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In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. [1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane.
Even over short distances, the accuracy of geographic distance calculations which assume a flat Earth depend on the method by which the latitude and longitude coordinates have been projected onto the plane. The projection of latitude and longitude coordinates onto a plane is the realm of cartography.
The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing through the sphere's interior is the chord between ...
and λ is the longitude, λ 0 is the central meridian, φ is the latitude, and R is the radius of the globe to be projected. The map has area 4 π R 2, conforming to the surface area of the generating globe. The x-coordinate has a range of [−2R √ 2, 2R √ 2], and the y-coordinate has a range of [−R √ 2, R √ 2].
The most common horizontal position representation is latitude and longitude. The parameters are intuitive and well known, and are thus suited for communicating a position to humans, e.g. using a position plot. However, latitude and longitude should be used with care in mathematical expressions (including calculations in computer programs).
Mercator's 1569 map was a large planisphere, [3] i.e. a projection of the spherical Earth onto the plane. It was printed in eighteen separate sheets from copper plates engraved by Mercator himself. [4] Each sheet measures 33×40 cm and, with a border of 2 cm, the complete map measures 202×124 cm. All sheets span a longitude of 60 degrees; the ...
The following graph illustrates the variation of both a degree of latitude and a degree of longitude with latitude. The definition of geodetic latitude (ϕ) and geocentric latitude (θ). Auxiliary latitudes. There are six auxiliary latitudes that have applications to special problems in geodesy, geophysics and the theory of map projections:
Graticule (cartography) Map of Europe with a 30° graticule in dark gray. A graticule (from Latin crāticula 'grill/grating'), on a map, is a graphical depiction of a coordinate system as a grid of lines, each line representing a constant coordinate value. [1] It is thus a form of isoline, and is commonly found on maps of many kinds, at scales ...