# Equirectangular projection

Equirectangular projection

The equirectangular projection (also called the equidistant cylindrical projection, geographic projection, plate carré or carte parallelogrammatique projection or CPP) is a very simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about 100 AD. ["Flattening the Earth: Two Thousand Years of Map Projections", John P. Snyder, 1993, pp. 5-8, ISBN 0-226-76747-7.] The projection maps meridians to equally spaced vertical straight lines, and parallels to equally spaced horizontal straight lines.

Definition

:$x = lambda cos\left(phi_1\right),$

:$y = phi,$

where :$lambda,$ is the longitude from the central meridian of the projection,:$phi,$ is the latitude:$phi_1,$ are the standard parallels (north and south of the equator) where the scale of the projection is true.

Note that on the right side of the equation, the coordinates $lambda,$ and $phi,$ are linear, not angular, measurements. The point $\left(0,0\right)$ is at the center of the resulting projection (in particular, this requires the input range to be $\left[-pi,pi\right]$ rather than $\left[0,2pi\right]$). This projection maps longitude and latitude directly into x and y, hence is sometimes called the longitude-latitude projection.

The _fr. plate carré (French, for "flat square"), is the special case where $phi_1,$ is zero.

Uses

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 de-facto standard for computer applications that process global maps, such as Celestia and NASA World Wind, because of the trivial connection between an image pixel and its geographic position.

ee also

*Cartography
*Cassini projection
*Dymaxion map
*Gall-Peters projection with resolution regarding the use of rectangular world maps
*Gnomonic projection
*Mercator projection
*Mollweide projection
*Nautical chart
*Reversed map
*Transverse Mercator projection

References

* [http://visibleearth.nasa.gov/view_rec.php?id=2430 Global MODIS based satellite map] The blue marble: land surface, ocean color and sea ice.
* [http://www.radicalcartography.net/?projectionref Table of examples and properties of all common projections] , from radicalcartography.net.
* [http://wiki.panotools.org/Equirectangular Panoramic Equirectangular Projection] , PanoTools wiki.

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