Description
The Van der Grinten I projection is a polyconic projection of the world in a circle. In this projection, the continents look similar to how they appear on the Mercator projection, except that the Van der Grinten I portrays the world with a curved graticule. Both the meridians and parallels are projected as circular arcs. National Geographic used the projection for their world maps between 1922 and 1988.
The projection was invented by Alphons J. van der Grinten in 1898. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
Projection properties
The subsections below describe the Van der Grinten I projection properties.
Graticule
Van der Grinten I is a polyconic projection. The equator and the central meridian are projected as straight lines of equal length. The other meridians are equally spaced circular arcs concave toward the central meridian. All parallels, except the equator, are also projected as circular arcs, but concave toward the nearest pole. They are unequally spaced and their spacing decreases away from the equator. The projection outline forms a circle. The poles are presented as points on the outline. The graticule is symmetric across the equator and the central meridian.
Distortion
The Van der Grinten I projection is neither conformal nor equal-area. Shapes, areas, distances, directions, and angles are all generally distorted. The scale is true along the equator and increases rapidly with the distance from the equator. The polar regions are greatly distorted and exaggerated. Distortion values are symmetric across the equator and the central meridian.
Usage
Due to its circular look, the Van der Grinten I projection is very appealing for global maps. The projection could be used for general world maps not requiring accurate areas, although its use is not recommended due to extreme distortion in polar regions. National Geographic used the projection for their world maps between 1922 and 1988.
Variants
There are two variants available in ArcGIS:
- Van der Grinten I uses the semimajor axis and spherical equations for ellipsoids. It correctly supports the sphere-based Earth models. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.
- Van der Grinten I auxiliary sphere uses a sphere specified by the Auxiliary Sphere Type parameter and spherical equations for ellipsoids. It correctly supports the sphere-based Earth models. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.3 and later.
Limitations
Neither variant supports an ellipsoid.
Parameters
Van der Grinten I parameters are as follows:
- False Easting
- False Northing
- Central Meridian
Van der Grinten I auxiliary sphere parameters are as follows:
- False Easting
- False Northing
- Central Meridian
- Auxiliary Sphere Type, with values as follows:
- 0 = Use semimajor axis or radius of the geographic coordinate system
- 1 = Use semiminor axis or radius
- 2 = Calculate and use authalic radius
- 3 = Use authalic radius and convert geodetic latitudes to authalic latitudes
Sources
Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.
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.