Hammer projection

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] .


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