of the rest-pose global matrix $\mathsf{H}$ when the tablecloth covers the Armadillo (as shown in Fig. \ref{['fig:armadillo']}). Subspace reuse does generate some low-frequency errors, but it still helps the convergence of the A-Jacobi significantly.