Gnomonic Projection

The gnomonic projection is a nonconformal map projection obtained by projecting points (or ) on the surface of sphere from a sphere's center to point in a plane that is tangent to a point (Coxeter 1969, p. 93). In the above figure, is the south pole, but can in general be any point on the sphere. Since this projection obviously sends antipodal points and to the same point in the plane, it can only be used to project one hemisphere at a time. In a gnomonic projection, great circles are mapped to straight lines. The gnomonic projection represents the image formed by a spherical lens, and is sometimes known as the rectilinear projection.

In the projection above, the point is taken to have latitude and longitude and hence lies on the equator. The transformation equations for the plane tangent at the point having latitude and longitude for a projection with central longitude and central latitude are given by

			(1)
			(2)

and is the angular distance of the point from the center of the projection, given by

(3)

The inverse transformation equations are

			(4)
			(5)

where

			(6)
			(7)

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

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