Java's transformation library is capable of only affine transformations. This put an end to my curiosity when it came to distorting existing java games and toys, though I always wanted to create something that could render on an arbitrary surface. This library is a proof-of-concept rendering library that can render to a plane, translate all the points through a function, then plot them to the screen.
As a quick example of what that transformation may be, the screenshot on this page is of a circle rendering onto a (ln(),ln()) plane. Arbitrary functions are possible, though the number of drawing primitives is limited due to speed issues, and I had to rewrite the way Java renders shapes in order to make the distortions possible.
Download Manifold.tar.gz.
Compile using make, run using Java Test. Examine the test script to see the API, but it's clear that it isn't very well developed yet.