lambert azimuthal equal-area projection

The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk (that is, a region bounded by a circle).

Lambert azimuthal equal-area projection (preserves areas)

In 1772 he created the Lambert conformal conic and Lambert azimuthal equal-area projections.

The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert azimuthal equal-area projection.

The equal-area lower-hemisphere projection defined by the Lambert azimuthal equal-area projection is also used, especially when the plot is to be subjected to subsequent statistical analysis such as density contouring.

Three years later, Ernst Hermann Heinrich Hammer suggested the use of the Lambert azimuthal equal-area projection in the same manner as Aitoff, producing the Hammer projection.

Directly inspired by the Aitoff projection, Hammer suggested the use of the equatorial form of the Lambert azimuthal equal-area projection instead of Aitoff's use of the azimuthal equidistant projection:

For example, the National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display.

The map shown above is based on this relationship; it shows a Lambert azimuthal equal-area projection map of the Earth, in yellow, overlaid on which is another map, in blue, shifted horizontally by 180 of longitude and inverted about the equator with respect to latitude.