Modified Stereographic
Projection
Stereographic Projection
The Stereographic
projection is the only true perspective projection of
any kind that is also conformal. Its point of projection is on the
surface of the sphere just opposite the point of tangency of the plane
or the center point of the projection. The North Pole is the center of
the map, the projection is from the South Pole. All of one hemisphere
can be shown comfortably shown, but it is impossible to show both
hemispheres in their entirety from one center. The point on the sphere
opposite the center of the maps projects at an infinite distance in the
plane of the map.
This projection is azimuthal and conformal. The central meridian and a
particular parallel are straight lines. All meridians on the polar
aspect and the Equator on the equatorial aspect are straight lines. All
other meridians and parallels are shown as arcs of circles. The scale
increases away from the center of the projection. Points opposite the
center of the projection cannot be plotted since it results in infinite
distortion.
Transforming the points
As in the previous implementation, the projection point is the center
of the cap K on the unit sphere S2. All the points on the
sphere are rotated so that the projection point p0=(0,0,1)
which is equivalent to the
North Pole.
The following mapping is then used to transform the points. Let us
define the central latitude as 
and central longitude as 
the
coordinates of the projection point. 
represents the transformed
latitude in radians and 
represents the transformed
longitude. The following transformation equations were used. These
transformation equations are based on the Stereographic Projection.
