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 map projection. It is a member of the cylindrical equal-area projection family. This projection is undistorted along the Equator (its standard parallel), but compression between parallels increases rapidly away from 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 invention of this projection is attributed to the Alsatian mathematician Johann Heinrich Lambert in 1772.

The projection is:

$x = \lambda - \lambda_0 \!$

$y = \sin \phi \!$

where $\phi\,$ is the latitude, $\lambda\,$ is the longitude and $\lambda_0\,$ is the central meridian.

See also

• Lambert azimuthal equal-area projection
• Lambert conformal conic projection

External links

• Table of examples and properties of all common projections, from radicalcartography.net
• An interactive Java Applet to study the metric deformations of the Lambert Cylindrical Equal-Area Projection.