Visualizing a sphere eversion

George Francis; John M. Sullivan

doi:10.1109/TVCG.2004.33

Visualizing a sphere eversion

George Francis, John M. Sullivan

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	509-515
Number of pages	7
Journal	IEEE Transactions on Visualization and Computer Graphics
Volume	10
Issue number	5
DOIs	https://doi.org/10.1109/TVCG.2004.33
State	Published - Sep 2004

Keywords

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

Online availability

10.1109/TVCG.2004.33

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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.",

keywords = "Boy surface, Immersions, Morin surface, Regular homotopy, Sphere eversion, The CAVE, Visualization, Willmore energy",

author = "George Francis and Sullivan, {John M.}",

note = "Funding Information: Parts of this paper are based on the authors{\textquoteright} earlier reports: The computations of the minimax eversion were described in [11], [12], the interactive animator in [29], [30], the virtual-reality CUBE in [31], and the history of sphere eversions in [7], [6]. John M. Sullivan is partially supported by US National Science Foundation grant DMS-00-71520. Some of the work described was done jointly with Rob Kusner, Stuart Levy, and others.",

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Visualizing a sphere eversion

Abstract

Keywords

ASJC Scopus subject areas

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