Suggestion: allow me to move in discrete steps of a specified length, and rotate in discrete steps too. Then I can see what happens in different geometries when I go forward n, left 90 degrees, forward n, etc.
In fact, how about implementing a Logo turtle graphics system :)?
This is really cool. My suggestion is similar to (perhaps the same as) jameshart's. I want to be able to form a sequence of known steps in flat space (say, draw a square), then see what that same sequence of steps produces in other spaces. It may help build some sort of intuition for the different spaces.
In fact, how about implementing a Logo turtle graphics system :)?