The equirectangular projection (also called the equidistant
cylindrical projection, geographic projection, or la carte
parallélogrammatique projection, and which includes the special case
of the plate carrée projection or geographic projection) is a simple
map projection attributed to Marinus of Tyre, who
Contents 1 Definition 1.1 Forward 1.2 Reverse 2 See also 3 References 4 External links Definition[edit] 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: λ is the longitude of the location to project; φ is the latitude of the location to project; φ1 are the standard parallels (north and south of the equator) where the scale of the projection is true; λ0 is the central meridian of the map; x is the horizontal coordinate of the projected location on the map; y is the vertical coordinate of the projected location on the map. Forward[edit] x = ( λ − λ 0 ) cos φ 1 y = ( φ − φ 1 ) displaystyle begin aligned x&=(lambda -lambda _ 0 )cos varphi _ 1 \y&=(varphi -varphi _ 1 )end aligned The plate carrée (French, for flat square), is the special case where φ1 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 (erroneously) to be “unprojected”. 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[edit] λ = x cos φ 1 + λ 0 φ = y + φ 1 displaystyle begin aligned lambda &= frac x cos varphi _ 1 +lambda _ 0 \varphi &=y+varphi _ 1 end aligned See also[edit] Atlas portal List of map projections
Cartography
Cassini projection
References[edit] ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 5–8, ISBN 0-226-76747-7. External links[edit] 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 Caree) in proj4 v t e Map projection History List Portal By surface Cylindrical Mercator-conformal Gauss–Krüger Transverse Mercator Equal-area Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert Smyth equal-surface Trystan Edwards Cassini Central Equirectangular Gall stereographic Miller Space-oblique Mercator Web Mercator Pseudocylindrical Eckert II Eckert IV Eckert VI Goode homolosine Kavrayskiy VII Mollweide Sinusoidal Tobler hyperelliptical Wagner VI Conical Albers Equidistant Lambert conformal Pseudoconical Bonne Bottomley Polyconic Werner Azimuthal (planar) General perspective Gnomonic Orthographic Stereographic Equidistant Lambert equal-area Pseudoazimuthal Aitoff Hammer Wiechel Winkel tripel By metric Conformal Adams hemisphere-in-a-square Gauss–Krüger Guyou hemisphere-in-a-square Lambert conformal conic Mercator Peirce quincuncial Stereographic Transverse Mercator Equal-area Bonne Sinusoidal Werner Bottomley Sinusoidal Werner Cylindrical Balthasart Behrmann Gall–Peters Hobo–Dyer Lambert cylindrical equal-area Smyth equal-surface Trystan Edwards Tobler hyperelliptical Collignon Mollweide Albers Briesemeister Eckert II Eckert IV Eckert VI Hammer Lambert azimuthal equal-area Quadrilateralized spherical cube Equidistant in some aspect Conic Equirectangular Sinusoidal Two-point Werner Gnomonic Gnomonic Loxodromic Loximuthal Mercator Retroazimuthal (Mecca or Qibla) Craig Hammer Littrow By construction Compromise Chamberlin trimetric Kavrayskiy VII Miller cylindrical Robinson Van der Grinten Wagner VI Winkel tripel Hybrid Goode homolosine HEALPix Perspective Planar Gnomonic Orthographic Stereographic Central cylindrical Polyhedral Cahill Butterfly Dymaxion Quadrilateralized spherical cube Waterman butterfly See also Latitude Longitude Tissot' |