The Minimax Sphere Eversion [chapter]

George Francis, John M. Sullivan, Rob B. Kusner, Ken A. Brakke, Chris Hartman, Glenn Chappell
1997 Visualization and Mathematics  
We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the Surface Evolver. This flow is not yet fully understood; however, our numerical simulations give evidence that the resulting eversion is isotopic
more » ... to one of Morin's classical sphere eversions. These simulations were presented as real-time interactive animations in the CAVE automatic virtual environment at Supercomputing'95, as part of an experiment in distributed, parallel computing and broad-band, asynchronous networking.
doi:10.1007/978-3-642-59195-2_1 dblp:conf/vismath/FrancisSKBHC95 fatcat:tkyn6grtgbh57lof4szbs5wf34