Hammer projection

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:

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

:$y\; =\; frac\; 1\; 2mathrm\{laea\}\_yleft(fraclambda\; 2,\; phi\; ight)$

where $mathrm\{laea\}\_x$ and $mathrm\{laea\}\_y$ are the x and y components of the equatorial Lambert azimuthal equal-area projection. Written out explicitly:

:$x\; =\; frac\{2\; sqrt\; 2\; cos(phi)sinleft(fraclambda\; 2\; ight)\}\{sqrt\{1\; +\; cos(phi)cosleft(fraclambda\; 2\; ight)$

:$y\; =\; frac\{sqrt\; 2sin(phi)\}\{sqrt\{1\; +\; cos\; phi\; cosleft(fraclambda\; 2\; ight)$

where $lambda$ is the longitude from the central meridian and $phi$ is the latitude. ["Flattening the Earth: Two Thousand Years of Map Projections", John P. Snyder, 1993, pp.130-133, ISBN 0-226-76747-7.]

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.

References

ee also

* Mollweide projection
* Aitoff projection

External links

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