Mapping a picture on a donut or a Hopf torus

The donut torus

Given a number (s \geqslant 1), the
following map:
[ (u, v) \mapsto (x, y, z) = \frac{\Bigl(s\cos\frac{u}{s},
s\sin\frac{u}{s}, \sin v\Bigr)}{\sqrt{s^2+1}-\cos v} ]
is …