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.
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.
The discrete Fourier transform also helps sort out the clustering problem:
From the slides, I don’t get what the connection is to (anti-fractal) smoothing. But…seahorses and seagulls:
PDF SLIDES via Artemy Kolchinsky