The coordinate system is the reference system to describe the spatial position of the existence of substances
Coordinate system, which describes the existence of matterspatial location CoordinateFrame of referenceBy defining specific benchmarks and their parameter forms.Coordinates are a group of numerical values that describe the position. They are generally divided intoOne-dimensional coordinate（Highway milestone）And 2D coordinates (Cartesian planeCartesian coordinates, GaussPlane rectangular coordinate）、3D coordinates（Geodetic coordinates, space rectangular coordinates).In order to describe or determine the position, it is necessary to establish a coordinate system. Only when coordinates exist in a coordinate system can they have practical significance and specific position.
Chinese name
Coordinate system
Overview
The coordinate system is used to describe the existence of substances
Global coordinates
Longitude and latitude: the most commonly used global coordinate system
The plane position, such as longitude and latitude, is called two-dimensional coordinates, which requires at least threeGPSSatellite data to locate two-dimensional coordinates.If trees, mountains or buildings block the satellite, you may only get 2D coordinates.Latitude, longitude and altitude are called 3D coordinates, and it requires at least 4 satellites to determine them.Almost allGPS receiver3D coordinates are provided as the standard.
After projecting the whole surface or a part of it to the plane, in order to locate accurately on the map, the coordinate system must be used.Generally speaking, there are differences between global and 2D (and/or 3D) coordinate systems.
The earth is a sphereLongitude and latitudeIt is called "spherical coordinate system" or "geographical coordinate system".It is very troublesome to calculate the angular distance on the sphere, and the map is printed on a flat paper. To draw objects on the sphere onto the paper, they must be flattened. This process of transforming the sphere into a plane is called "projection".
Through the process of projection, spherical coordinates are converted into plane rectangular coordinates, which is convenient for printing and calculating angles and distances.However, since the sphere cannot be fully developed into a plane without deformationglobeIn addition, all maps have some degree of deformation, some can keep the area unchanged, some can keep the orientation unchanged, depending on their use.
A projection commonly used internationally is the Transverse Mercator Projection, also known asGauss Kruger projection(Gauss KrugerProjection), which keeps the shape unchanged in a small range, is convenient for various applications.It can be imagined thatcylinderLie horizontally, cover it outside the earth, project the surface onto the cylinder, and then unfold the cylinder into a plane.The cylinder is tangent to the earth along the north-south longitudetangentIs called“Central meridian”。
In order to use numbers to determine a location on a map, you need to use theCartesian coordinatesIts y-axis points east in the positive direction, and its x-axis points north in the positive direction.The origin has different definitions in different systems, and GRASS is usually on the leftLower corner。With geography andGeocentric coordinateDifferent, coordinates are only valid within a certain range (such as a longitude band).Many coordinate systems are widely used.Except for the difference of origin and unit,ellipsoidThe difference from projection is also fundamental.This makescoordinate transformation Usually, it can only be completed through complex operations.common3D coordinatesThe system includes Gauss Kruger coordinate system and UTM coordinate system.
Global coordinates
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Coordinate system
Longitude and latitude: is the most commonly used globalCoordinate systemThe system is longitude, latitude and elevation.(It does not involve projection)Reference planefrom0 ° longitudeAnd the equator.Therefore, the earth fromGreenwich180 longitudes are divided to the east and west respectively.From the equator, 90 latitudes are divided to the south and north respectively.Elevation is calculated from the geocenter, but different definitions still have differences.Unit isHexadecimal(degrees: minutes: seconds, letters indicate direction) ordecimal system(positive/negative decimal system).It can also be calledreal world The coordinate system of is used to determine the position of the figure on the earth.
Cartesian coordinate systemCartesian Coordinatesbevel angleA general term for coordinate systems.Two lines intersecting at the originNumber axis, forming a planeaffine coordinate system 。If the measurement units on the two number axes are equal, the affine coordinate system is called Cartesian coordinate system.Cartesian coordinate system where two number axes are perpendicular to each other is called CartesianRectangular coordinate system, otherwise it is called Cartesian oblique coordinate system.
The three non coplanar number axes intersecting at the origin form an affine coordinate system in space.The affine coordinate system with equal units of measurement on three number axes is called spaceCartesian coordinate system。The Cartesian coordinate system with three number axes perpendicular to each other is called the space Cartesian rectangular coordinate system, otherwise it is called the space Cartesian oblique coordinate system.
significance
Cartesian coordinates, which represent the position of a point in spaceCartesian coordinatesThere is a difference. The two coordinates can be converted to each other.For example, if Cartesian coordinate of a point is 493454967, its X axis coordinate is 4+9+3=16. The Y-axis coordinate is 4+5+4=13, and the Z-axis coordinate is 9+6+7=22. Therefore, the rectangular coordinate of this point is (16, 13, 22), and the coordinate value cannot be negative (because threeNatural numberAdd cannot be negative).
Gauss projection
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summary
Gauss Kruger projection“Gauss projection”, also known as“Isometric crosscutting elliptic cylinder projection”, between the earth ellipsoid and the planeOrthomorphic projectionOne of.Carl Friedrich Gauss (1777-1855), a German mathematician, physicist and astronomer, drafted the projection formula in the 1920s, and was supplemented by Johannes Kruger (1857-1928), a German geodetic, in 1912.
