Eckert II projection

Eckert II projection of the world

The Eckert II projection is an equal-area pseudocylindrical map projection presented by Max Eckert-Greifendorff in 1906. In the equatorial aspect (where the equator is shown as the horizontal axis) the network of longitude and latitude lines consists solely of straight lines, and the outer boundary has the distinctive shape of an elongated hexagon.

Description

The projection is symmetrical about the straight equator and straight central meridian. Parallels vary in spacing in order to preserve areas. As a pseudocylindric projection, spacing of meridians along any given parallel is constant. The poles are represented as lines, each half as long as the equator. The projection has correct scale only on the central meridian at latitudes 55°10′ north and south.[1]

The projection's x and y coordinates can be computed as

\begin{align} x &= 2 R \left(\lambda - \lambda_0 \right) \sqrt{\frac{4-3\sin|\varphi|}{6\pi}} \\ y &= R \sqrt{\frac{2 \pi}{3}} \left(2 - \sqrt{4 - 3 \sin |\varphi|}\right) \end{align}

where λ is the longitude, λ0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. Here, y assumes the sign of φ.

See also

Notes

  1. ↑ John P., Snyder (1989). An Album of Map Projections (U.S. Geological Survey Professional Paper 1453). Denver: US Geological Survey. p. 88.

References

External links

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