The stereographic projection is a special kind of perspective projection. It is a conformal azimuthal projection with a projection centre Z that is diametrically opposed the (tangential) projection plane (cp. figure from [3] under literature).
The stereographic projection is first mentioned by Hipparchus. The cartesian co-ordinates x, y of the map picture onto the plane are
x = * cos(u) and y =
* sin(u)
with
= 2 * R * tan(
/ 4 - v / 2 ) .
Thereby is
R = radius of the (Earth) sphere,
v = geographic latitude and
u = geographic longitude .