The projection is based on the projection beltCentral meridianProjected as a straight line with the same length and sumEquatorial projectionThe Gauss Kruger projection formula is obtained by determining the form of the function under the condition of straight line.After projection, except the centermeridianIt is a straight line with the equator, and other meridians are curves symmetrical to the central meridian.Imagine using an elliptical column to cross cut atEllipsoidThe central meridian of the upper projection zone is fixed on both sides of the central meridian according to the above projection conditionsMeridional aberrationEllipsoid within the rangeOrthomorphic projectiontoElliptical cylinder。The elliptical cylinder is flattened along the generatrix passing through the North and South Poles, which is called the Gauss projection plane.Take the projection of the intersection of the central meridian and the equator as the origin, and the projection of the central meridian isOrdinateThe x-axis, the projection of the equator is the abscissa y-axis, forming the Gauss KrugerRectangular coordinate system 。
characteristic
The deformation of Gauss Kruger projection is very small in length and area, and there is no deformation of the central meridian. The deformation gradually increases from the central meridian to the edge of the projection zone, and the maximum deformation is located at both ends of the equator in the projection zone.Because of its high projection accuracy, small deformation, and simple calculation (the coordinates of each projection zone are consistent, as long as the data of one zone is calculated, other zones can be used)Large scale topographic mapIt can meet various military needs, and can carry out accurate measurement and calculation on the map.
UTM series
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UTM coordinate system
UTM (UNIVERSALTRANSVERSEMERCARTORGRIDSYSTEM) coordinates are plane rectangular coordinatesCoordinate gridThe system and the projection on which it is based have been widely usedTopographic map, asSatellite imageandNatural resource databaseAnd other applications requiring precise positioning.In the UTM system, the earth between 84 degrees north latitude and 80 degrees south latitudeSurface areaIt is divided into north-south vertical zone (projection zone) according to longitude of 6 degrees.
from180 degree longitudeStart numbering these projection zones eastward from 1 to 60 (Beijing is in the 50th zone).Each band is subdivided intoLatitudinal difference8 degreequadrilateral。The horizontal row of a quadrilateral followsSouth LatitudeStart at 80 degrees.Mark in sequence with the letters C to X (excluding I and O) (line X includesNorthern HemisphereAll land area from 72 to 84 degrees north latitude, 12 degrees in total) Numbers and letters for each quadrangleCombination mark。
The reference grid is read right up.Each quadrangle is divided into many cells with a side length of 1000000 metersCombined systemTag.In each projection zone, the meridian at the center of the zone givesAbscissaThe value is 500000 meters.For the equator of the northern hemisphere, the marked coordinate value is 0, and for the southern hemisphere, it is 10000000 meters, decreasing southward.
largescaleThe distance between the main lines of the map UTM grid is generally 1KM, so the UTM system is sometimes called the grid.Because UTM system adoptstransverse mercator projection , along each north-south grid line (one grid line with center is longitude)Scale factorIs a constant, and is a variable in the east-west direction.The scale coefficient of the central grid line along each UTM grid should be 0.99960 (smaller scale), on the edge of the widest part (equator) of the north-south vertical line, including the overlapping part of the beltCenter pointAbout 363km, with a scale factor of 1.00158.
UTM (Universal Transverse Mercator) systems are usually based onWGS84ellipsoid。At 84 ° north latitude andSouth LatitudeThere are 60 longitude zones between 80 °, and they are 6 ° zoning.To avoid the longitude deformation of the boundary, intersection is usedcylinderPerform projection.thereforeCentral meridianIt is no longer equidistant, and its reduction ratio is 0.9996.In the Gauss Kruger projection, the northward distance is calculated from the equator.On the contrary, in order to avoid negative values, UTM increases by 10000 km in the southern hemisphere.Distance from central meridian, andGauss Kruger projectionSimilarly, it needs to offset 500 kilometers.
The corresponding coordinates are marked with E (east) and N (north).The central meridians are 3 °, 9 °, 15 °, etc.SouthNorth PoleThe area between is divided into 8 dimension belts, which are marked with letters.This system is used in the United States and NATOMilitary map。Due to the global universality of UTM coordinate system, Germany and Europe are using this coordinate system.
GIS Department
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GIS
The coordinate system isGISgraphic display、data organization The basis of analysis, so establish perfect coordinatesProjection systemIt is very important for GIS application. There are three coordinate systems of GIS: PlannarCoordinateSystem（Plane coordinateSystem, or Custom user-defined coordinate system), GeographicCoordinateSystem（Geographic coordinate system）, ProjectionCoordinateSystem (projection coordinate system).These three are not completely independent, and each has its own application characteristics.
For example, plane coordinate systems often do not need projection orcoordinate transformation In Arcgis, the data is opened by default and the coordinates are not knownsystem information In this case, it is treated as CustomCS, that is, plane coordinate system.The geographical coordinate system and the projection coordinate system are interrelated, and the geographical coordinate system is one of the bases of the projection coordinate system.
