Efficient Simulation through Linear Algebra
I spent a lot of time working on a project in which physically plausible simulation of soft materials with pressure chambers was a key part, and in doing so, we managed to improve a part of our simulation by a significant amount. I was very happy with how this small part of the whole system turned out, and I’ve been wanting to share it for a while.
A fair warning though, we need to spend a little time setting up the context in order to see why this is a thing that can happen very naturally, as opposed to a magic algebraic trick that we can pull out of a hat.
If you haven’t seen physically based simulations before, don’t worry too much about the details. It helps if we can get on the same page regarding why we are even here in the first place, but the details of the context really doesn’t matter for the point I’m trying to get across.
If you have seen physically based simulations before, also don’t worry too much about the details. There isn’t anything fancy going on here; no second order elements, no fancy time stepping, no dynamics, basically nothing that hasn’t been around for 20 years1. The trick is somewhat fancy though, to me anyways.
