In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles. It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.
Intuitively, then, the stereographic projection is a way of picturing the sphere as the 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.
Read more about Stereographic Projection: History, Definition, Properties, Wulff Net, Other Formulations and Generalizations
Famous quotes containing the word projection:
“Those who speak of our culture as dead or dying have a quarrel with life, and I think they cannot understand its terms, but must endlessly repeat the projection of their own desires.”
—Muriel Rukeyser (1913–1980)