On Real Projective Plane Constructions and Their Isomorphisms

Abstract

The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three constructions. Additionally we investigate their relationship to direction-sensitive photosensors which use lens(es) to transform light's direction to a position on a local plane. This transformation, done by lenses is a physical version of an isomorphism between projective plane constructions