Stretching a rectangle into a torus

Ivan Cnop
icnop@vub.ac.be

Simple programming

for stretching a rubber rectangle into a torus. 
The animation is best viewed cyclically.

rm = 2; rn =  .8;
Block[{n = 1}, 
      Do[ParametricPlot3D[{(rm + rn Cos[v]) Cos[
                  u], (rm + rn Cos[v]) Sin[u], 
              rn Sin[v]}, {u, -((n π)/24), ((n π)/24)}, {v, -((n π)/24), ((n π)/24)}, 
            PlotRange -> {{-3, 3}, {-3, 3}, {-1, 1}}, 
            ViewPoint -> {-4, 1, 2}] n++, {24}]]

Question

Is it possible to modify the parametric plot to obtain a sphere?

Doing this will exhibit strange behavior near the poles, where parallel lines become more dense.