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Small Steps in Physics Simulation
Miles Macklin, Kier Storey, Michelle Lu, Pierre Terdiman, Nuttapong Chentanez, Stefan Jeschke, Matthias Muller
Shows that many small substeps with simple per-step constraint projection outperforms fewer large-step implicit integration for cloth and soft bodies.
Abstract
In this paper we re-examine the idea that implicit integrators with large time steps offer the best stability/performance trade-off for stiff systems. We make the surprising observation that performing a single large time step with n constraint solver iterations is less effective than computing n smaller time steps, each with a single constraint solver iteration. Based on this observation, our approach is to split every visual time step into n substeps of length Δt/n and to perform a single iteration of extended position-based dynamics (XPBD) in each such substep. When compared to a traditional implicit integrator with large time steps we find constraint error and damping are significantly reduced. When compared to an explicit integrator we find that our method is more stable and robust for a wider range of stiffness parameters. This result holds even when compared against more sophisticated implicit solvers based on Krylov methods. Our method is straightforward to implement, and is not sensitive to matrix conditioning nor is it to overconstrained problems.
How to read this
- Category
- Method: a time-integration strategy for physics simulation
- Contributions
- The observation that many small substeps with one constraint iteration each beat a single large step with many iterations
- A substepping scheme applying one iteration of XPBD per substep to reduce constraint error and damping
- Demonstrated improved stability and robustness over explicit and sophisticated implicit (Krylov-based) solvers across a wide stiffness range
- Context
- Directly extends XPBD (Macklin et al. 2016) and re-examines the conventional wisdom that large-step implicit integrators give the best stiffness/performance trade-off.Builds on: XPBD: Position-Based Simulation of Compliant Constrained Dynamics
- Correctness
- The central claim is shown empirically for stiff cloth and soft bodies and argued via reduced damping and conditioning insensitivity; it is a trade-off result, so the substep count and benefits still depend on the stiffness and contact regime tested.
- Clarity
- Notably clear and easy to implement; a first pass conveys the core insight, a second pass clarifies the substep/XPBD formulation and the Verlet interpretation.
- How to read it
- Read the abstract and core argument first to grasp why substepping reduces damping, then do a second pass on the per-substep XPBD update and comparisons if you plan to adopt or benchmark it.
Built upon by
Nothing yet.
Related work
- Efficient and Stable Approach to Elasticity and Collisions for Hair Animation 2015 / DigiPro
- Robust Treatment of Collisions, Contact and Friction for Cloth Animation 2002 / SIGGRAPH
- Position Based Dynamics 2007 / JVCA
- Large Steps in Cloth Simulation 1998 / SIGGRAPH
Keywords
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