Equidistant Cylindrical (Plate Carrée)

Classification: Conformal cylindrical

Available forms: Forward and inverse

Defined area: Global, but best used near the equator

Alias: eqc, plate_carrée, simple_cylindrical

Domain: 2D

Input type: Geodetic coordinates

Output type: Projected coordinates

Projection String

+proj=eqc
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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.

Special Cases of Cylindrical Equidistant Projection:

• 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

Example using EPSG 32662 (WGS84 Plate Carrée):

echo 2 47 | proj +proj=eqc +ellps=WGS84
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Output: 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
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Output: 192811.01 3339584.72

Parameters

• +lon_0 (Central meridian)
• +lat_0 (Latitude of origin)
• +lat_ts (Latitude of true scale)
• +x_0 (False easting)
• +y_0 (False northing)
• +ellps (Ellipsoid name)
• +R (Radius of the sphere)

Mathematical Definition

Forward projection:

$$x = \lambda \cos(\phi_{ts})$$ $$y = \phi - \phi_0$$

Inverse projection:

$$\lambda = x / \cos(\phi_{ts})$$ $$\phi = y + \phi_0$$

Further Reading

• Wikipedia
• Wolfram Mathworld