Visualizing a sphere eversion

Author

Francis, George ; Sullivan, John M.

Author_Institution

Dept. of Math., Illinois Univ., Urbana, IL, USA

Volume

10

Issue

5

fYear

2004

Firstpage

509

Lastpage

515

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

computational geometry; data visualisation; minimax techniques; solid modelling; virtual reality; Boy surface; Morin surface; The Optiverse video; Willmore energy; mathematical process; optimal minimax eversion; regular homotopy; sphere eversion visualization; surface immersion; virtual environment; Glass; Humans; Mathematics; Minimax techniques; Numerical simulation; Turning; Virtual environment; Visual system; Visualization; Windows; Boy surface; Index Terms- Visualization; Morin surface; Willmore energy; immersions; regular homotopy; sphere eversion; the CAVE.; Algorithms; Artificial Intelligence; Computer Graphics; Computer Simulation; Computer-Aided Design; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Models, Theoretical; Signal Processing, Computer-Assisted; User-Computer Interface;

fLanguage

English

Journal_Title

Visualization and Computer Graphics, IEEE Transactions on

Publisher

ieee

ISSN

1077-2626

Type

jour

DOI

10.1109/TVCG.2004.33

Filename

1310276