The Display command of the WorldMap object can display maps of the world using various projections by specifying the projection=proj keyword option.

Some projections accept additional parameters for the central meridian (${\mathrm{\lambda }}_0$) and/or the standard parallel (${\mathrm{\phi }}_1$).

Examples in all sections below use the WorldMap object with no point stored:

m:=DataSets:-Builtin:-WorldMap();

$m≔\left(\begin{array}{cc}\left[\mathrm{PLOT}\left(\mathrm{...}\right)\right]& \begin{array}{c}\mathrm{A\; map\; of\; the\; world}\\ \mathrm{projection:\; MillerCylindrical}\end{array}\end{array}\right)$

The Geographic projection directly maps longitude and latitude pairs to $x$ and $y$ coordinates in the map.

It is a special case of the Equirectangular projection with the standard parallel (${\mathrm{\phi }}_1$) equal to 0 degrees.

Display(m,projection=Geographic);

The Cassini projection is the transverse aspect of the Geographic projection.

The Cassini projection can accept an additional parameter for the central meridian (${\mathrm{\lambda }}_0$).

If no parameter is specified, the resulting projection is equivalent to Cassini(0).

Display(m,projection=Cassini);

The Mercator projection is a conformal cylindrical map projection which is widely used for nautical purposes.

It greatly exaggerates areas far from the equator, and the poles are projected to infinity, so the map must be truncated near the poles.

Display(m,projection=Mercator);

The TransverseMercator projection is the transverse aspect of the Mercator projection.

It delivers accurate scales near the central meridian.

Display(m,projection=TransverseMercator);

The MillerCylindrical projection is a compromise cylindrical map projection that is intended to look similar to the Mercator projection while displaying the poles.

The MillerCylindrical projection is the default projection used by the Display command.

Display(m,projection=MillerCylindrical);

The CylindricalEqualArea projection is a family of cylindrical and equal area projections.

The general CylindricalEqualArea projection can accept an additional parameter for the standard parallel (${\mathrm{\phi }}_1$).

If no parameter is specified, the resulting projection is the HoboDyer projection.

Supported special cases include LambertCylindricalEqualArea, Behrmann, SmythEqualSurface, TrystanEdwards, HoboDyer, GallPeters, and Balthasart. The value of the standard parallel for these projections is listed in the table below.

Display(m,projection=CylindricalEqualArea(37.5));

The LambertAzimuthalEqualArea projection maps the earth onto a disk, and it preserves areas of all regions.

The LambertAzimuthalEqualArea projection can accept two parameters for the central meridian (${\mathrm{\lambda }}_0$) and the standard parallel (${\mathrm{\phi }}_1$).

If no parameter is specified, the resulting projection is the equatorial aspect of the LambertAzimuthalEqualArea projection.

The point (${\mathrm{\lambda }}_0$,${\mathrm{\phi }}_1$) becomes the center of the projected map.

Display(m,projection=LambertAzimuthalEqualArea(20.4, -15));

The AzimuthalEquidistant projection can accept two parameters for the central meridian (${\mathrm{\lambda }}_0$) and the standard parallel (${\mathrm{\phi }}_1$).

If no parameter is specified, the resulting projection is the north pole aspect of the AzimuthalEquidistant projection.

The point (${\mathrm{\lambda }}_0$,${\mathrm{\phi }}_1$) becomes the center of the projected map.

Distances from the center to all other points are preserved.

Display(m,projection=AzimuthalEquidistant(0,90));

The VanderGrinten projection is a compromise projection that maps the earth onto a circle. The polar regions exhibit great distortions.

It was used by the National Geographic Society from 1922 to 1988.

Display(m,projection=VanderGrinten);

The Bonne projection is a pseudoconical equal area projection which is an intermediate between the Werner projection and the Sinusoidal projection.

The Bonne projection can accept two parameters for the central meridian (${\mathrm{\lambda }}_0$) and the standard parallel (${\mathrm{\phi }}_1$).

If no parameter is specified, the resulting projection is equivalent to Bonne(0,45).

Display(m,projection=Bonne(0,45));

The Bottomley projection is a pseudoconical equal area projection that is designed as a better looking alternative to the Bonne projection.

The Bottomley projection can also be seen as an intermediate between the Werner projection and the Sinusoidal projection.

The Bottomley projection can accept an additional parameter for the standard parallel (${\mathrm{\phi }}_1$).

If no parameter is specified, the resulting projection is equivalent to Bottomley(45).

Display(m,projection=Bottomley(45));

The Werner projection is a limiting case of both the Bonne and the Bottomley projection.

It is equivalent to Bonne(0,90) and Bottomley(90).

Display(m,projection=Werner);

The Sinusoidal projection is also a limiting case of both the Bonne and the Bottomley projection.

The Sinusoidal projection can accept an additional parameter for the central meridian (${\mathrm{\lambda }}_0$).

The Sinusoidal(0) projection is equivalent to Bottomley(0). The Sinusoidal(${\mathrm{\lambda }}_0$) projection is equivalent to Bonne(${\mathrm{\lambda }}_0$, 0).

If no parameter is specified, the resulting projection is equivalent to Sinusoidal(0).

Display(m,projection=Sinusoidal(-12));

The Robinson projection is a pseudocylindrical compromise projection that is designed to produce a nice looking map for the entire world.

It was used by the National Geographic Society from 1988 to 1998.

Display(m,projection=Robinson);

The WinkelTripel projection is a pseudoazimuthal compromise projection that tries to minimize area, direction, and distance distortions all at the same time.

It has been used by the National Geographic Society since 1998.

Display(m,projection=WinkelTripel);

The Globe projection displays a 3-D plot of the earth as a sphere.

Display(m,projection=Globe);