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.
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