Hi! This is a toy project I'm using to play with rust, stats, and images. The problem I wanted to solve - how can we visualize functions of R3, like a multivariate normal distribution (MVN), or a gaussian mixture model made of MVNs?
Here is an idea: place a camera at some location, an for each pixel of the camera, cast a ray through the distribution. Integrate the value of the function along that ray. I think this technique is called volumetric rendering?
The best way to numerically integrate a function is to know both the function itself and its first derivative - together these do a good job of estimating the area under the curve. So, I wanted to try also implementing automatic differentiation, so that we would get derivatives for free on any R3 function. Today, I'm still too confused about how AD works outside the context of functions from R1 to R1, so I don't end up relying on the derivatives during numerical integration. :)
Here are renderings of a gaussian mixture PDF, from a camera rotating around.
I'm plotting the value linearly into Red and Green, and I plot the log of the value into Blue. I love this trick for highlighting the function's true value while allowing you to see the lower-value features that would otherwise be obscured by the larger values.
At the request of Scott Steele from Rust DC, , a stereographic render. Cross your eyes to see the blobs popping out at you.
This final one is a rendering of the gradient of the PDF. The x derivitate is in Red, the y derivative is in Green and z is in Blue.
