Equidistant Cylindrical (Plate Carrée)

The simplest of all projections. Standard parallels (0° when omitted) may be specified that determine latitude of true scale (k=h=1).

Classification	Conformal cylindrical
Available forms	Forward and inverse
Defined area	Global, but best used near the equator
Alias	eqc
Domain	2D
Input type	Geodetic coordinates
Output type	Projected coordinates

proj-string: +proj=eqc

Usage

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.

The following table gives special cases of the cylindrical equidistant projection.

Projection Name	(lat ts=) \(\phi_0\)
Plain/Plane Chart	0°
Simple Cylindrical	0°
Plate Carrée	0°
Ronald Miller—minimum overall scale distortion	37°30′
E.Grafarend and A.Niermann	42°
Ronald Miller—minimum continental scale distortion	43°30′
Gall Isographic	45°
Ronald Miller Equirectangular	50°30′
E.Grafarend and A.Niermann minimum linear distortion	61°7′

Example using EPSG 32662 (WGS84 Plate Carrée):

$ echo 2 47 | proj +proj=eqc +ellps=WGS84
222638.98       5232016.07

Example using Plate Carrée projection with true scale at latitude 30° and central meridian 90°W:

$ echo -88 30 | proj +proj=eqc +lat_ts=30 +lon_0=90w
192811.01       3339584.72

Parameters

+lon_0=<value>

Central meridian/longitude of natural origin, longitude of origin or longitude of false origin (naming and meaning depend on the projection method).

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lon_0=1.570796r

See Projection Units for more information.

+lat_0=<value>

Latitude of natural origin, latitude of false origin or latitude of projection centre (naming and meaning depend on the projection method).

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lat_0=1.570796r

See Projection Units for more information.

+lat_ts=<value>

Latitude of true scale. Defines the latitude where scale is not distorted. Takes precedence over +k_0 if both options are used together.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lat_ts=1.570796r

See Projection Units for more information.

+x_0=<value>

False easting, easting at false origin or easting at projection centre (naming and meaning depend on the projection method). Always in meters.

Defaults to 0.0.

+y_0=<value>

False northing, northing at false origin or northing at projection centre (naming and meaning depend on the projection method). Always in meters.

Defaults to 0.0.

+ellps=<value>

The name of a built-in ellipsoid definition.

See Ellipsoids for more information, or execute proj -le for a list of built-in ellipsoid names.

Defaults to "GRS80".

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.

Mathematical definition

The formulas describing the Equidistant Cylindrical projection are all taken from [Snyder1987].

\(\phi_{ts}\) is the latitude of true scale, i.e., the standard parallel where the scale of the projection is true. It can be set with +lat_ts.

\(\phi_0\) is the latitude of origin that match the center of the map. It can be set with +lat_0.

Forward projection

\[x = \lambda \cos \phi_{ts}\]

\[y = \phi - \phi_0\]

Inverse projection

\[\lambda = x / cos \phi_{ts}\]

\[\phi = y + \phi_0\]

Further reading

1. Wikipedia

2. Wolfram Mathworld