G6,3 Geometric Algebra; Description and Implementation

This paper introduces a new non-Euclidean geometry, that consist in a generalization of conformal geometry G4,1. In this geometry, it is possible to handle not only spheres, but also quadratic surfaces and their intersections easily as well. The Clifford algebra G6,3 is being used as the framework, which allows the creation of a nine dimensional geometry with some additional transformations, i.e. anisotropic dilatation, allowing rotations for all G4,1 entities. It also eases the use of quadratic surfaces including conics in the 3D space.