Lambert cylindrical equal-area projection

Lambert cylindrical equal-area projection of the world.
Lambert cylindrical equal-area projection of the world, central meridian at 160°W to focus the map on the oceans.
Lambert cylindrical equal-area projection with Tissot's indicatrix of deformation.
How the Earth is projected onto a cylinder

In cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is a cylindrical equal-area projection. This projection is undistorted along the equator, which is its standard parallel, but distortion increases rapidly towards the poles. Like any cylindrical projection, it stretches parallels increasingly away from the equator. The poles accrue infinite distortion, becoming lines instead of points.

History

The projection is attributed to the Alsatian mathematician Johann Heinrich Lambert in 1772.[1]

In the work On the Sphere and Cylinder, Archimedes shows that a sphere has the same area as a cylinder around it, and although Archimedes did not discuss the projection explicitly his argument shows that the projection preserves areas.

Formulae

\begin{align} x &= \lambda - \lambda_0\\ y &= \sin \varphi \end{align}

where φ is the latitude, λ is the longitude and λ0 is the central meridian.[2]

Comparison of the Lambert cylindrical equal-area projection and some cylindrical equal-area map projections with Tissot indicatrix, standard parallels and aspect ratio

See also

References

  1. ↑ Mulcahy, Karen. "Cylindrical Projections". City University of New York. Retrieved 2007-03-30.
  2. ↑ Map Projections – A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 76–85

External links


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