How to write on a surface?

Question

How do I include text on a curved surface? For example, and as a starting point, how can I reproduce the following image

I've seen some examples where people geometrically described letters to do this, for example, the code

R = 10; r = 3;
map[p1_, p2_] := {R Sin[p1] + r Cos[p2] Sin[p1], 
   R Cos[p1] + r Cos[p2] Cos[p1], r Sin[p2]};
charA2D[p_, pos_, size_] := 
  Plus[#, pos] & /@ {{0.5 p, p}, {0.5 + 0.5 p, 1 - p}, {0.25 + 0.5 p, 
     0.5}};
txt[p_] := Join[charA2D[p, {0, -.5}, 1], charA2D[p, {1.1, -.5}, 1]];
g1 = {Graphics3D[Thickness[0.02]], 
    ParametricPlot3D[map @@@ txt[p], {p, 0, 1}]} // Show;
g2 = ParametricPlot3D[map[p1, p2], {p1, 0, 2 Pi}, {p2, 0, 2 Pi}];
Show[g2, g1]

gives the string "AA" inscribed on the surface of a torus

This, however, seems a bit too complicated. Using the raw text as an image (.SVG, for example), we could perhaps simply use the mapping of photographic images to 3D surfaces, gives something like

I wonder if there is a more straightforward tool for text and strings. Any ideas?