Hammer projection

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A Hammer projection of the Earth
A Hammer projection of the Earth

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}_x\left(\frac\lambda 2, \phi\right)
y = \frac 1 2\mathrm{laea}_y\left(\frac\lambda 2, \phi\right)

where laeax and laeay are the x and y components of the equatorial Lambert azimuthal equal-area projection. Written out explicitly:

x = \frac{2 \sqrt 2 \cos(\phi)\sin\left(\frac\lambda 2\right)}{\sqrt{1 + \cos(\phi)\cos\left(\frac\lambda 2\right)}}
y = \frac{\sqrt 2\sin(\phi)}{\sqrt{1 + \cos \phi \cos\left(\frac\lambda 2\right)}}

where λ is the longitude from the central meridian and φ is the latitude.[1]

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

  1. ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp.130-133, ISBN 0-226-76747-7.

[edit] See also

[edit] External links