I was working on a little job today with a 2D temporally variant scalar field.

You know, B&W footage.

I needed to find the parts of the data that were changing the most and compare them to the overall data and the maximum delta.

What I ended up with, once Ben pointed it out to me, was a simple example of calculus laid out in a couple tools.   The simplest case is just taking the frames I have and interpolating the same number of frames, so there’s no missing samples.  It’s silly, really.

But you can try it with other sampling, so there’s also an example of a Sobel filter, with a 1D kernel perpendicular to the normal 2D one.  Cute really.

If you checked out my interactive smoothing comp, you can see how I used a Sobel filter to make the forward facing laser pointer by looking at the differentiation of the R and G channels over time.  Same idea, just different way of expressing the temporal dimension.

I’m tossing in a Laplacian filter too, just for fun, it’s not useful for the calculus part, but it was easy to do, and shows how you can change the kernel to make different effects.  It’s possible to also evaluate 2D or 3D kernels this way, too.  The temporal offsets can be combined with spatial offsets so you could make a 3D blur filter, or a 3D sharpen.  Or a 3D Unsharp Mask, as I’ve also included.

Because we’re often trying to simulate small wet transparent things we rely pretty heavily on stochastic raytracing. We can handle transparency, large light sources, depth of field, light scattering, etc. all at the same time. It’s a general purpose setup that works well for a broad range of “soft” phenomenon. Brazil is pretty fast, but there are limits to our patience, especially since the sampling isn’t reusable. Once you make any change at all to the scene, you essentially have to start over. So we try to get a lot of revisions done to refine a look and still keep the speeds good so we can get those revisions turned around quickly.

When you reduce the number of samples, you get a large increase in speed, but the downside is aliasing, which generally looks like noise, since it is stochastic.

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