Computing Sphere Eversions

  • George Francis
  • John M. Sullivan
  • Chris Hartman


We consider several tools for computing and visualizing sphere eversions. First, we discuss a family of rotationally symmetric eversions driven computationally by minimizing the Willmore bending energy. Next, we describe programs to compute and display the double locus of an immersed surface and to track this along a homotopy. Finally, we consider ways to implement computationally the various eversions originally drawn by hand; this requires interpolation of splined curves in time and space.


Rotational Symmetry Height Function Plane Curf Riemann Sphere Klein Bottle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • George Francis
    • 1
  • John M. Sullivan
    • 1
  • Chris Hartman
    • 1
  1. 1.Mathematics DepartmentUniversity of IllinoisUrbanaUSA

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