Chris Doran, Anthony Lasenby and Joan Lasenby
Conformal Geometry, Euclidean Space and Geometric Algebra
In J. Winkler ed Uncertainty in Geometric Computations, Kluwer 2002

Abstract: Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to programming complicated geometrical operations. But there is a fundamental weakness in this approach --- the Euclidean distance between points is not handled in a straightforward manner. Here we discuss a solution to this problem, based on conformal geometry. The language of geometric algebra is best suited to exploiting this geometry, as it handles the interior and exterior products in a single, unified framework. A number of applications are discussed, including a compact formula for reflecting a line off a general spherical surface.

Available on: cs.CG/0203026