Plate carrée projection

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Image:Equidistant Cylindrical Projection Earth.png Image:Earth satellite plane.jpg The plate carrée projection or geographic projection or equirectangular projection, is a very simple map projection that has been in use since the earliest days of spherical cartography. The name is from the French for "flat and square". It is a special case of the equidistant cylindrical projection in which the horizontal coordinate is the longitude and the vertical coordinate is the latitude.

The spherical earth can only be mapped onto a developable surface by allowing distortion, so certain geometric properties on the sphere are not preserved. The Plate Carrée projection is a cylindrical projection but unlike the Mercator projection, the entire sphere, including the poles can be represented on a finite sized map. The projection is not a conformal map so angles are not preserved.

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. It has also become a de-facto standard for computer applications that process global maps, such as Celestia, because a given co-ordinate is very easily identifiable in an image file.

The following equations describe the mapping of geographic coordinates in terms of latitude φ and longitude λ onto the x and y coordinates of a point on the map. from its latitude φ and longitude λ (with φ₀ and λ₀ being the latitude and longitude in the center of map) and k being an approriate scale factor at the equator:

<math>

\begin{matrix} x &=& k \left( \lambda - \lambda_0 \right) \\y &=& k \left( \phi - \phi_0 \right) \end{matrix} </math>

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