# Equirectangular projection

*https://en.wikipedia.org/wiki/Equirectangular_projection*

The **equirectangular projection** (also called the **equidistant cylindrical projection** or **la carte parallélogrammatique projection**, and which includes the special case of the **plate carrée projection** (also called the **geographic projection**, **lat/lon projection**, or **plane chart**), is a simple
map projection attributed to
Marinus of Tyre, who
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,
NASA World Wind, and
Natural Earth, because of the particularly simple relationship between the position of an
image pixel on the map and its corresponding geographic location on Earth. In addition it is frequently used in panoramic photography to represent a spherical panoramic image.^{
[2]}

## 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:

- is the longitude of the location to project;
- is the latitude of the location to project;
- are the standard parallels (north and south of the equator) where the scale of the projection is true;
- is the central parallel of the map;
- is the central meridian of the map;
- is the horizontal coordinate of the projected location on the map;
- is the vertical coordinate of the projected location on the map;
- is the radius of the globe.

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

### Forward

The *plate carrée* (
French, for *flat square*), 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(g) projection or is said to be “unprojected”. Despite sometimes being called “unprojected”, it is actually projected.

When the is not zero, such as
Marinus's ,^{
[3]} or
Ronald Miller's ,^{
[4]} the projection can portray particular latitudes of interest at true scale.

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

### Alternative names

In spherical panorama viewers, usually:

- is called "yaw";
^{ [5]} - is called "pitch";
^{ [6]}

where both are defined in degrees.

## See also

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

## References

**^***Flattening the Earth: Two Thousand Years of Map Projections*, John P. Snyder, 1993, pp. 5–8, ISBN 0-226-76747-7.**^**"Equirectangular Projection - PanoTools.org Wiki".*wiki.panotools.org*. Retrieved 2021-05-04.**^***Flattening the Earth: Two Thousand Years of Map Projections*, John P. Snyder, 1993, pp. 7, ISBN 0-226-76747-7.**^**PROJ Contributors. "Equidistant Cylindrical (Plate Carrée)".*PROJ coordinate transformation software library*. Retrieved 25 August 2020.**^**"Yaw - PanoTools.org Wiki".*wiki.panotools.org*. Retrieved 2021-05-04.**^**"Pitch - PanoTools.org Wiki".*wiki.panotools.org*. Retrieved 2021-05-04.

## External links

- 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 Carrée) in proj4