I am looking for software that will allow me to prepare my flat images for printing on both the outside of globes and the inside of umbrellas (so that it will appear that the umbrella user is inside the globe.)

My question is: How does one alter the flat image to compensate for curvatures: how does one distort the sizes to fool the eye? I'm not Michelangelo, who knew how to do this inside a dome. Is there software that does this?

Thank you.
PS. Cost is a consideration