Sleeping & Stability

In a stack of 100 boxes, only the top one moves typically. The rest can SLEEP.

Sleep heuristic:

• Body's velocity below threshold for N consecutive frames → sleep.
• Skip simulation for sleeping bodies.
• Wake on contact / impulse from another body.

Dramatic perf win for static-heavy scenes (rooms full of boxes).

Numerical stability:

• Tiny velocities accumulate over time (Euler error).
• After many frames, motion deviates from physical reality.
• Verlet is more stable.
• Substepping: run 2-4 sub-steps per frame for stiff systems.

Stiff constraints:

• High spring constants → small dt needed → instability.
• Implicit integration: Verlet, position-based dynamics.
• Or: lower constants + iterations.

Stacking stability:

• N stacked boxes: tower of impulses.
• Iterative solver needs O(N) iterations per frame to fully stabilize.
• Without enough: jitter or sinking.

Solutions:

• More iterations (8-30 typical).
• Warm starting: reuse last frame's impulse as initial guess.
• Position-based: solve at position level, not velocity.
• Specialized stack stabilization.

Tunneling:

• Fast-moving body passes through thin object in one timestep.
• Common with bullets / fast platforms.

Solutions:

• Smaller timestep.
• Continuous collision detection (CCD): swept volumes.
• Conservative advancement: cast bodies along velocity, find first hit.

Box2D's CCD:

• For "bullet" objects only (flagged).
• Solver does extra check.
• Small perf cost.

Determinism:

• Same input → same output.
• Critical for networked games.
• Float order-of-ops matters: parallel = non-deterministic.
• Solutions: fixed point math, or carefully-ordered float ops.

Modern engines balance: speed, accuracy, stability, feature set.