A conic projection of points on a unit sphere centered at 
consists of extending the line 
for each point 
until it intersects a cone
with apex 
which tangent to the sphere along a circle passing through a point 
in a point 
. For a cone with apex a height 
above 
, the angle from the z-axis
at which the cone is tangent is given by
 |
(1)
|
and the radius of the circle of tangency and height above 
at which it is located are given by
 |  |  |
(2)
|
 |  |  |
(3)
|
Letting 
be the colatitude of a point 
on a sphere, the length of the vector 
along 
is
 |
(4)
|
The left figure above shows the result of re-projecting onto a plane perpendicular to the z-axis (equivalent to looking at the cone
from above the apex), while the figure on the right shows the cone cut along the
solid line and flattened out. The equations transforming a point on a sphere 
to a point on the flattened
cone are
 |  |  |
(5)
|
 |  |  |
(6)
|
This form of the projection, however, is seldom used in practice, and the term "conic projection" is used instead to refer to any projection in which lines of longitude are mapped to equally spaced radial lines and lines of latitude (parallels) are mapped to circumferential lines with arbitrary mathematically spaced separations (Snyder 1987, p. 5).
