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Position Based Dynamics
Matthias Muller, Bruno Heidelberger, Marcus Hennix, John Ratcliff
Position-based simulation framework for real-time cloth, hair, and deformable bodies widely adopted in games and interactive applications.
Abstract
This paper introduces position-based dynamics, a constraint-based simulation approach that works directly with vertex positions rather than forces or velocities, enabling unconditional stability and direct control of object deformations. The method projects constraints by solving nonlinear equations iteratively using a Gauss-Seidel-like approach and naturally conserves linear and angular momentum for internal constraints. A real-time cloth simulator demonstrates the approach, supporting features like two-way rigid body interaction, self-collision, and independent control of bending and stretching properties through constraint formulation.
How to read this
- Category
- Method / framework: position-based dynamics
- Contributions
- A constraint-based simulation approach that works directly on vertex positions rather than forces or velocities, giving unconditional stability and direct control of deformation.
- Iterative Gauss-Seidel-like constraint projection that conserves linear and angular momentum for internal constraints.
- A real-time cloth simulator supporting two-way rigid-body interaction, self-collision, and independent bending and stretching control.
- Context
- A general position-based alternative to force- and velocity-based dynamics, providing a unified constraint-projection framework for cloth, hair, and deformable bodies.
- Correctness
- Demonstrated through a real-time cloth simulator with the stated stability and control benefits; constraint stiffness behavior is iteration- and timestep-dependent, which a reader should keep in mind as a known characteristic of the projection scheme.
- Clarity
- Very accessible and widely cited as an entry point; a first pass conveys the whole idea, a second pass for the constraint-projection details and specific constraint formulations.
- How to read it
- First pass to internalize the position-projection loop and why it is stable; second pass on the constraint definitions if you are implementing PBD, since this is the canonical reference.
Builds on
Nothing in the archive, this is a starting point.
Built upon by
- Wrinkle Meshes 2010
- Projective Dynamics: Fusing Constraint Projections for Fast Simulation 2014
- Strain Based Dynamics 2014
- Unified Particle Physics for Real-Time Applications 2014
- Position-Based Skinning for Soft Articulated Characters 2015
- XPBD: Position-Based Simulation of Compliant Constrained Dynamics 2016
- Two-Way Coupling of Skinning Transformations and Position Based Dynamics 2023
Related work
- Projective Dynamics: Fusing Constraint Projections for Fast Simulation 2014 / SIGGRAPH
- Wrinkle Meshes 2010 / SCA
- Robust Treatment of Collisions, Contact and Friction for a Skinned Cloth Simulation 2002 / SIGGRAPH
- Strain Based Dynamics 2014 / SCA
Keywords
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