The Geometric Algebras \(G_{6,0,2}^+\) , \(G_{6,3}\) , \(G_{9,3}^+\) , \(G_{6,0,6}^+\)

The geometric algebra of a 3D Euclidean space \(G_{3,0,0}\) has a point basis and the motor algebraMotor algebra  \(G_{3,0,1}^+\) a line basis. In the latter, the lines expressed are expressed in terms of Plücker coordinates and the points and planes in terms of bivectors. The reader can find a comparison of representations of points, lines, and planes using vector calculus, \(G_{3,0,0}\) and \(G_{3,0,1}^+\) in Chap. 7 of [1]. Extending the degrees of freedom of the mathematical system, in the conformal geometric algebraConformal geometric algebra  \(G_{4,1}\) , using the horosphere framework points, one can model lines, planes, circles, and spheres and also certain Lie groups as a versors.