Movatterモバイル変換


[0]ホーム

URL:


Jump to content
WikipediaThe Free Encyclopedia
Search

Albers projection

From Wikipedia, the free encyclopedia
Conic equal-area map projection
Albers projection of the world with standard parallels 20°N and 50°N
The Albers projection with standard parallels 15°N and 45°N, withTissot's indicatrix of deformation
An Albers projection shows areas accurately, but distorts shapes.

TheAlbers equal-area conic projection, orAlbers projection, is aconic,equal areamap 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.[1]

Official adoption

[edit]

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

CountryAgency
Brazilfederal government, throughIBGE, for Census Statistical Grid[2]
Canadagovernment ofBritish Columbia[3]
Canadagovernment of theYukon[4] (sole governmental projection)
USUnited States Geological Survey[5]
USUnited States Census Bureau[5]

Some "official products" also adopted Albers projection, for example most of the maps in theNational Atlas of the United States.[6]

Formulas

[edit]

For sphere

[edit]

Snyder[6] describes generating formulae for the projection, as well as the projection's characteristics. Coordinates from a sphericaldatum can be transformed into Albers equal-area conic projection coordinates with the following formulas, whereR{\displaystyle {R}} is the radius,λ{\displaystyle \lambda } is the longitude,λ0{\displaystyle \lambda _{0}} the reference longitude,φ{\displaystyle \varphi } the latitude,φ0{\displaystyle \varphi _{0}} the reference latitude andφ1{\displaystyle \varphi _{1}} andφ2{\displaystyle \varphi _{2}} the standard parallels:

x=ρsinθ,y=ρ0ρcosθ,{\displaystyle {\begin{aligned}x&=\rho \sin \theta ,\\y&=\rho _{0}-\rho \cos \theta ,\end{aligned}}}

where

n=12(sinφ1+sinφ2),θ=n(λλ0),C=cos2φ1+2nsinφ1,ρ=RnC2nsinφ,ρ0=RnC2nsinφ0.{\displaystyle {\begin{aligned}n&={\tfrac {1}{2}}(\sin \varphi _{1}+\sin \varphi _{2}),\\\theta &=n(\lambda -\lambda _{0}),\\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

[edit]

If just one of the two standard parallels of the Albers projection is placed on a pole, the result is theLambert equal-area conic projection.[7]

See also

[edit]

References

[edit]
  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. Retrieved6 December 2024.
  2. ^"Grade Estatística"(PDF). 2016. Archived fromthe original(PDF) on 2018-02-19.
  3. ^"Data Catalogue".
  4. ^"Support & Info: Common Questions".Geomatics Yukon. Government of Yukon. Retrieved15 October 2014.
  5. ^ab"Projection Reference". Bill Rankin.Archived from the original on 25 April 2009. Retrieved2009-03-31.
  6. ^abSnyder, 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. Retrieved2017-08-28.
  7. ^"Directory of Map Projections"."Lambert equal-area conic".

External links

[edit]
Wikimedia Commons has media related toAlbers projection.
Cylindrical
Mercator-conformal
Equal-area
Pseudocylindrical
Equal-area
Conical
Pseudoconical
Azimuthal
(planar)
General perspective
Pseudoazimuthal
Conformal
Equal-area
Bonne
Bottomley
Cylindrical
Tobler hyperelliptical
Equidistant in
some aspect
Gnomonic
Loxodromic
Retroazimuthal
(Mecca or Qibla)
Compromise
Hybrid
Perspective
Planar
Polyhedral
See also


Stub icon

Thiscartography ormapping term article is astub. You can help Wikipedia byadding missing information.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Albers_projection&oldid=1334504540"
Categories:
Hidden categories:

[8]ページ先頭

©2009-2026 Movatter.jp