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Projective Dynamics: Fusing Constraint Projections for Fast Simulation
Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, Mark Pauly
Fast implicit simulation framework using local-global constraint projection, unifying cloth, soft bodies, and position-based dynamics.
Abstract
We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many different types of constraints. We propose specially designed energy potentials that can be solved efficiently using an alternating optimization approach. Inspired by continuum mechanics, we derive a set of continuum-based potentials that can be efficiently incorporated within our solver. We demonstrate the generality and robustness of our approach in many different applications ranging from the simulation of solids, cloths, and shells, to example-based simulation. Comparisons to Newton-based and Position Based Dynamics solvers highlight the benefits of our formulation.
How to read this
- Category
- Method: implicit-integration simulation framework (local-global solver)
- Contributions
- A method for implicit time integration that bridges nodal Finite Element methods and Position Based Dynamics into one simple, robust solver
- Specially designed energy potentials solved efficiently via an alternating (local-global) optimization, plus continuum-based potentials
- Demonstrations across solids, cloth, shells, and example-based simulation, with comparisons to Newton-based and Position Based Dynamics solvers
- Context
- Generalizes and grounds Position Based Dynamics (Mueller et al.'s 'Position Based Dynamics') in a continuum-mechanics energy formulation, sitting between PBD and full nodal FEM.Builds on: Position Based Dynamics
- Correctness
- Claims of speed, robustness, and accuracy are supported by comparisons to Newton and PBD solvers; note the efficiency hinges on the special quadratic-friendly potentials and the local-global split, so behavior for energies that do not fit that structure is outside the demonstrated scope.
- Clarity
- Clearly written; a first pass conveys the local-global idea and the PBD/FEM bridge, and a second pass pays off for the constraint-projection energy derivation.
- How to read it
- Read for the alternating local-global formulation and the constraint-projection energies; a second pass on the potential design and the global-step linear solve is worth it if you plan to implement or extend it.
Builds on
Built upon by
- Vivace: A Practical Gauss-Seidel Method for Stable Soft Body Dynamics 2016
- Hyper-Reduced Projective Dynamics 2018
- Projective Skinning 2018
- Smeat: ADMM Based Tools for Character Deformation 2018
- Fast Simulation of Deformable Characters with Articulated Skeletons in Projective Dynamics 2019
- Latent-space Dynamics for Reduced Deformable Simulation 2019
- Projective Dynamics with Dry Frictional Contact 2020
- BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics 2025
Related work
- Nonlinear Cloth Simulation with Isogeometric Analysis 2024 / CASA
- Position Based Dynamics 2007 / JVCA
- Multi-Resolution Isotropic Strain Limiting 2010 / SIGGRAPH Asia
- Strain Based Dynamics 2014 / SCA
Keywords
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