Clifford algebra of three dimensional geometry

Abstract

The use of Clifford or geometric algebra for dealing with three dimensional geometry is discussed. One issue is the representation of the rigid body motions of rotations and translations as elements within the algebra. The approach used is to work with projective geometry and choose the square of an additional basis element to be large (infinite). This allows Euclidean points to be represented as vectors in the algebra and transforms on these to be handled using bivectors. This paper looks at the use of Clifford algebra for handling the types of transforms required in robotic applications. A number of example applications are given.