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Nonperspective Azimuthal Projections

Azimuthal equidistant map

Azimuthal equidistant projection, north polar aspect

Azimuthal equidistant map

Azimuthal equidistant projection, equatorial aspect

Unlike the “classic” orthographic, stereographic and gnomonic designs, azimuthal projections like the equidistant and equal-area were derived mathematically without a real perspective process. Both can map a full sphere, with an “inner” hemisphere surrounded by a ringlike “outer” one. However, for lesser overall distortion the latter may be presented in a separate map centered on the antipodal point.

Azimuthal Equidistant Projection

Able to present the whole Earth in a single map and with constant radial scale (distances increase linearly from the center of projection), the azimuthal equidistant projection is further discussed elsewhere due to its important features.

In the north polar aspect, the azimuthal equidistant is familiar as part of both flag and emblem of the United Nations Organization, with olive branches replacing Antarctica. The austral continent, here turned “inside-out”, illustrates this projection's extreme distortion of shapes and areas far from the center.

Azimuthal equal-area maps
Equal-area azimuthal projection

North polar aspect

Equal-area azimuthal projection

Equatorial aspect, central meridian 5°E

Equal-area azimuthal projection

Western hemisphere, central meridian 110°W

Equal-area azimuthal projection

Eastern hemisphere, central meridian 70°E

Simple in construction, this projection is sometimes clipped to a single hemisphere, and often restricted to insets for polar caps.

Lambert's Azimuthal Equal-area Projection

Like the superficially similar azimuthal equidistant, the azimuthal projection published by Johann H. Lambert in 1772 strongly distorts shapes in the boundary of a worldwide map. However, the radial scale is not constant: in the polar aspect, parallels get closer together towards the border, just enough to preserve areas.

Relatively simple in construction, this projection is frequently used in all aspects.

The polar aspect of Lambert's azimuthal projection was independently devised by Anton-Mario Lorgna (1789), and during a short period named after him.

Ginzburg azimuthal maps
Ginzburg I azimuthal projection

Ginzburg I, north polar

Ginzburg I azimuthal projection

Ginzburg I, eastern equatorial (central meridian 70°E)

Ginzburg I azimuthal projection

Ginzburg II, north polar

Ginzburg I azimuthal projection

Ginzburg's II, eastern equatorial

Ginzburg's Modified Azimuthal Projections

In 1949, Russian Georgiy A.Ginzburg proposed two azimuthal projections for hemispheres in school maps. Since Lambert's equal-area projection compresses distances from the center of the map, causing considerable shape distortion near the borders, Ginzburg added a power term to Lambert's equations, slightly expanding the map. The result is neither conformal nor equivalent.

Ginzburg I azimuthal projection

Tissot indicatrices comparing the distortion of one hemisphere drawn in Ginzburg's and Lambert's equal-area projections at identical scaling factors.


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www.progonos.com/furuti/MapProj/Normal/ProjAz/ProjAzNP/projAzNP.html — June 16, 2018
Copyright © 1996, 1997, 2008 Carlos A. Furuti