How can I generate UVs from a direction vector field?

I’ve been recently trying to recreate this line-hatching/smearing effect by Pedro Borges (https://x.com/peteborks/status/1839279984625496545
https://x.com/peteborks/status/1843676863920558529), so far I’ve managed to get the velocity buffer into a render target which gives me the directions of each pixel relative to the screen but now I have a problem, how do I transform these directions into UVs?

This is how the direction vector field currently looks (its current range goes from -1 to 1)

Gif

This is how I think it should look (I’ve just put the field through the VectorToRadialValue node, this is solution doesnt work since it creates new issues for when an object moves linearly)

In these pictures I’ve used an sphere rotating but my intent is for it to work on an animated mesh like in the Pedro Borges posts.