Description
The Gall stereographic projection is a cylindrical map projection with two standard parallels at latitudes 45° north and south. The projection is a special case of the perspective cylindrical projection with the perspective ratio of 1 and the standard parallel at 45°. It can be constructed geometrically by projecting the globe onto a secant cylinder from the point on the equator opposite the given central meridian.
This projection was introduced by James Gall in 1855. 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 Gall stereographic projection properties.
Graticule
Gall stereographic is a cylindric projection. The meridians are equally spaced straight lines. The parallels and both poles are straight lines, perpendicular to meridians and the same length as the projected equator. The spacing between the parallels increases from the equator to the poles. The graticule is symmetric across the equator and the central meridian.
Distortion
The Gall stereographic projection is neither conformal nor equal-area. Shapes, areas, distances, directions, and angles are all generally distorted. The projection has correct scale and no distortion along the standard parallels at 45° north and south. Distortion increases away from the standard parallels, and it is extreme at the polar regions. Along any given latitude, distortion values are constant.
Usage
This projection can be used for general world maps not requiring accurate areas, and its phenomena change with longitude, although its use is not recommended due to extreme distortion in polar regions.
Limitations
Gall stereographic 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
Gall stereographic parameters are as follows:
- False Easting
- False Northing
- Central Meridian
Sources
Bugayevskiy, L. M. and Snyder, J. P. (1995). Map Projections: A Reference Manual. London: Taylor & Francis.
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.