AIPS memo 27 (Greisen 1983) identified four common choices, which
are discussed here because of their wide use. For three of these four
projections, the choice for the tangent point,
the point common to the celestial sphere and the plane on which
it is projected, is arbitrary. AIPS adopted the convention that
the reference pixel, given by the values of `CRPIX`** n**, is at this
tangent point. If the tangent point of the projection is outside the
image, then the values of the

In the TAN (tangent) or gnomic geometry, the projection of a point of
the celestial sphere onto the plane is found by extending the line
from the center of the sphere to the point on the tangent plane. This
projection is common in optical astronomy. In the SIN (sine) or
orthographic geometry,
common in radio aperture synthesis, the projection point is on
the perpendicular between the point on the sphere and the surface of
the tangent plane. In the ARC geometry, the projection point is on an
arc passing through the point on the sphere and the tangent plane,
with the center of the arc at the reference point. This projection
preserves angular distances. It is the natural projection of Schmidt
camera imagery, such as the Palomar Sky Survey,
and is also used in single-dish radio
telescope mapping. GC note that the NCP geometry discussed in the AIPS
memo, a projection onto a plane perpendicular to the North Celestial
Pole used by the Westerbork Synthesis Radio Telescope and a few other
east-west radio interferometers, can be treated as a special case of the
orthographic (SIN) projection. The SIN and TAN projections are special
cases of the *perspective zenithal projections*, which are generated
from a point and carried through from the unit sphere to the plane of
projection.

The proposal adopts the notation that has been used in AIPS, using the last
four characters of the value field of the `CTYPE`** n** keywords
to identify the projection. Table 4.1
shows the codes for the projections described above.

GC define 25 projection codes in all, including the spherical cube
projection used by the COBE project (`CSC`). Many standard
projections are special cases of these 25. The `-NCP` designation of
the original AIPS memo is no longer used. For each projection they
provide the transformation equations and a diagram.

The following indexed keyword is reserved under this proposal for defining projections:

`PROJP`** n** (floating) is the

GC call the deprojected coordinate system that results from this
step the *native coordinates*.