Code for an interactive version of

The Optiverse

showing the minimax sphere eversion

The Optiverse is a computer-graphics video, showing an optimal way to turn a sphere inside-out. Most of the scenes of the movie were produced with custom software to display the computed homotopy (sequence of surfaces in 3D). This software is now available for use on Unix, Windows or Mac machines.

To use the software, you will need the datafiles and, which contain the various topes (or stages) of the eversion as surfaces in 3D. (These files have a somewhat cruder triangulation than that in the video, to save space.) To download these, be sure to shift-click, or whatever is appropriate in your browser: if you simply click on these links the files may be fed to an inappropriate movie player instead of being downloaded.

Then you also need the executable file for the program avn. For Unix machines (including Mac), you can download the executables for Linux x86 or. Mac OS X or Sun Sparc or SGI Irix directly. Or you can download the source code avn.c and the Makefile (or the special Mac version of the Makefile) and compile it yourself.

For Windows machines, you should probably download which will unpack to include avn.exe as well as two DLL files, libsnd.dll and glut32.dll. (The ZIP file also includes auxilliary files you would need to recompile the source code.)

We no longer actively support old Macs, not running OS X. But you can download the StuffIt file avnmac.sit, which should unpack to contain the executable AVNMac, as well as various OpenGL extensions. If there's any trouble downloading that, you can try the somewhat bigger BinHex version avnmac.sit.hqx which does contain the full Mac file info. The individual files, in Unix Mac-binary format, are in this list, but they may be hard to download. The various OpenGL files need to be added as Extensions in your System Folder; they should allow AVNMac to run. The source code for old Macs is slightly different: avnmac.c.

In any case, execute "avn h2d78", or the equivalent on your system, and you should be up and running, with an interactive version of The Optiverse. Move the mouse to control the rotation speed, hit 'm' to start and stop the homotopy, and read the heads-up display to find other options. Hit the escape key to quit.