vgrint1

Van der Grinten I Projection

Classification

Polyconic

Identifier

vgrint1

Graticule

Central Meridian: A straight line.

Meridians: Circular curves spaced equally along the equator and concave toward the central meridian.

Parallels: The Equator is a straight line. All other parallels are circular arcs concave toward the nearest pole.

Poles: Points.

Symmetry: About the Equator or the central meridian.

Features

In this projection, the world is enclosed in a circle. Scale is true along the Equator and increases rapidly away from the Equator. Area distortion is extreme near the poles. This projection is neither conformal nor equal-area.

Parallels

There are no standard parallels for this projection.

Remarks

  • This projection was presented by Alphons J. Van der Grinten in 1898. He obtained a U.S. patent for it in 1904. It is also known simply as the Van der Grinten projection (without the “I”).

  • Mapping Toolbox™ uses a different implementation of the Van der Grinten I projection for displaying coordinates on map axes than for projecting coordinates using the projfwd or projinv function. These implementations may produce differing results.

  • The implementation of the Van der Grinten I projection for displaying coordinates on map axes is applicable only for coordinates that are referenced to a sphere. The implementation of the Van der Grinten I projection for projecting coordinates using the projfwd or projinv function is applicable for coordinates referenced to either a sphere or an ellipsoid.

Limitations

This projection is available only for the sphere.

Example

landareas = shaperead('landareas.shp','UseGeoCoords',true);
axesm ('vgrint1', 'Frame', 'on', 'Grid', 'on');
geoshow(landareas,'FaceColor',[1 1 .5],'EdgeColor',[.6 .6 .6]);
tissot;

Introduced before R2006a