

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.
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.
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.
Here is the official site for Geri from Pixar Animation Studios.
Related sites are at this location and this one.