Why are blender simulations jittery on small scale?

Question

It's been common wisdom that, when a rigid body, or cloth simulation gets jittery, it helps to just scale up the entire scene and the simulations start to behave more predictably. And while I have myself experienced that this is good advice, I don't quite understand why. Since the simulations are just calculations, they should behave exactly the same when everything is 10x smaller, with mass, speed, and so on adjusted accordingly. And yet the results differ wildly. Could someone explain why?

Answer 1

Jitter is often caused by floating point instability. If you're not familiar with floating point and the problems which cause this, I have attempted to write a high level overview which I hope might be helpful. However the standard disclaimers apply; I'm not an expert on physics simulation nor a bullet or blender developer nor an authority in any sense.

Bullet, the physics library blender uses for rigid body simulation, uses floating-point arithmetic. Floating point numbers have the impossible task of representing all real numbers in a fixed number of bits, and so not all numbers are actually representable; arithmetic in floating-point is almost always rounded to a number a little different from the exact correct answer.

This tends to translate to jitter in rigid body simulations when an object is in constant contact with another object. Imagine that the precise position the object should sit so that it exactly collides with a collider (i.e. is neither inside it nor outside) is not representable. When calculating the next position for the object, bullet inevitably calculates a position inside or outside the collider. Lets say its inside; then a collision occurs and the object gets pushed outside, and then gravity (or any number of other forces) pushes the object back again and an oscillation starts. If the velocity of the object starts increasing, the jitter can quickly magnify in a positive feedback loop.

This is of course a simplified version of events, there are countermeasures which bullet employs to avoid this sort of thing and I don't pretend to know half of them (but Split Impulse is one you have control over from blender) but there are also many other ways things can go wrong in any complex simulation with multiple simultaneous interactions.

As to why shrinking things tends to help, that is likely because the standard format for floats (IEEE 745) is clever and manages to offer a higher density of representable numbers near zero; the logic being that larger errors matter less with bigger numbers. As for why making things larger can help; that may have more to do with collision detection being better behaved with a reasonable number of simulation steps for the size and velocities of the objects involved. (even with all the physics properties scaled, properties such as substeps and behavior of things like split impulse may not scale in a perfectly analogous way.. but i'm at the end of my knowledge here)

It would be possible to not use floating point arithmetic, but writing the physics engine would likely be harder especially while achieving comparable performance. The author of the bullet physics library has commented on this possibility and suggests it would be a completely separate engine.