GIMP :: Map Pixels Of Square To Circle

I have a square selection that I'd like to map into a circle of equal size. I see apply lens and map object...sphere, but neither of these seem to do a proper job.

The algorithm I'm after would basically take the pixels of the square and map them onto their new locations within the circle so that each pixel moves inward toward the center until it reaches its appropriate location along the the line from the origin to its radius.

I'm about to the point to just code it in C++.