Albers projection

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File:Usgs map albers equal area conic.PNG
An Albers projection shows areas accurately, but distorts shapes.
Albers projection of the world with standard parallels 20°N and 50°N.

The Albers equal-area conic projection, or Albers projection (named after Heinrich C. Albers), 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.

The Albers projection is one of the standard projections for British Columbia,[1] and is the sole standard projection used by the government of Yukon.[2] It is also used by the United States Geological Survey and the United States Census Bureau.[3]

Snyder[4] (Section 14) 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,[5] where λ is the longitude, λ0 the reference longitude, φ the latitude, φ0 the reference latitude and φ1 and φ2 the standard parallels:

x = \rho  \sin\theta
y = \rho_0 - \rho  \cos\theta

where

n = {\tfrac12} (\sin\varphi_1+\sin\varphi_2)
\theta = n(\lambda - \lambda_0)
C = \cos^2 \varphi_1 + 2 n \sin \varphi_1
\rho = \frac{\sqrt{C - 2 n \sin \varphi}}{n}
\rho_0 = \frac{\sqrt{C - 2 n \sin \varphi_0}}{n}

See also

References

  1. British Columbia
  2. "Support & Info: Common Questions". Geomatics Yukon. Government of Yukon. Retrieved 15 October 2014.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  3. "Projection Reference". Bill Rankin. Archived from the original on 25 April 2009. Retrieved 2009-03-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  4. Snyder, John P. (1987). Map Projections – A Working Manual. U.S. Geological Survey Professional Paper 1395. United States Government Printing Office, Washington, D.C.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> This paper can be downloaded from USGS pages.
  5. Weisstein, Eric. "Albers Equal-area Conic Projection". Wolfram MathWorld. Wolfram Research. Retrieved 2013-05-04.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

External links