Once I understood non-linear vector spaces and coordinate transformations… wait what am I saying?

One day, I realized you can do cool stuff if you have geometry data as x, y, z:

t = x + y;

xt = sin(t);

yt = cos(t);

zt = sqrt(xt**2 + yt**2);

You’d only do it that way explicitly in a vertex shader—but congratulations, that’s a coordinate transformation!

Now do it with more xyzwqp’s, then, profit!

In my example, I compressed x+y down to one parameter. You’ll be combining 4 spacial dimensions into combinations of xyz for use with a rendering pipeline.

Or, alternatively projecting straight to xy. Not sure which is preferable.