Stereographic projection

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.

Illustration by Rubens for "Opticorum libri sex philosophis juxta ac mathematicis utiles", by François d'Aiguillon. It demonstrates how the projection is computed.

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.^[1][2] 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.

1. Ranjan Khatu (2021-11-19), Complex Analysis | Unit 1 | Lecture 18 | Stereographic Projection, retrieved 2025-06-28
2. "1.4: Stereographic Projection". Geosciences LibreTexts. 2020-10-05. Retrieved 2025-06-28.