Pencils and set operators in 3D CGA	

Clément Chomicki --LIGM, Université Gustave Eiffel, CNRS	

Geometric Algebra can be considered as a language that unifies mathematics, physics and computer sciences etc.  Among other, CGA is of special interest for its powerful transformations and its ability to represent any hypersphere or hyperplane. Moreover, CGA is an algebra capable of representing pencils of spheres. This paper presents a reinterpretation of every objects of 3D CGA as pencils of spheres and introduces set operators on its elements (i.e. union, intersection, complement, etc).  As an application, these operators are used to find the smallest tangent sphere of two skew lines.