Here is a manual unroll of a catenary shaped surface, using unwrap script.
(Just messing around to see if there is a possibility of a script.)
Put an isocurve in the center. Unwrapped three curves. Drew two outer lines. Did Planar.
I think it would only work on certain surfaces, like rolled up paper... (?)

edit: well, the length of the sides is not right...
The two curved edges would remain a bit curved, when unrolled...
Have to call it the unwrolled script, with a w. :-)