The Representation of Rigid Body Motions in the Conformal Model of Geometric Algebra

Abstract

In geometric algebra, the conformal model provides a much more powerful framework to represent Euclidean motions than the customary “homogeneous coordinate” methods. It permits elementary universal operators that can act to displace not only points, but also lines and planes, and even circles and spheres. We briefly explain this model, focusing on its essential structure. We show its potential use for motion capture by presenting a closed form for the bivector logarithm of a rigid body motion, permitting interpolation of motions and combination of motion estimates.