Stereographic Projection

The stereographic projection is a special kind of perspective projection. It is a conformal azimuthal projection with a projection centre Z that is diametrically opposed the (tangential) projection plane (cp. figure from [3] under literature).

    

The stereographic projection is first mentioned by Hipparchus. The cartesian co-ordinates x, y  of the map picture onto the plane are

    x =  * cos(u)     and     y =  * sin(u)
    with
     = 2 * R * tan(  / 4 - v / 2 ) .

Thereby is

    R = radius of the (Earth) sphere,
    v = geographic latitude   and
    u = geographic longitude .