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VFX · 45 min
Integration Schemes for Particles
IntermediateNeeds: VectorsNeeds: Forces
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You will be able to
- Compare Euler, semi-implicit Euler, Verlet and RK4 by stability and cost.
- Predict when a solver will explode and why.
- Pick a scheme appropriate for a given VFX budget.
The concept
Explicit Euler adds energy and blows up on stiff forces. Semi-implicit Euler (update velocity first, then position) is nearly free and vastly more stable — which is why almost every game particle system uses it. Verlet is position-based and naturally handles constraints. RK4 is accurate but costs four force evaluations per step, so it is rare in real time.
In your engine
Niagara's Solve Forces and Velocity module is semi-implicit Euler; substepping is exposed on the emitter.
Practice (4)
Concept check
The difference between explicit and semi-implicit Euler is:
Predict the result
A spring simulation explodes at 30 fps but is stable at 120 fps. Cheapest correct fix?
Tune the value
How many force evaluations per step does RK4 require?
Find the bug
Verlet particles pass through thin colliders at high speed. Correct fix?
Knowledge check
01Explicit Euler tends to:
02Verlet stores:
03Substepping trades:
04Most shipping game particle systems use:
Build challenge
Implement the same falling-and-colliding particle setup with semi-implicit Euler and Verlet. Find the timestep at which each first becomes visibly unstable and report both numbers.
SELF-CHECK RUBRIC