Visualizing a sphere eversion

George Francis, John M. Sullivan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)509-515
Number of pages7
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number5
StatePublished - Sep 2004


  • Boy surface
  • Immersions
  • Morin surface
  • Regular homotopy
  • Sphere eversion
  • The CAVE
  • Visualization
  • Willmore energy

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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