List of Projections - Maple Help

List of Projections for Use with WorldMap

Description

 • 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();
 ${m}{≔}\left(\begin{array}{cc}\left[{\mathrm{PLOT}}{}\left({\mathrm{...}}\right)\right]& \begin{array}{c}{\mathrm{A map of the world}}\\ {\mathrm{projection: MillerCylindrical}}\end{array}\end{array}\right)$ (1)

Geographic

 • 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);

Cassini

 • 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);

Mercator

 • 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);

TransverseMercator

 • The TransverseMercator projection is the transverse aspect of the Mercator projection.
 • It delivers accurate scales near the central meridian.
 > Display(m,projection=TransverseMercator);

MillerCylindrical

 • 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);

CylindricalEqualArea

 • 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.

 Projections ${\mathrm{\phi }}_{1}$ LambertCylindricalEqualArea 0 Behrmann 30 SmythEqualSurface 37 + 4 / 60 + 17 / 3600 (that is, 37° 4' 17") TrystanEdwards 37.4 HoboDyer 37.5 GallPeters 45 Balthasart 50

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

LambertAzimuthalEqualArea

 • 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));

AzimuthalEquidistant

 • 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));

VanderGrinten

 • 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);

Bonne

 • 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));

Bottomley

 • 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));

Werner

 • 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);

Sinusoidal

 • 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));

Robinson

 • 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);

WinkelTripel

 • 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);

Globe

 • The Globe projection displays a 3-D plot of the earth as a sphere.
 > Display(m,projection=Globe);
 >