The stereographic projection


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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.

1. The purpose of the stereographic projection in crystallography

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.

Stereographic projection

Washington, DC: Math. Snyder, J. Map Projections--A Working Manual. Sign up to receive regular email alerts from Physical Review A. Journal: Phys. X Rev.

The Stereographic Projection

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    Stereographic projection crystallography

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    The stereographic projection The stereographic projection

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