Reflections in Conics, Quadrics and Hyperquadrics via Clifford Algebra

Abstract

In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the Pin group of this geometric algebra corresponds to inversions with respect to axis aligned quadrics. We discuss the construction for the two- and three-dimensional case in detail and give the construction for arbitrary dimension. Key Words: Clifford algebra, geometric algebra, generalized inversion, conic, quadric, hyperquadric