Aitoff projection

The Aitoff projection is a modified azimuthal map projection. Proposed by David A. Aitoff in 1889, it is the equatorial form of the azimuthal equidistant projection, but stretched into a 2:1 ellipse while halving the longitude from the central meridian:

:$x\; =\; mathrm\{azeq\}\_xleft(fraclambda\; 2,\; phi\; ight),$

:$y\; =\; frac\; 1\; 2\; mathrm\{azeq\}\_y\; left(fraclambda\; 2,\; phi\; ight)$

where $mathrm\{azeq\}\_x$ and $mathrm\{azeq\}\_y$ are the x and y components of the equatorial azimuthal equidistant projection. Written out explicitly, the projection is:

:$x\; =\; frac\{2\; cos(phi)\; sinleft(fraclambda\; 2\; ight)\}\{mathrm\{sinc\}(alpha)\},$

:$y\; =\; frac\{sin(phi)\}\{mathrm\{sinc\}(alpha)\},$

where

:$alpha\; =\; arccosleft(cos(phi)cosleft(fraclambda\; 2\; ight)\; ight),$

and $mathrm\{sinc\}(alpha)$ is the unnormalized sinc function with the discontinuity removed. In all of these formulas, $lambda$ is the longitude from the central meridian and $phi$ is the latitude.

Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal-area projection in the same manner as Aitoff, producing the Hammer projection. While Hammer was careful to cite Aitoff, there has been some confusion since, wherein Aitoff has been attributed to Hammer's projection. ["Flattening the Earth: Two Thousand Years of Map Projections", John P. Snyder, 1993, pp.130-133, ISBN 0-226-76747-7.]

References

ee also

* Mollweide projection
* Hammer projection
* [http://map.gsfc.nasa.gov/m_mm.html]

External links

* [http://www.radicalcartography.net/?projectionref Table of common projections]
* [http://www.uff.br/mapprojections/Aitoff_en.html An interactive Java Applet to study the metric deformations of the Aitoff Projection] .