Equirectangular projection


The equirectangular projection is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, and circles of latitude to horizontal straight lines of constant spacing. 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 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.

Definition

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:
Longitude and latitude variables are defined here in terms of radians.

Forward

The plate carrée, is the special case where 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 projection or is said to be “unprojected”. Despite sometimes being called “unprojected”, it is actually projected.
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