Description
The Eckert-Greifendorff projection is a modification of the Lambert azimuthal equal-area projection. The projection appears to have straight parallels, but they are actually slightly curved. The boundary meridians bulge outward excessively, producing considerable shape distortion near the map outline.
The Eckert-Greifendorff projection was introduced by Max Eckert (at the time of its publication, he was known as Max Eckert-Greifendorff) in 1935. The equations for an ellipsoid of revolution were developed at Esri. It is available in ArcGIS Pro 1.2 and later and in ArcGIS Desktop 10.4 and later.
Projection properties
The subsections below describe the Eckert-Greifendorff projection properties.
Graticule
Eckert-Greifendorff is a modified azimuthal projection. The equator and central meridian are projected as straight lines, where the central meridian is 0.46 times the size of the projected equator. Other meridians and parallels are unequally spaced curved lines. The meridians are concave toward the central meridian, while parallels are concave toward the nearest pole. The poles are presented as points, and they appear as protruding edges. The projection's outline is similar to a sinusoidal or quartic authalic projection. The graticule is symmetric across the equator and the central meridian.
Distortion
Eckert-Greifendorff is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are distorted. The distortions are moderate near the projection center. Bulging meridians produce considerable distortion toward the edges of the projection. Distortion values are symmetric across the equator and the central meridian.
Usage
This projection is appropriate for thematic world maps although its use is not advisable.
Parameters
Eckert-Greifendorff parameters are as follows:
- False Easting
- False Northing
- Central Meridian
- Latitude Of Origin
Sources
Eckert-Greifendorff, M. (1935). "Eine neue flächentreue (azimutaloide) Erdkarte". Petermanns Mitteilungen, 81 (6), p. 190-192.
Bugayevskiy, L. M. and Snyder, J. P. (1995). Map Projections: A Reference Manual. London: Taylor & Francis.
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.