Hammer projection
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The Hammer projection is an equal-area map projection, described by Ernst Hammer in 1892. Directly inspired by the Aitoff projection, Hammer suggested the use of the equatorial form of the Lambert azimuthal equal-area projection instead of Aitoff's use of the azimuthal equidistant projection:
where laeax and laeay are the x and y components of the equatorial Lambert azimuthal equal-area projection. Written out explicitly:
The inverse is calculated with the intermediate variable
The longitude and latitudes can then be calculated by
![\begin{align}
\lambda &= 2 \arctan \left[\frac{zx}{2(2z^2 - 1)}\right] \\
\phi &= \arcsin(zy)
\end{align}](http://upload.wikimedia.org/math/7/8/6/786cf5902deb031767dbd48a73a95bb7.png)
where λ is the longitude from the central meridian and φ is the latitude.[1][2]
Visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of its equal-area property. The Mollweide projection is another equal-area projection of similar aspect, though with straight parallels of latitude, unlike the Hammer's curved parallels.
[edit] References
- ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp.130-133, ISBN 0-226-76747-7.
- ^ Weisstein, Eric W. "Hammer-Aitoff Equal-Area Projection." From MathWorld--A Wolfram Web Resource
