Position-Based Dynamics

A simulation method that satisfies constraints by directly correcting object positions, fast and stable, popular for cloth and soft bodies.

Position-Based Dynamics was proposed by Matthias Müller and colleagues (then at the physics-engine company AGEIA) at the VRIPHYS workshop in 2006. Conventional simulation first computes forces, then integrates acceleration into velocity and position; with a large timestep this easily overshoots or even diverges. PBD skips the force-and-velocity layer entirely: it predicts each particle's new position from inertia, then checks each constraint in turn — such as “the distance between two points must stay fixed” or “this point cannot pass through the ground” — and directly projects any violating point back to a valid position; after a few iterations, velocity is derived from the position change. It is stable, controllable, and handles collisions simply, and was first used for real-time cloth in games. Its drawback is that material stiffness drifts with the number of iterations and the timestep; in 2016, NVIDIA's Macklin and colleagues introduced XPBD, which adds compliance (the inverse of stiffness) and Lagrange multipliers so stiffness no longer depends on either, while also allowing constraint forces to be estimated. NVIDIA's Newton physics engine includes an XPBD solver that can simulate both rigid and soft bodies.

ExampleTo simulate a tablecloth, discretize the cloth into a grid of particles, add a “fixed distance” constraint between neighboring particles, and each step pull any over-stretched edge back — after a few iterations, the cloth naturally drapes instead of stretching indefinitely.

Also called

PBD, XPBD, Extended Position-Based Dynamics

Related

Cloth Simulation · Deformable-Body Simulation · Constraint Solver · Physics Engine · Newton Physics Engine · Projected Gauss-Seidel

Sources

Position Based Dynamics (Müller et al., VRIPHYS 2006)
XPBD: Position-Based Simulation of Compliant Constrained Dynamics (Macklin et al., MIG 2016)
Newton Physics 文档：Solvers（SolverXPBD） (Chinese)

As of

2026-09