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The Universal Transverse Mercator (UTM) is a map projection system for assigning coordinates to locations on the surface of the Earth. Like the traditional method of latitude and longitude , it is a horizontal position representation , which means it ignores altitude and treats the earth surface as a perfect ellipsoid .
Informally, specifying a geographic location usually means giving the location's latitude and longitude.The numerical values for latitude and longitude can occur in a number of different units or formats: [2]
To convert Transverse Mercator coordinates to lat-lon, first calculate ′, the footprint latitude— i.e. the latitude of the point on the central meridian that has the same N as the point to be converted; i.e. the latitude that has a meridian distance on the spheroid equal to N/.
Thomas–UTM: The λ expansions of Krüger were also confirmed by Paul Thomas in 1952: [12] they are readily available in Snyder. [13] His projection formulae, completely equivalent to those presented by Redfearn, were adopted by the United States Defence Mapping Agency as the basis for the UTM . [ 14 ]
The intersection of a UTM zone and a latitude band is (normally) a 6° × 8° polygon called a grid zone, whose designation in MGRS is formed by the zone number (one or two digits – the number for zones 1 to 9 is just a single digit, according to the example in DMA TM 8358.1, Section 3-2, [1] Figure 7), followed by the latitude band letter ...
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [1] It is the simplest, oldest and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others.
A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of spatial reference system that represents locations on Earth using Cartesian coordinates (x, y) on a planar surface created by a particular map projection. [1]
Formulas for the Web Mercator are fundamentally the same as for the standard spherical Mercator, but before applying zoom, the "world coordinates" are adjusted such that the upper left corner is (0, 0) and the lower right corner is ( , ): [7] = ⌊ (+) ⌋ = ⌊ ( [ (+)]) ⌋ where is the longitude in radians and is geodetic latitude in radians.