Numerical Evaluation of Versors with Clifford Algebra

This paper has two main parts. In the first part we discuss multivector null spaces with respect to the geometric product. In the second part we apply this analysis to the numerical evaluation of versors in conformal space. The main result of this paper is an algorithm that attempts to evaluate the best transformation between two sets of 3D-points. This transformation may be pure translation or rotation, or any combination of them. This is, of course, also possible using matrix methods. However, constraining the resultant transformation matrix to a particular transformation is not always easy. Using Clifford algebra it is straightforward to stay within the space of the transformation we are looking for.