About the Stereographic Projection
The Stereographic projection is considered an ancient projection, and was first used for polar star maps by Hipparchus, Ptolemy, and probably earlier Egyptians.
The Stereographic projection is an azimuthal projection that projects from the antipode to the tangent plane that has a tangent point at the map's central point. Ie. a North Pole Stereographic Projection will project from the South Pole on to a tangent plane that touches the Earth at the North Pole.
The projection is conformal (ie. local shapes are accurate) but scale and area are both distorted. Local angles are also accurate.
The Stereographic projection is a popular choice for terrestrial polar maps, and has also been used in an oblique aspect for planetary maps. Due to the local angle property, this projection is also used extensively in crystallography to plot crystal faces, and important directions in the crystal lattice.
Implementation Notes: The Proj.4 library implements two variants of the Stereographic Projection: stere and sterea. stere uses simpler formulae, but sterea has less distortion near the center. sterea is also discontinuous along the antipode of the central meridian - ie. it should only be used for the near hemisphere.
See our interactive Stereographic Projection Northern Hemisphere map.