Towards Generalized Position-Based Dynamics

TL;DR

This paper generalizes position-based dynamics to handle arbitrary nonlinear force models, enabling more versatile and efficient real-time simulation of complex deformable bodies.

Contribution

It reformulates PBD to incorporate nonlinear forces via force-based implicit integration, broadening its applicability beyond linear constraints.

Findings

Enables simulation of data-driven cloth models not possible with traditional PBD.

Improves performance over Newton-based solvers at high mesh resolutions.

Demonstrates applicability to volumetric neo-Hookean elasticity with inversion barrier.

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.