Along the sphere eversion lines, there is also the energy-minimizing sphere eversion constructed by Rob Kusner. I think there is a video of it at http://www.youtube.com/watch?v=I6cgca4Mmcc, though it isn't labelled as such.
Rob also has a page at http://new.math.uiuc.edu/laterna/minimax/ with some history of the minimax eversion.
