Projected coordinate system
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A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of
When the first standardized coordinate systems were created during the 20th century, such as the
History
The
Among the earliest was the State Plane Coordinate System (SPCS), which was developed in the United States during the 1930s for surveying and engineering, because calculations such as distance are much simpler in a Cartesian coordinate system than the three-dimensional trigonometry of GCS. In the United Kingdom, the first version of the British National Grid was released in 1938, based on earlier experiments during World War I by the Army and the Ordnance Survey.[4]
During
After the War, UTM gradually gained users, especially in the scientific community. Because UTM zones do not align with political boundaries, several countries followed the United Kingdom in creating their own national or regional grid systems based on custom projections. The use and invention of such systems especially proliferated during the 1980s with the emergence of
System specification
Because the purpose of any coordinate system is to accurately and unambiguously measure, communicate, and perform calculations on locations, it must be defined precisely. The
- An abstract two-dimensional US foot).
- A choice of Transverse Mercator), a coordinate system definition will specify the parameters to be used, such as a center point, standard parallels, scale factor, false origin, and such. With these parameters, the underlying formulas of the projection convert latitude and longitude directly into the (x, y) coordinates of the system.
- A choice of geodetic datum, which includes a choice of earth ellipsoid. This binds the coordinate system to actual locations on the Earth by controlling the measurement framework for latitude and longitude (GCS). Thus, there will be a significant difference between the coordinate of a location in "UTM NAD83 Zone 14N" and for the same location in "UTM NAD27 Zone 14N", even though the UTM formulas are identical, because the underlying latitude and longitude values are different. In some GIS software, this part of the definition is called the choice of a particular geographic coordinate system.
Projections
To establish the position of a geographic location on a map, a map projection is used to convert geodetic coordinates to plane coordinates on a map; it projects the datum ellipsoidal coordinates and height onto a flat surface of a map. The datum, along with a map projection applied to a grid of reference locations, establishes a grid system for plotting locations. Conformal projections are generally preferred. Common map projections include the transverse mercator (used in Universal Transverse Mercator, the British National Grid, the State Plane Coordinate System for some states), Lambert Conformal Conic (some states in the SPCS), and Mercator (Swiss coordinate system).
Map projection formulas depend on the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on the type of project and the conventions chosen for the projection. For the transverse Mercator projection used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor.[7] Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions.[7]: 45–54
Easting-Northing
Every map projection has a natural origin, e.g., at which the ellipsoid and flat map surfaces coincide, at which point the projection formulas generate a coordinate of (0,0).[7] To ensure that the northing and easting coordinates on a map are not negative (thus making measurement, communication, and computation easier), map projections may set up a false origin, specified in terms of false northing and false easting values, that offset the true origin. For example, in UTM, the origin of each northern zone is a point on the equator 500km west of the central meridian of the zone (the edge of the zone itself is just under 400km to the west). This has the desirable effect of making all coordinates within the zone positive values, being east and north of the origin. Because of this, they are often referred to as the easting and northing.
Grid north
Grid north (GN) is a
The grid lines on Ordnance Survey maps divide the UK into one-kilometre squares, east of an imaginary zero point in the Atlantic Ocean, west of Cornwall. The grid lines point to a Grid North, varying slightly from True North. This variation is zero on the central meridian (north-south line) of the map, which is at two degrees West of the
At the
Grid reference encodings
Locations in a projected coordinate system, like any cartesian coordinate system, are measured and reported as easting/northing or (x, y) pairs. The pair is usually represented conventionally with easting first, northing second. For example, the peak of Mount Assiniboine (at 50°52′10″N 115°39′03″W / 50.86944°N 115.65083°W on the British Columbia/Alberta border in Canada) in UTM Zone 11 is at (0594934mE, 5636174mN)
, meaning that is almost 600km east of the false origin for Zone 11 (95km east of the true central meridian at 117°W) and 5.6 million meters north of the equator.
While such precise numbers are easy to store and calculate in GIS and other computer databases, they can be difficult for humans to remember and communicate. Thus, since the mid 20th century, there have been alternative encodings that shorten the numbers or convert the numbers into some form of alphanumeric string.
