The gnomonic projection is a nonconformal map projection obtained by projecting points 
(or 
) on the surface of a 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. For a
sphere of unit radius, the
transformation equations for a point with latitude 
and longitude 
onto the plane
tangent at 
are
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the angular distance from 
to 
, 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.
