Stereographic projection

particular mapping that projects a sphere onto a plane
Illustration by Rubens for "Opticorum libri sex philosophis juxta ac mathematicis utiles", by Fran├žois d'Aiguillon. It demonstrates how the projection is computed.

In geometry, a stereographic projection is a function that maps the points of a sphere onto a plane. The projection is defined on the entire sphere, except for one point, called the projection point.

Intuitively, the stereographic projection is a way of picturing a sphere as a plane, with some inevitable compromises. Because the sphere and the plane appear in many areas of mathematics and its applications, so does the stereographic projection; it finds use in diverse fields including complex analysis, cartography, geology, and photography. In practice, the projection is carried out by computer or by hand using a special kind of graph paper called a stereonet or Wulff net.

A simple example of such a projection, encountered in everyday life is the sun casting a shadow of a globe onto the ground.