The Adams square II projection shows the world in a square. It is one of the two projections presented by Oscar S. Adams in 1925. The projection is conformal except in the four corners of the square. In Adams's original design, the projection displays the equator and central meridian as diagonals of the square.
A beneficial property of this projection is that it can be tessellated or mosaicked. This projection or a similar projection was used by Athelstan Spilhaus in 1979, with the help of Robert Hanson and Ervin Schmid, from the National Geodetic Survey, for his world ocean map (see the second image, below).
The equations for an ellipsoid of revolution were developed at Esri. The Adams square II projection is available in ArcGIS Pro 2.5 and later and in ArcGIS Desktop 10.8 and later.
The subsections below describe the Adams square II projection properties.
In an equatorial aspect, the equator and central meridian are projected as straight lines forming diagonals of the square. The antimeridian is projected as a straight line bent at the equator forming the square outline of the map. Other meridians are complex curves. The parallels are complex curves, unequally spaced along the central meridian and concave toward the nearest pole. Their spacing grows with the distance from the equator. Both poles project as a point in opposite corners of the square. The graticule is symmetric across the equator and the central meridian.
The Adams square II is a conformal map projection. Directions, angles, and shapes are maintained at infinitesimal scale. Conformality fails at the four corners of the square. Areas are hugely exaggerated in polar regions and along the antimeridian. In an equatorial aspect, distortion values are symmetric across the equator and the central meridian.
This projection has no practical use aside from designing a world map in a square or to tessellate or mosaic a large, flat surface.
Adams square II parameters are as follows:
- False Easting
- False Northing
- Scale Factor
- Longitude Of Center
- Latitude Of Center
- XY Plane Rotation
Adams, O. S. (1929). Conformal projection of the sphere within a square. Washington: U.S. Coast and Geodetic Survey Special Publication 153.
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.
Spilhaus, A. (1983). "World ocean maps: The proper places to interrupt." Proceedings of the American Philosophical Society, 127(1), p. 50-60