The Wiechel projection is an pseudoazimuthal, equal-area map projection, and a novelty map presented by William H. Wiechel in 1879. When centered on the pole, it has semicircular meridians arranged in a pinwheel. Distortion of direction, shape, and distance is considerable in the edges.[1]

Wiechel Projection of the Earth

In polar aspect, the Wiechel projection can be expressed as so:[1]

The Wiechel can be obtained via an area-preserving polar transformation of the Lambert azimuthal equal-area projection. In polar representation, the required transformation is of the form

where and are the polar coordinates of the Lambert and Wiechel maps, respectively. The determinant of the Jacobian of the transformation is equal to unity, ensuring that it is area-preserving. The Wiechel map thus serves as a simple example that equal-area projections of the sphere onto the disk are not unique, unlike conformal maps which follow the Riemann mapping theorem.

See also

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References

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  1. ^ a b Map Projections: A Reference Manual. Lev Moiseevič Bugaevskij, John Parr Snyder. 1995. p. 132. ISBN 9780748403042. Retrieved 2013-02-15.