Old Wine in New Bottles

Old Wine in New Bottles: A new algebraic framework for computational geometry

A "horosphere" is a non-Euclidean model of Euclidean space, originally constructed by F. A. Wachter, a student of Gauss. After nearly two centuries as a mathematical curiosity, this model has reemerged in the guise of geometric algebra with remarkable computational advantages. A compact formulation of the model and its noteworthy features is presented. It provides an ideal algebraic framework for computational geometry, with rich applications to computer-aided geometry, computer vision, robotics and related fields.

David Hestenes. In: E. Bayro-Corrochano & G. Sobczyk (eds), Advances in Geometric Algebra with Applications in Science and Engineering, © Birkhauser, Boston (2001). p. 1-14.