Harvard University,FAS
Fall 2004

Mathematics Math21b
Fall 2004

Linear Algebra and Differential Equations

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu

Computer Graphics

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 here.

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