Verlet Cloth Banner

About this animation

Verlet integration is the reason cloth simulations are short enough to read: there is no velocity stored anywhere, only the previous position, and the motion is whatever gap sits between that and the current one. Position updates therefore stay stable under constraints that would make a velocity-based integrator oscillate. The same property is the trap everyone falls into. Because velocity is implied rather than stored, assigning a new position to a particle without moving its previous position by the same amount tells the system that the particle covered that entire distance in one step — so dragging the cloth with a pointer, or clamping a point to a floor, injects an enormous impulse and the sheet detonates. Two more details separate a working cloth from a rubbery one. The distance constraints have to be relaxed several times per step, because satisfying one link breaks the link beside it; three to five passes converge, and far more only makes the sheet rigid and jittery. And the timestep must be fixed, since implied velocity is measured per step rather than per second: feeding a variable frame delta into Verlet silently rescales every velocity in the system, so a single long frame throws the cloth off screen. An accumulator runs whole steps at a constant delta and carries the remainder, with the incoming delta clamped so a backgrounded tab cannot return and run hundreds of steps at once. One diagonal brace per cell stops the mesh folding flat like a parallelogram, and pinning two or three fixings rather than the whole top edge is what makes it read as a hanging object instead of a stretched texture.