Update:

I managed to work out a system by which I can calculate a 2D parametric function
to "draw" on the "global" UV-patch, determine which patch each particular point
is on, and what the uv coordinates are for that point on the patch.

Then I take those uv coordinates and use the Bernstein polynomials to map it
onto the Bezier patch on the surface of the torus.

Confused the hell out of me, took way longer than it should have, and some bugs
seem to have crept in, but all the code is there, and now I think I can go back,
refactor everything, tighten up the code a bit, and see where the errors are.

It's _supposed to be_ a noiseless torus with a coil wrapping around it 5 times -
but these things almost never work out right the first time around.

And I still need to write functions for partial derivatives to get tangent
vectors, and then cross those vectors to get the normals.

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