# Math Shapes: Geri

Tony DeRose is one of the major designers responsible for the character
Geri, who appears in the Academy Award-winning short film
"Geri's Game"
as well as in "Toy Story II". He is well known for his presentations about
computer graphics and the steps that people have to go through to learn
about careers in that subject. Another person at Pixar with a keen interest
in outreach as well as major responsibility for the production of Pixar
animations is the CTO,
Edwin Catmull.

Computer animation depends on mathematics. Mathematical modeling
techniques develop all of the characters in an animated film, and all of
the positions and movements have explicit mathematical descriptions. It is
impossible to think of modern computer graphics without at the same time
thinking of the mathematics that underlies it. A Simple Java applet will
let you experiment with these ideas.

To create Geri, Pixar Animation Studios used a fairly novel surface
modeling method known as *subdivision surfaces*. The idea behind
subdivision surfaces is that a smooth surface is from a fairly coarse
polyhedron by iteractively refining — that is, subdividing — the
polygonal facets. If your refinement rules are constructed properly you can
show that in the limit you converge to a smooth surface. Geri's head was
constructed with a single subdivision surface where the coarse polyhedron
contained about 4500 vertices.

*Computer Graphics World* wrote an article on
the
construction of Geri, indicating many of the mathematical ideas involved
in this kind of work. (It is possible to enroll at this site and see the text
and some of the pictures in the article, without agreeing to subscribe or to
receive e-mail solicitations from the magazine.)

Here is a description of the subdivision surface
process, using illustrations from the original of the above article which are not
included in the online version.

There is an official
Geri web site,
hosted by Pixar Animation Studios, that
includes a short clip from "Geri's Game".
Related sites are the Internet
Movie Database entry for Geri and
Pixar's Shorts.