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
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...
attributed to
Marinus of Tyre
Marinus of Tyre ( grc-gre, Μαρῖνος ὁ Τύριος, ''Marînos ho Týrios''; 70–130) was a Greek geographer, cartographer and mathematician, who founded mathematical geography and provided the underpinnings of Claudius Ptolemy' ...
, who
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
claims invented the projection about AD 100. 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
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...
or
cadastral
A cadastre or cadaster is a comprehensive recording of the real estate or real property's metes-and-bounds of a country.Jo Henssen, ''Basic Principles of the Main Cadastral Systems in the World,'/ref>
Often it is represented graphically in a cad ...
mapping and finds its main use in
thematic map
A thematic map is a type of map that portrays the geographic pattern of a particular subject matter (theme) in a geographic area. This usually involves the use of map symbols to visualize selected properties of geographic features that are n ...
ping. In particular, the plate carrée has become a standard for global
raster datasets, such as
Celestia
Celestia is a real-time 3D astronomy software program that was created in 2001 by Chris Laurel. The program allows users to virtually travel through our universe and explore real objects that have been catalogued. Celestia also doubles as a pl ...
,
NASA World Wind
NASA WorldWind is an open-source (released under the NOSA license and the Apache 2.0 license) virtual globe. According to the website (https://worldwind.arc.nasa.gov/), "WorldWind is an open source virtual globe API. WorldWind allow ...
, the
USGS
The United States Geological Survey (USGS), formerly simply known as the Geological Survey, is a scientific agency of the United States government. The scientists of the USGS study the landscape of the United States, its natural resources, a ...
Astrogeology Research Program
The Astrogeology Science Center is the entity within the United States Geological Survey concerned with the study of planetary geology and planetary cartography. It is housed in the Shoemaker Building in Flagstaff, Arizona. The Center was establ ...
, 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 or other spherical solar system bodies. In addition it is frequently used in panoramic photography to represent a spherical panoramic image.
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
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
of the location to project;
*
is the
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
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 (
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
, or
Ronald Miller's
, 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";
*
is called "pitch";
where both are defined in degrees.
See also
*
Cartography
Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...
*
Cassini projection
The Cassini projection (also sometimes known as the Cassini–Soldner projection or Soldner projection) is a map projection described by César-François Cassini de Thury in 1745. It is the transverse aspect of the equirectangular projection, in ...
*
Gall–Peters projection with resolution regarding the use of rectangular world maps
*
List of map projections
*
Mercator projection
*
360 video projection
References
External links
Global MODIS based satellite mapThe 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.
{{Map projections
Map projections
Equidistant projections