Van der Grinten projection

Van der Grinten projection of the world
The Van der Grinten projection with Tissot's indicatrix of deformation

The van der Grinten projection is a compromise map projection, which means that it is neither equal-area nor conformal. Unlike perspective projections, the van der Grinten projection is an arbitrary geometric construction on the plane. Van der Grinten projects the entire Earth into a circle. It largely preserves the familiar shapes of the Mercator projection while modestly reducing Mercator's distortion. Polar regions are subject to extreme distortion. Lines of longitude converge to points at the poles.[1]


Alphons J. van der Grinten invented the projection in 1898 and received US patent #751,226 for it and three others in 1904.[2] The National Geographic Society adopted the projection for their reference maps of the world in 1922, raising its visibility and stimulating its adoption elsewhere. In 1988, National Geographic replaced the van der Grinten projection with the Robinson projection.[1]

Geometric construction

The geometric construction given by van der Grinten can be written algebraically:[3]

where x takes the sign of λλ0, y takes the sign of φ, and

If φ = 0, then

Similarly, if λ = λ0 or φ = ±π/2, then

In all cases, φ is the latitude, λ is the longitude, and λ0 is the central meridian of the projection.

Van der Grinten IV Projection

The van der Grinten IV projection is a later polyconic map projection developed by Alphons J. van der Grinten. The central meridian and Equator are straight lines. All other meridians and parallels are arcs of circles.[4][5][6]

See also


  1. ^ a b Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 258–262,ISBN 0-226-76747-7.
  2. ^ A Bibliography of Map Projections, John P. Snyder and Harry Steward, 1989, p. 94, US Geological Survey Bulletin 1856.
  3. ^ Map Projections – A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 239–242.
  4. ^ "Van der Grinten IV Projection".
  5. ^ "An Album of Map Projections". p. 205.
  6. ^ "van der Grinten IV".


External links

Media files used on this page

Van der Grinten with Tissot's Indicatrices of Distortion.svg
Author/Creator: Justin Kunimune, Licence: CC BY-SA 4.0
The world on a Van der Grinten projection, with 10° graticule and Tissot's indicatrices overlaid. Each red circle is 1,000 km in diameter. Coastline data from Colors inspired by Eric Gaba. Projection generated with my own code, at
Van der Grinten projection SW.jpg
Author/Creator: Strebe, Licence: CC BY-SA 3.0
The world on Van der Grinten projection. 15° graticule. Imagery is a derivative of NASA’s Blue Marble summer month composite with oceans lightened to enhance legibility and contrast. Image created with the Geocart map projection software.