> You'd need more than a function u:ℝ->ℝ to do that. Actually, if you normalize the bell height to 1, you can take u from 0 to 1 as the inner surface (tracing

> You'd need more than a function u:ℝ->ℝ to do that. Actually, if you normalize the bell height to 1, you can take u from 0 to 1 as the inner surface (tracing down from the top), and u from 1 to 2 as the outer (tracing back up from the bottom). I'm not sure that's mathematically convenient, but it does work. (You could also use a periodic function on 0..pi for inner and pi..tau for outer, which might be nicer math-wise and also allows you to say that the height (pi) is half of whatever the function's period is.)