EPSG

"Map Projections - A Working Manual" by John P. Snyder, USGS Professional Paper 1395.

2023-06-29

See method code 1028 for ellipsoidal development. If the latitude of natural origin is at the equator, also known as Plate Carrée. See also Pseudo Plate Carree, method code 9825.

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided. This method has one of the simplest formulas available. If the latitude of natural origin (lat1) is at the equator the method is also known as Plate Carrée. It is not used for rigorous topographic mapping because its distortion characteristics are unsuitable. Formulas are included to distinguish this map projection method from an approach sometimes mistakenly called by the same name and used for simple computer display of geographic coordinates - see Pseudo Plate Carrée (coordinate operation method code 9825). For the forward calculation: E = FE + R . (lon - lonO) . cos(lat1) N = FN + R . lat where lat1, lonO, lat and lon are expressed in radians. R is the radius of the sphere and will normally be one of the CRS parameters. If the figure of the earth used is an ellipsoid rather than a sphere then R should be calculated as the radius of the conformal sphere at the projection origin at latitude lat1 using the formula for RC given in EPSG Guidance Note 7-2, section 1.2, table 3. Note however that if applying spherical formula to ellipsoidal coordinates, the equidistant projection properties are not preserved. For the reverse calculation: lat = (N - FN)/ R lon = lonO + ([E - FE] / R cos(lat1)) where R is as for the forward method.