A lot of Mathematics is involved in a little computer animation. Examples:
surfaces are modeled by unions of algebraic surfaces which are in the simplest case triangles.
Given a bunch of points, the task to find a surface fitting those points is a data fitting
problem. Least square formulas lead to best approximations.
In order to render the picture, many light ray paths are computed.
Doing this calculation requires geometric transformations like reflections
or rotations. Ray tracing programs cleverly start from the camera with the
rays, then see, whether the ray ends up at a light source. Like this, one does
not to have to compute rays which do not end up in the camera.
Sound is compressed. Here as MP3 embedded in Flash. Compression algorithms are
based on linear algebra. Represent a chunk of sound as a vector, rotate the vector
so that irrelevant coordinates are seperated, then set these irrelevant coordinates to
zero, then rotate back. Irrelevant coordinates are for example waves which frequency
so hight that one can not hear it anymore.
Source: the miniature "Lion Seul" was circulating in emails during the year 2002-2003.
Added: March 22, 2005. We got informed that the author of the movie is
Pierre Coffin. The Lion Seul movie can be found