TL;DR: This work has computed an optimal minimax eversion, requiring the least bending energy, and discusses techniques used to help visualize this eversion for visitors to virtual environments and viewers of the video The Optiverse.
Abstract: The mathematical process of everting a sphere (turning it inside-out allowing self-intersections) is a grand challenge for visualization because of the complicated, ever-changing internal structure. We have computed an optimal minimax eversion, requiring the least bending energy. Here, we discuss techniques we used to help visualize this eversion for visitors to virtual environments and viewers of our video The Optiverse.