Eckert-Greifendorff projection

The Eckert-Greifendorff projection is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.

Development

Directly inspired by the Hammer projection, Eckert-Greifendorff 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]

gollark: ```curl -H "I-Am: A Potato" https://osmarks.tk```
gollark: ```curl --curl -X CURL -H "cUrl: CURL" curl://curl.curl/curl?curl=cUrl```
gollark: Please note that MCaaS Tau digits are *not* guaranteed to be accurate near the end beyond 100000 digits.
gollark: Pi and Tau only.
gollark: Best page: https://osmarks.tk/joe/index.html

See also

References

  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
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