Sphere Eversions: from Smale through “the Optiverse”
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چکیده
For decades, the sphere eversion has been a favorite subject for mathematical visualization. The 1998 video The Optiverse shows minimax eversions, computed automatically by minimizing elastic bending energy using Brakke’s Evolver. We contrast these geometrically optimal eversions with earlier ones, including those by Morin, Phillips,
منابع مشابه
“the Optiverse” and Other Sphere Eversions
For decades, the sphere eversion has been a classic subject for mathematical visualization. The 1998 video The Optiverse shows geometrically optimal eversions created by minimizing elastic bending energy. We contrast these minimax eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston. The minimax eversions were automatically generated by flowing downhill in energy u...
متن کاملComputing Sphere Eversions
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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 full...
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Our 1998 video The Optiverse [18] illustrates an optimal sphere eversion, computed automatically by minimizing an elastic bending energy for surfaces. This paper describes AVN, the custom software program we wrote to explore the computed eversion. Various special features allowed us to use AVN also to produce our video: it controlled the camera path throughout and even rendered most of the frames.
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تاریخ انتشار 2001