List of Projections for Use with WorldMap

Description


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

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Some projections accept additional parameters for the central meridian (${\mathrm{\lambda}}_{0}$) and/or the standard parallel (${\mathrm{\phi}}_{1}$).

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

>

m:=DataSets:Builtin:WorldMap();

${m}{\u2254}\left(\begin{array}{cc}\left[{\mathrm{PLOT}}{}\left({\mathrm{...}}\right)\right]& \begin{array}{c}{\mathrm{A\; map\; of\; the\; world}}\\ {\mathrm{projection:\; MillerCylindrical}}\end{array}\end{array}\right)$
 (1) 


Geographic


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

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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


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

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The Cassini projection can accept an additional parameter for the central meridian (${\mathrm{\lambda}}_{0}$).

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

>

Display(m,projection=Cassini);



Mercator


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

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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


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

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It delivers accurate scales near the central meridian.

>

Display(m,projection=TransverseMercator);



MillerCylindrical


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

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

>

Display(m,projection=MillerCylindrical);



CylindricalEqualArea


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

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The general CylindricalEqualArea projection can accept an additional parameter for the standard parallel (${\mathrm{\phi}}_{1}$).

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

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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


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

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The LambertAzimuthalEqualArea projection can accept two parameters for the central meridian (${\mathrm{\lambda}}_{0}$) and the standard parallel (${\mathrm{\phi}}_{1}$).

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

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The point (${\mathrm{\lambda}}_{0}$,${\mathrm{\phi}}_{1}$) becomes the center of the projected map.

>

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



AzimuthalEquidistant


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The AzimuthalEquidistant projection can accept two parameters for the central meridian (${\mathrm{\lambda}}_{0}$) and the standard parallel (${\mathrm{\phi}}_{1}$).

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

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The point (${\mathrm{\lambda}}_{0}$,${\mathrm{\phi}}_{1}$) becomes the center of the projected map.

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Distances from the center to all other points are preserved.

>

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



VanderGrinten


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

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

>

Display(m,projection=VanderGrinten);



Bonne


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

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The Bonne projection can accept two parameters for the central meridian (${\mathrm{\lambda}}_{0}$) and the standard parallel (${\mathrm{\phi}}_{1}$).

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

>

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



Bottomley


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

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

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The Bottomley projection can accept an additional parameter for the standard parallel (${\mathrm{\phi}}_{1}$).

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

>

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



Werner


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

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

>

Display(m,projection=Werner);



Sinusoidal


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

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The Sinusoidal projection can accept an additional parameter for the central meridian (${\mathrm{\lambda}}_{0}$).

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

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

>

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



Robinson


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

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

>

Display(m,projection=Robinson);



WinkelTripel


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

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

>

Display(m,projection=WinkelTripel);



Globe


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

>

Display(m,projection=Globe);


