You might be able to find a lisp that will do this since it's very simple as far as "unfolding" goes, but here's how you could manually map it.
To sum it up, the length of the "flat" pattern will be equal to the circumference. Divide the circular object into as many segments as necessary to achieve the required precision, then Divide the Line into the same number of segments. Draw a line from each segment around the perimeter up to the top of your shape, then map that line to the corrosponding segment on the line. Once you have all the mapping points, use a SPLINE to define the edge.
