Jump to content

Hammer projection

From Wikipedia, the free encyclopedia
Hammer projection of the world
The Hammer projection with Tissot's indicatrix of deformation

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]
  1. ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 130–133, ISBN 0-226-76747-7.
  2. ^ Weisstein, Eric W. "Hammer–Aitoff Equal-Area Projection." From MathWorld—A Wolfram Web Resource
  3. ^ Briesemeister, William (April 1953). "A new oblique equal-area projection". Geographical Review. 43 (2): 260–261. doi:10.2307/211940. Retrieved 2024-01-18.
  4. ^ 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.
[edit]