Physically Based Simulation

Physically based simulation generates motion by numerically solving the equations governing rigid bodies, deformable objects, cloth, and fluids, producing physically plausible behavior automatically.

Definition

Physically based simulation is the computation of motion by formulating and numerically integrating the differential equations of mechanics for the objects in a scene.

Scope

This topic covers rigid-body dynamics with collision detection and response, mass-spring and continuum models for cloth and deformable solids, grid- and particle-based fluid simulation, and the numerical integration schemes, particularly implicit methods, that keep these simulations stable.

Core questions

• How is the motion of colliding rigid bodies computed?
• How are cloth and deformable materials modeled?
• How are fluids simulated for visual effects?
• How are simulations kept numerically stable at large time steps?

Key concepts

• Rigid-body dynamics
• Collision detection and response
• Mass-spring and continuum models
• Cloth simulation
• Fluid simulation
• Implicit time integration

Key theories

Implicit integration for stability

Stiff systems such as cloth become unstable under explicit time stepping, so implicit integration is used to take large stable steps by solving a linear system each frame, a key enabler of practical cloth simulation.

Stable fluids

Fluid motion for graphics can be solved unconditionally stably by combining semi-Lagrangian advection with a projection step that enforces incompressibility, making real-time and visually convincing fluids feasible.

Clinical relevance

Physically based simulation produces the destruction, cloth, water, smoke, and crowd dynamics seen in film visual effects and games, and supports engineering visualization, virtual prototyping, and training simulators.

History

Rigid-body and deformable simulation developed through the 1980s and 1990s; Baraff and Witkin's implicit cloth method and Stam's stable-fluids solver, both from the late 1990s, made robust cloth and fluid simulation standard in production.

Key figures

• David Baraff
• Andrew Witkin
• Jos Stam

Seminal works

• stam1999
• baraff1998

Frequently asked questions

Why is simulation used instead of animating effects by hand?

Effects like cloth, water, and shattering involve far too many interacting elements to pose by hand, so simulating the physics produces convincing, automatically coordinated motion that would be impractical to keyframe.

Why can simulations blow up?

Numerically integrating stiff equations with steps that are too large amplifies errors until values diverge; implicit methods and careful time stepping are used to keep the simulation stable.