Smooth texture mapping

Maybe this is an obvious one. I am mapping images as textures onto curved surfaces. The surfaces are, of course, represented by a collection of triangular faces. The representation is sometimes rather coarse, and this shows in the appearance of the image. Is there a simple way to smooth the image? If not, the only solution seems to be to refine the mesh, which leads to my second question: can someone point me to some code that can handle this refinement, i.e. generate nodes that interpolate the geometry smoothly, and the associated triangles? I can code this, but I hate reinventing the wheel.


Perhaps post a screen shot demonstrating the problem?