stereographic projection

Noun

stereographic projection (plural stereographic projections)

1. (projective geometry) A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole.
   • 1974 [Prentice-Hall], Richard A. Silverman, Complex Analysis with Applications, Dover, 1984, Unaltered republication, page 19,
     Thus we see that stereographic projection establishes a one-to-one correspondence between the extended complex plane and the Riemann sphere.
   • Proposition 2. The stereographic projection π_N:S²→Oxy of the sphere S² onto the xy-plane from the North Pole N preserves the angles between tangent vectors. Thus, the coordinates specified on S²⧵N by the stereographic projection π_N are isothermal.1991, E. J. F. Primrose (translator), Simeon Ivanov (editor of translation), A. T. Fomenko, A. A. Tuzhilin, Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space...