About the projecting cones of stereographic projection

Abstract

In a gramstereographic projection, every plane is projected by an arc of a great circle, that is, an arc passing through two diametrically opposite points of the projection circle. This circle represents one circular section of a cone having a center at the point of convergence of the rays; another circular section of the same cone is the diametrical circle of a sphere at projected plane. Apparently, not a single crystallographer has yet noted that these projecting cones are not cones of a general nature, but are special cones, called cones of Pappus, who was the first to note their simple construction. Both special axes of the projecting cone are perpendiculars to both circular sections, that is, perpendiculars to both the given plane and the projection plane (see article).