A map projection obtained by projecting points on the surface of sphere from the sphere's north pole to point in a plane tangent to the south pole Coxeter , p.
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In such a projection, great circles are mapped to circles , and loxodromes become logarithmic spirals. Stereographic projections have a very simple algebraic form that results immediately from similarity of triangles. In the above figures, let the stereographic sphere have radius , and the -axis positioned as shown.
Then a variety of different transformation formulas are possible depending on the relative positions of the projection plane and -axis. The transformation equations for a sphere of radius are given by. The inverse formulas for latitude and longitude are then given by.
For an oblate spheroid , can be interpreted as the "local radius," defined by. Coxeter, H.
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Introduction to Geometry, 2nd ed. New York: Wiley, pp. Geometry Revisited.
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The Stereographic Projection
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