Major edits 21oct20, 26dec19, 10aug19, 28jul19, 15jan19, 1nov18, 13sep18 by

Welcome to the Homotopy Pinakothek

This site is dedicated to the preservation, restoration and reanimation of real-time interactive CAVE animations (RTICA) from the nineties. All of the experiments here use David Eck's glsim.js library to re-implement code in C/IrisGL (originally written at the NCSA for the CAVE) into HTML5/WebGL.

Current versions for public presentations:

Collage IST/Graz, 21oct20

ICERM Collage
Five Homotopies by Morin 1987, Apery-Hartman 1992, JinlinXu-Francis 2019.
Fathauer's Crystal by Fathauer-Duchnowsky 2007, Holder and Goudeseune 2019.

Classic homotopies in reverse chronological order.

Experimental implementations of the Morin-Denner-Apery Cuboctahedral Eversions 1992

jazzOptiverse Experimental and partial implementation of the Minimax Eversions by the Optiverse Team, NCSA 1996.
It animates a sequence of models (called "topes" instead of 2D "frames") computed on Brakke's Evolver.

jazzVenus The original collaboration with Donna Cox and Ray Idaszak, NCSA, 1987.

Works best in Brave, Chrome or Firefox and on a keyboard. But they are meant to work also on your phone or pad computer. Email me if it doesn't.

jazzSkel Template RTICA by Glenn Chappel and Chris Hartman 1992

jazzDunce John Dalbec's animation of the Zeeman-Duncehat contraction

jazzNeck Morin's Eversion of an annulus


In Place of an Introduction to the sphere eversion projects by the illiMath Collective: The indroduction to the 2001 and final edition of the course notes for the graduate version of MA428 taught at the Beckman Institute, U. Illinois.

The Minimax Sphere Eversion the first paper in the series by J.M.Sullivan et al on the Optiverse eversion of the sphere. Video at SIGGRAPH 1998 and ICM 1998, Berlin.

Short Venus Abstract

My Etruscan Venus page has a few broken links. Sorry!

Incomplete Venus Documentation, but enough for an introduction.

Short Snail Abstract

Snail Documentation in Chapter 13, Thomas Davis, Scientific Visualization in Mathematics and Science Teaching, AACE, 1995.

Neck Eversion Documentation Morin's eversion of the annulus underlies all of the eversions of the sphere using Morin's central model.

Dunce Hat Documentation This is the only known documentation written by John Dalbec himself. The video created for the 1993 joint meeting of the AMS and DMG in Heidelberg is lost.

Older Versions
jazzNeck Morin's Eversion of an annulus
Oldest version of jazzSnail

Earlier version of jsSnail

First version of oc1 and tr1

First version jsSkel.html