Stereographic is a perspective projection in which points are projected from a position on the opposite side of the globe onto a plane tangent to the Earth. All of one hemisphere can easily be shown, but it is impossible to show both hemispheres in their entirety from one center. It is the only azimuthal projection that preserves truth of angles and local shape. Scale increases and parallels become more widely spaced farther from the center.
Polar aspect: meridians are straight lines radiating from the point of tangency.
Oblique and equatorial aspects: meridians are arcs of circles concave toward a straight central meridian. In the equatorial aspect, the outer meridian of the hemisphere is a circle centered at the projection center.
Polar aspect: parallels are concentric circles.
Oblique aspect: parallels are nonconcentric arcs of circles concave toward one of the poles with one parallel being a straight line.
Equatorial aspect: parallels are nonconcentric arcs of circles concave toward the poles; the Equator is straight.
Graticule spacing increases away from the center of the projection in all aspects and it retains the property of conformality.
Scale increases toward the periphery of the projection.
Portraying large, continent-sized areas of similar extent in all directions.
Geophysics for solving problems in spherical geometry.
Topographic maps and navigational charts (polar aspect).
In the equatorial aspect, all parallels except the Equator are circular arcs. In the polar aspect, latitude rings are spaced farther apart, with increasing distance from the pole.
The Stereographic is the only azimuthal projection which is conformal.
The following figure shows two views:
A) Equatorial aspect, often used in the 16th and 17th centuries for maps of hemispheres.
B) Oblique aspect, centered on 40°N.