The Geometric Algebras $$G_{6,0,2}^+$$, $$G_{6,0,6}^+$$

Abstract

The geometric algebra of a 3D Euclidean space \(G_{3,0,0}\) has a point basis and the motor algebra \(G_{3,0,1}^+\) a line basis. In the latter, the lines are expressed in terms of Plucker 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. Extending the degrees of freedom of the mathematical system, in the conformal geometric algebra \(G_{4,1}\), using the horosphere framework points, one can model lines, planes, circles, and spheres and also certain Lie groups as versors.