Hammer projection
![](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b2/Hammer_projection_SW.jpg/350px-Hammer_projection_SW.jpg)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Hammer_with_Tissot%27s_Indicatrices_of_Distortion.svg/350px-Hammer_with_Tissot%27s_Indicatrices_of_Distortion.svg.png)
The Hammer projection is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.
Development
[edit]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
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.
Briesemeister
[edit]William A. Briesemeister presented a variant of the Hammer in 1953. In this version, the central meridian is set to 10°E, the coordinate system is rotated to bring the 45°N parallel to the center, and the resulting map is squashed horizontally and reciprocally stretched vertically to achieve a 7:4 aspect ratio instead of the 2:1 of the Hammer. The purpose is to present the land masses more centrally and with lower distortion.[3][4]
Nordic
[edit]Before projecting to Hammer, John Bartholomew rotated the coordinate system to bring the 45° north parallel to the center, leaving the prime meridian as the central meridian. He called this variant the "Nordic" projection.[4]
See also
[edit]References
[edit]- ^ 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
- ^ Briesemeister, William (April 1953). "A new oblique equal-area projection". Geographical Review. 43 (2): 260–261. doi:10.2307/211940. Retrieved 2024-01-18.
- ^ a b Snyder, John P.; Voxland, Philip M. (1989). An Album of Map Projections. Professional Paper 1453. Denver: USGS. p. 162. ISBN 978-0160033681. Archived from the original on 2010-07-01. Retrieved 2018-03-29.
External links
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