Often in games, we treat light as having infinite speed, displaying the end result of our computations with it instantly. In this repo, I use a Navier-Stokes simulation to explore the opposite: declaring light as an object the user can create, and visualizing how its shape changes over time if we treat it as a high-density, high-velocity fluid.
I referred to Stam's classic paper on Navier-Stokes fluid simulations for the math, and have used code and inspiration from Muratori's Handmade Hero series for things like project organization and performance, down to some finer details like window management and drawing pixels onscreen. Relatedly, I built this from scratch in C++ (the better the performance, the more pixels we can afford to display). I call the .NET API directly for things like windowing, input, and drawing onscreen, and specify the libraries that I use in a batch file rather than using any external make utilities.
This is a program for Windows, and can be run by cloning this repo and running build/driver.exe.
From here, I'd like to play around to having this density measurement map to somewhere on a HSV scale, rendering this as colored light rather than in greyscale. I'd also be curious to see if we could speed this up by using a more direct method of solving for diffusion, and manually correcting for overflow: the Gauss-Seidel relaxation that I'm currently using is accurate, but at 20 passes per pixel is the biggest performance bottleneck. I would want to further optimize this (alongside adding more error checking and Windows compatibility) before using as any kind of shippable utility.