Euclidean Geometric Objects in the Cliord Geometric Algebra of {Origin, 3-Space, Infinity}

This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and (useful) parameterisations of the 3D Euclidean ob- ject models are explicitly demonstrated in order to show how 3D Euclidean information on positions, orientations and radii can be extracted.