[patrickthebold]

Just a thought: Make the velocity of the path constant. There should be some way to take a derivative an set it to a constant and solve for z. ( or really reparameterize the curve t' = f(t)) so the velocity is constant.

Actually, now that I think about it, choosing z = c * t is kind of both influencing how the path is parameterized as well as the path carved out on the sphere.