Expressing Discrete Geometry using the Conformal Model

Abstract Primitives and transformations in discrete geometry, such as lines, cir-cles, hyperspheres, hyperplanes, have been defined with classical linear algebra in dimension 2 and 3, leading to different expressions and algorithms. This paper ex-plores the use of the conformal algebra to express these discrete primitives in arbi-trary dimensions with a minimum of expressions and then algorithms. Starting with hyperspheres and hyperplanes, a generalization to k-sphere is then proposed. This gives one simple and compact formula, valid for all geometric conformal elements in Rn, from the circle to the hypersphere, and the line to the hyperplane