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.
