Misplaced Pages

The Albers equal-area conic projection, or Albers projection, is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels. It was first described by Heinrich Christian Albers (1773-1833) in a German geography and astronomy periodical in 1805.

Official adoption

The Albers projection is used by some big countries as "official standard projection" for Census and other applications.

Some "official products" also adopted Albers projection, for example most of the maps in the National Atlas of the United States.

Formulas

For Sphere

Snyder describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a spherical datum can be transformed into Albers equal-area conic projection coordinates with the following formulas, where ${\displaystyle {R}}$ is the radius, ${\displaystyle \lambda }$ is the longitude, ${\displaystyle \lambda _{0}}$ the reference longitude, ${\displaystyle \varphi }$ the latitude, ${\displaystyle \varphi _{0}}$ the reference latitude and ${\displaystyle \varphi _{1}}$ and ${\displaystyle \varphi _{2}}$ the standard parallels:

${\displaystyle {\begin{aligned}x&=\rho \sin \theta \\y&=\rho _{0}-\rho \cos \theta \end{aligned}}}$

where

${\displaystyle {\begin{aligned}n&={\tfrac {1}{2}}\left(\sin \varphi _{1}+\sin \varphi _{2}\right)\\\theta &=n\left(\lambda -\lambda _{0}\right)\\C&=\cos ^{2}\varphi _{1}+2n\sin \varphi _{1}\\\rho &={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi }}\\\rho _{0}&={\tfrac {R}{n}}{\sqrt {C-2n\sin \varphi _{0}}}\end{aligned}}}$

Lambert equal-area conic

If just one of the two standard parallels of the Albers projection is placed on a pole, the result is the Lambert equal-area conic projection.

See also

• List of map projections

References

1. Albers, H. C. (November 1805). "Beschreibung einer neuen Kegelprojection". (von Zach's) Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde. 12: 450–459. Retrieved 6 December 2024.
2. "Grade Estatística" (PDF). 2016. Archived from the original (PDF) on 2018-02-19.
3. "Data Catalogue".
4. "Support & Info: Common Questions". Geomatics Yukon. Government of Yukon. Retrieved 15 October 2014.
5. ^ "Projection Reference". Bill Rankin. Archived from the original on 25 April 2009. Retrieved 2009-03-31.
6. ^ Snyder, John P. (1987). "Chapter 14: ALBERS EQUAL-AREA CONIC PROJECTION". Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, D.C.: United States Government Printing Office. p. 100. Archived from the original on 2008-05-16. Retrieved 2017-08-28.
7. "Directory of Map Projections". "Lambert equal-area conic".

External links

• Mathworld's page on the Albers projection
• Table of examples and properties of all common projections, from radicalcartography.net
• An interactive Java Applet to study the metric deformations of the Albers Projection.

This cartography or mapping term article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

• Equal-area projections
• Cartography stubs