Eckert I

Description

The Eckert I projection is a compromise pseudocylindrical map projection with rectilinear meridians and an odd appearance. The projection is simple, but it has no practical use other than making a world map with an unusual shape.

The projection was introduced by Max Eckert in 1906. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

The Eckert I compromise projection centered on Greenwich is shown.

Projection properties

The subsections below describe the Eckert I projection properties.

Graticule

Eckert I is a pseudocylindric projection. The meridians are regularly distributed straight lines interrupted at the equator. The central meridian is a straight line, half the length of the projected equator. The parallels are equally distributed straight lines, perpendicular to the central meridian. The poles are straight lines, half the length of equator. The graticule is symmetric across the equator and the central meridian.

Distortion

Eckert I is neither conformal nor equal area. It generally distorts shapes, areas, distances, directions, and angles. Scale is correct along the 47°10' North and South parallels and constant along any given parallel and meridian. Due to the discontinuity, distortion cannot be determined at the equator. Distortion values are symmetric across the equator and the central meridian.

Usage

The Eckert I projection has no practical use other than designing a world map with an unusual shape.

Limitations

Eckert I is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius. Some distortion properties are not maintained when an ellipsoid is used.

Parameters

Eckert I parameters are as follows:

• False Easting
• False Northing
• Central Meridian

Sources

Canters, F. (2002). Small-scale Map Projection Design. London: Taylor & Francis.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453.Washington, DC: United States Government Printing Office.