File this under fourier analysis + linear algebra = bad#ss.

Fourier transform of toes

On the right you’re seeing the configuration space of the toes as opposed to physical space of the toes.

Ponies

Take a 3-D mesh wireframe stallion and do the Fourier transform.

Now you have a summary of the position, so you can move hoof-leg-and-shoulder by just moving 1 point in the transformed space.

In other words the DFT takes you into the configuration space of the horsie. Inverse DFT takes a leg-and-hoof configuration and gives you back a wireframe horsie.

clustering

The discrete Fourier transform also helps sort out the clustering problem:

smoothing

From the slides, I don’t get what the connection is to (anti-fractal) smoothing. But…seahorses and seagulls:

PDF SLIDES via Artemy Kolchinsky

If you thought linear regression was a hammer for every nail … wait until you play around with the Fourier transform!

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