Verlet Integrator

Hi all 🙂

Currently the particle system support 3 integrators types (in english integrators are what actually advance particles in time)
and for many users that´s the kind of options that fall under the I-always-will-use-the-default-value category,
and while for many set ups different integrators provide very similar results, in others they could make the difference.

The simplest integrator, Euler, is very fast but not very accurate, internally Blender performs only one cycle of some calculations.

The second integrator, Midpoint , is sligthly slower because it performs 2 cycles but is more accurate than Euler and is the default integrator.

And the third , RK4 (Runge-Kutta) , as you may guess is the slowest and more accurate of them, and performs 4 cycles of calculations in Blender

The good news here is that I have found another integrator type that is as fast as the Euler integrator (the fastest) since it requires only one cycle of calculations and is more accurate than the Midpoint even, the error is of fourth order: The Verlet integrator  http://en.wikipedia.org/wiki/Verlet_integration#Basic_Verlet
have several advantages over the others and is very stable and fast, and gives realistic results.
with many particles interacting each others the Verlet integrator clearly shows the speed boost even over the Euler integrator.

the hand made patch is at http://www.pasteall.org/9364/diff

I have implemented it in Blender seamlessly and I suggest it as the default integrator, the previous integrators suffer from an increase of energy in time, note how the amplitude of each bounce is biger than the others in the previos integrators while in the Verlet is uniform as should behave in a conservative enviroment (no friction,damping,etc).

It is very easy to implement in Blender and is a small step toward improvement, hope you like it
Cheers Farsthary

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Verlet Integrator

10 thoughts on “Verlet Integrator

  1. toontje says:

    I think we need a full time mathematician for Blender. I have the feeling that a lot of the math are from the school books. Genscher found better and faster matrix math stuff for his smoke sim, and now this Vertlet Integrator. There is a lot of cutting edge math stuff being devised that just flies beneath the radar. A little patch with big results. Thanks man.

    Like

  2. where does this put cloth and hair, are they as easily integrated. It seems the most unified system would be the best system where all systems(e.g. cloth, hair, and particles)are unified under the same solver, working together not separate…so faster does not always mean better…….just a thought.

    still…this is really neat and good news, keep it up!

    Like

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