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vgrint1

Van der Grinten I Projection

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

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