Towards Generalized Position-Based Dynamics

2025-11-28

AI Summary

Existing position-based dynamics (PBD) methods support only linear constraints, limiting their ability to model arbitrary nonlinear constitutive forces—such as high-resolution data-driven cloth or neo-Hookean hyperelasticity with inversion barriers. This work proposes a generalized PBD framework: by reformulating the implicit time integration equation, nonlinear internal forces are explicitly embedded into the PBD iteration loop while preserving the original constraint-solving structure. Nonlinear systems are solved efficiently via Gauss–Seidel–style iterations. Our method is the first to unify complex nonlinear material models within the PBD paradigm, enabling stable, penetration-free, high-fidelity deformation simulation. It achieves significant speedups over Newton’s method on high-resolution meshes—delivering both real-time performance and physically accurate behavior.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Extends position-based dynamics to handle arbitrary nonlinear force models
• Enables simulation of data-driven cloth models beyond existing PBD variants
• Applies generalized PBD to volumetric neo-Hookean elasticity with inversion barriers

Innovation

• Generalizes PBD for nonlinear force models
• Reformulates implicit integration using Gauss-Seidel
• Enables data-driven cloth and volumetric elasticity