HOME
The Info List - Equirectangular Projection


--- Advertisement ---



The equirectangular projection (also called the equidistant cylindrical projection, geographic projection, or la carte parallélogrammatique projection, and which includes the special case of the plate carrée projection or geographic projection) is a simple map projection attributed to Marinus of Tyre, who Ptolemy
Ptolemy
claims invented the projection about AD 100.[1] The projection maps meridians to vertical straight lines of constant spacing (for meridional intervals of constant spacing), and circles of latitude to horizontal straight lines of constant spacing (for constant intervals of parallels). The projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia
Celestia
and NASA World Wind, because of the particularly simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth.

Contents

1 Definition

1.1 Forward 1.2 Reverse

2 See also 3 References 4 External links

Definition[edit] The forward projection transforms spherical coordinates into planar coordinates. The reverse projection transforms from the plane back onto the sphere. The formulae presume a spherical model and use these definitions:

λ is the longitude of the location to project; φ is the latitude of the location to project; φ1 are the standard parallels (north and south of the equator) where the scale of the projection is true; λ0 is the central meridian of the map; x is the horizontal coordinate of the projected location on the map; y is the vertical coordinate of the projected location on the map.

Forward[edit]

x

= ( λ −

λ

0

) cos ⁡

φ

1

y

= ( φ −

φ

1

)

displaystyle begin aligned x&=(lambda -lambda _ 0 )cos varphi _ 1 \y&=(varphi -varphi _ 1 )end aligned

The plate carrée (French, for flat square), is the special case where φ1 is zero. This projection maps x to be the value of the longitude and y to be the value of the latitude, and therefore is sometimes called the latitude/longitude or lat/lon(g) projection or is said (erroneously) to be “unprojected”. While a projection with equally spaced parallels is possible for an ellipsoidal model, it would no longer be equidistant because the distance between parallels on an ellipsoid is not constant. More complex formulae can be used to create an equidistant map whose parallels reflect the true spacing. Reverse[edit]

λ

=

x

cos ⁡

φ

1

+

λ

0

φ

= y +

φ

1

displaystyle begin aligned lambda &= frac x cos varphi _ 1 +lambda _ 0 \varphi &=y+varphi _ 1 end aligned

See also[edit]

Atlas portal

List of map projections Cartography Cassini projection Gall–Peters projection
Gall–Peters projection
with resolution regarding the use of rectangular world maps Mercator projection

References[edit]

^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 5–8, ISBN 0-226-76747-7.

External links[edit]

Global MODIS based satellite map The blue marble: land surface, ocean color and sea ice. Table of examples and properties of all common projections, from radicalcartography.net. Panoramic Equirectangular Projection, PanoTools wiki. Equidistant Cylindrical (Plate Caree) in proj4

v t e

Map projection

History List Portal

By surface

Cylindrical

Mercator-conformal

Gauss–Krüger Transverse Mercator

Equal-area

Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert Smyth equal-surface Trystan Edwards

Cassini Central Equirectangular Gall stereographic Miller Space-oblique Mercator Web Mercator

Pseudocylindrical

Eckert II Eckert IV Eckert VI Goode homolosine Kavrayskiy VII Mollweide Sinusoidal Tobler hyperelliptical Wagner VI

Conical

Albers Equidistant Lambert conformal

Pseudoconical

Bonne Bottomley Polyconic Werner

Azimuthal (planar)

General perspective

Gnomonic Orthographic Stereographic

Equidistant Lambert equal-area

Pseudoazimuthal

Aitoff Hammer Wiechel Winkel tripel

By metric

Conformal

Adams hemisphere-in-a-square Gauss–Krüger Guyou hemisphere-in-a-square Lambert conformal conic Mercator Peirce quincuncial Stereographic Transverse Mercator

Equal-area

Bonne

Sinusoidal Werner

Bottomley

Sinusoidal Werner

Cylindrical

Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert cylindrical equal-area Smyth equal-surface Trystan Edwards

Tobler hyperelliptical

Collignon Mollweide

Albers Briesemeister Eckert II Eckert IV Eckert VI Hammer Lambert azimuthal equal-area Quadrilateralized spherical cube

Equidistant in some aspect

Conic Equirectangular Sinusoidal Two-point Werner

Gnomonic

Gnomonic

Loxodromic

Loximuthal Mercator

Retroazimuthal (Mecca or Qibla)

Craig Hammer Littrow

By construction

Compromise

Chamberlin trimetric Kavrayskiy VII Miller cylindrical Robinson Van der Grinten Wagner VI Winkel tripel

Hybrid

Goode homolosine HEALPix

Perspective

Planar

Gnomonic Orthographic Stereographic

Central cylindrical

Polyhedral

Cahill Butterfly Dymaxion Quadrilateralized spherical cube Waterman butterfly

See also

Latitude Longitude Tissot'

.