Copyright 1995 Geometry Center, University of Minnesota.
This directory contains the C++ program "evert" for turning the sphere inside out without tears, creases, or pinches. The program was written by Nathaniel Thurston, and is based on ideas of Bill Thurston. Silvio Levy wrote the documentation and organized the distribution.
This software was developed at the Geometry Center (University of Minnesota).
The documentation consists of a Latex file manual.tex, also available in Postscript (manual.ps). It assumes you are familiar with the basic ideas of the algorithm for turning the sphere inside out described in the computer-animated video Outside In. This video, directed by Silvio Levy, Tamara Munzner and Delle Maxwell, gives an elementary description of the eversion, and shows it step by step, from different points of view. You should also consult the full-color illustrated book Making Waves: A Guide to the Ideas Behind Outside In, which comes with the video. Outside In and Making Waves are distributed by
A K Peters
289 Linden Street
Wellesley MA 02181
phone 617-235-2210
fax 617-235-2404
You can also point your favorite Web browser to http://geom.umn.edu/locate/oi.
Comments and questions about this document or the program can be sent to Silvio Levy at levy@geom.umn.edu, or to Nathaniel Thurston at njt@math.berkeley.edu.
PREPARATION
Evert is written in C++, GNU dialect (gcc). Binary executables are provided for the Sparc, the SGI, and the NeXT (68000 or HP running NextStep) in directory Binaries. Moreover, the program should compile and run on any system having gcc. If you're using a different machine and want to recompile, type "make" and see what happens. There will be some harmless warning messages at all events. If there is more serious trouble, send mail to software@geom.umn.edu: we will try to help you, but no guarantees.
Evert takes no input, other than command-line options. Its output is a file of numbers representing the sphere (or, more usually, a piece of it) at a given point in the eversion. This means that, in order to see the output, you need to be able to transform the numbers -- that is, the geometry of the sphere into a picture. There are various programs that do this. One is called Geomview, and is freely available from the Geometry Center, by anonymous ftp from the server geom.umn.edu, in directory pub/software.
If you don't have Geomview but have a different viewing program, you may be able to adapt the output of evert to serve as input to your program, either by changing the code or by writing an output filter. If you do that, we would appreciate hearing from you and getting a copy of your code.
For information on how to run evert, see manual.tex or manual.ps.