ABSTRACT
A plane-based Clifford algebra model for the dual quaternions has been proposed by J. Selig and elaborated on by C. Gunn. Two important subalgebras reside inside the plane model of Clifford algebra: the quaternions and the dual quaternions. The representation of geometry in the plane model is somewhat exotic. To see how one should represent planes in this Clifford algebra model for the dual quaternions, the authors start with the representation of planes in the space of dual quaternions. Lines are typically represented in the space of dual quaternions using either Plucker coordinates or dual Plucker coordinates. Since people are working in the plane model for dual quaternions, it is natural here to use dual Plucker coordinates to represent lines. Duality in the Clifford algebra associated to a vector space of dimension n captures relationships between subspaces of dimension k and subspaces of dimension n-k.
