Hi Finema, the Transform > Deform > Flow command can be useful for something like that:
http://moi3d.com/3.0/docs/moi_command_reference8.htm#flow

For your case you could try making a base plane and flat object and then apply it onto the outer surface like this:



It also might be convenient to trim out a smaller area and use that as the target rather than targeting a small area of a larger surface.

If you want some kind of picture applied to it that is usually be the kind of thing you would do with texture mapping in a rendering program.

- Michael