As both ends are open as opposed to a dished out circular seat it would seem straight forward to me either on a a router table or a ts. A ts most likely would be faster whether you use a dado blade or not. Lay out your desired curve and starting our at the outside of the curvature place your fence to where blade is in right spot, raise the blade to appropriate height, cut all the way through seat, turn seat 180 degrees and repeat. move the fence out according to the next cut in adjust blade and repeat and keep repeating until you've hogged out the basic shape. Doing it in this manner ensures a centered removal of the major part of the waste. Then just use a spoke shave to even out the "steps (don't know what else to call it) and then sand to your finished grit and pop a finish on this. Thanx by the way I wanted to make a folding stool for the shop or maybe some for the kitchen to sit and do prep work and could not figure out a logical way to dish out the circular stool shape I was thinking of using and didn't think of this answer in shapes. I unfortunately don't own a lathe. hope this helps
later, biloxi tom and remember " DO NOT have a good day, have a WILD and WONDERFUL ONE!"