For example, a truncated grid reference may be used where the general location is already known to participants and may be assumed.949-361
by concealing 05nnn34 56nnn74
, assuming the significant digits (3,4, and 5 in this case) are known to both parties.[11]
Alphanumeric encodings typically use codes to replace the most significant digits by partitioning the world up into large grid squares. For example, in the Military Grid Reference System, the above coordinate is in grid 11U (representing UTM Zone 11 5xxxxxx mN), and grid cell NS within that (representing the second digit 5xxxxxmE x6xxxxxm N), and as many remaining digits as are needed are reported, yielding an MGRS grid reference of 11U NS 949 361 (or 11U NS 9493 3617 or 11U NS 94934 36174).
The
Precision
The more digits added to a grid reference, the more precise the reference becomes. To locate a specific building in Little Plumpton, a further two digits are added to the four-digit reference to create a six-digit reference. The extra two digits describe a position within the 1-kilometre square. Imagine (or draw or superimpose a Romer) a further 10x10 grid within the current grid square. Any of the 100 squares in the superimposed 10×10 grid can be accurately described using a digit from 0 to 9 (with 0 0 being the bottom left square and 9 9 being the top right square).
For the church in Little Plumpton, this gives the digits 6 and 7 (6 on the left to right axis (Eastings) and 7 on the bottom to top axis (Northings). These are added to the four-figure grid reference after the two digits describing the same
Grid references comprising larger numbers for greater precision could be determined using large-scale maps and an accurate
Examples of projected CRS
- Universal Transverse Mercator (UTM): not a single coordinate system, but a series of 60 zones (each being a gore 6° wide), each a system with its own Transverse Mercator projection.
- Universal Polar Stereographic (UPS): a pair of coordinate systems covering the Arctic and Antarctica using a Stereographic projection.
- Ordnance Survey National Grid (OSNG): a transverse mercator projection centered on 2°W that covers Great Britain with its own encoding scheme.
- stateof the United States or a portion thereof.
- Swiss coordinate system (LV95): covers Switzerland, using a Mercator projection.
- Irish Transverse Mercator (ITM): jointly created by the Republic of Ireland and United Kingdom to cover the island of Ireland.
- Bermuda National Grid
- Hellenic Geodetic Reference System 1987 (Greece)
- Israeli Transverse Mercator (NIG)
- Swedish grid (RT90)
See also
- Discrete global grid (DGG)
- East north up
- Geocodes
- Geodetic datum
- Geographical distance
- Graticule (cartography)
- Horizontal plane
- Lattice graph (grid as mathematical abstraction)
- Map projection
- Spatial reference system
- Spatial grid
References
- ISBN 978-1-259-92964-9.
- ^ a b "OGC Abstract Specification Topic 2: Referencing by coordinates Corrigendum". Open Geospatial Consortium. Retrieved 2018-12-25.
- ^ a b "Using the EPSG geodetic parameter dataset, Guidance Note 7-1". EPSG Geodetic Parameter Dataset. Geomatic Solutions. Retrieved 15 December 2021.
- ^ Russell, Don. "Understanding Maps: The British National Grid". Uncharted 101. Retrieved 21 December 2021.
- ^ a b Raisz, Erwin (1948). General Cartography. McGraw-Hill. pp. 225–229.
- S2CID 131732222.
- ^ a b c "Geomatics Guidance Note Number 7, part 2 Coordinate Conversions and Transformations including Formulas" (PDF). International Association of Oil and Gas Producers (OGP). pp. 9–10. Archived from the original (PDF) on 6 March 2014. Retrieved 5 March 2014.
- ISBN 978-0-470-23058-9.
- ^ "Moving the South Pole" Archived 2011-07-16 at the Wayback Machine, NASA Quest
- ^ "Truncated Grid References". Bivouac.com – Canadian Mountain Encyclopedia. 2006-11-17.
- ^ "Grids and Reference Systems". National Geospatial-Intelligence Agency. Retrieved 4 March 2014.