Towards Generalized Position-Based Dynamics

TL;DR

Problem: Position-based dynamics struggle with nonlinear energy models. Approach: Generalized PBD (GPBD) expresses implicit time integration as per-force displacements and solves a reduced Newton problem per force; XPBD equivalence emerges under linear-energy cases. Applications demonstrated: data-driven HYLC cloth and volumetric neo-Hookean elasticity with inversion barrier are supported in a GPU-accelerated GPBD pipeline, maintaining PBD flexibility. Impact: enables real-time simulation of complex nonlinear materials at high mesh resolutions, outperforming traditional Newton-based solvers in certain regimes and integrating with existing PBD workflows.

Abstract

The position-based dynamics (PBD) algorithm is a popular and versatile technique for real-time simulation of deformable bodies, but is only applicable to forces that can be expressed as linearly compliant constraints. In this work, we explore a generalization of PBD that is applicable to arbitrary nonlinear force models. We do this by reformulating the implicit time integration equations in terms of the individual forces in the system, to which applying Gauss-Seidel iterations naturally leads to a PBD-type algorithm. As we demonstrate, our method allows simulation of data-driven cloth models [Sperl et al. 2020] that cannot be represented by existing variations of position-based dynamics, enabling performance improvements over the baseline Newton-based solver for high mesh resolutions. We also show our method's applicability to volumetric neo-Hookean elasticity with an inversion barrier.

Figures (8)

• Figure 1: Qualitative comparison between our method GPBD and sperl2020hylc on HYLC material models: Stockinette drape (left) and Honeycomb stretch (right).
• Figure 2: 10% scaled Satin material $128 \times 128$ grid mesh (16641 verts, 32768 tris) with wrinkles.
• Figure 3: A log-log plot of the average frame time vs. mesh resolution for different simulation methods. Timings are averaged over 100 frames with a timestep of $10^{-4}\,\mathrm s$ for a cloth sheet with the HYLC Satin material model stretched from two sides.
• Figure 4: "Cloth stretched". $128\times128$ grid mesh(16641 verts, 32768 tris) results on data-driven cloth material. The reader is encouraged to compare these with sperl2020hylc Fig 16
• Figure 6: We perform various stress tests on a neo-Hookean energy model using a cube composed of $15^3$ and $20^3$ hexahedral cells.