Duality in Geometric algebras
A bit better: Variants of duality in geometric algebras with degenerate metricsIn geometric algebra, the pseudoscalar has traditionally been used to perform non-metric operations such as calculating coordinates and the regressive product.In algebras with degenerate metrics
this approach breaks down,leading to a search for non-metric forms of duality.The article compares the dual coordinate map a double algebra duality, and the hodge
duality a single algebra duality for this purpose.While the two maps are computationally identical, only is coordinate-free and provides direct support for geometric duality, whereby every geometric primitive appears twice, once as a point-based and once as a plane-based form, an essential feature not only of projective geometry but also of euclidean
kinematics and dynamics.Our analysis concludes with a proposed duality-neutral software implementation, requiring a single bit field per multi-vector.