Stereographic Projection

A map projection obtained by projecting points on the surface of sphere from the sphere's north pole to point in a plane tangent to the south pole (Coxeter 1969, p. 93). In such a projection, great circles are mapped to circles, and loxodromes become logarithmic spirals.

Stereographic projections have a very simple algebraic form that results immediately from similarity of triangles. In the above figures, let the stereographic sphere have radius , and the -axis positioned as shown. Then a variety of different transformation formulas are possible depending on the relative positions of the projection plane and -axis.

The transformation equations for a sphere of radius are given by

			(1)
			(2)

where is the central longitude, is the central latitude, and

(3)

The inverse formulas for latitude and longitude are then given by

			(4)
			(5)

where

			(6)
			(7)

and the two-argument form of the inverse tangent function is best used for this computation.

For an oblate spheroid, can be interpreted as the "local radius," defined by

(8)

where is the equatorial radius and is the conformal latitude.