Typing with a stylus

Create an arrangement of letters and punctuation to minimize the distance traveled while using it as an on-screen keyboard.

I'm guessing Spacebar will be in the center, and Shift will be next to I. Throw in a Fitts Law constraint in there -- a time penalty for small area keys.

An additional degree of freedom: some letters may be duplicated.

Different layouts for different aspect ratios or shapes the whole keyboard fits into.