Introduction to geographic coordinate system

Introduction to geographic coordinate system

Geographic coordinate system, also known as the real-world coordinate system, is a coordinate system used to determine the location of a ground object on the earth. A specific geographic coordinate system consists of a specific elliptical body and a specific map projection.
An elliptical body is a mathematical description of the shape of the earth, while a map projection is a mathematical method for converting a spherical coordinate into a plane coordinate. Most maps follow a known geographic coordinate system to display coordinate data.
1. Earth elliptical body
The earth is a complex sphere on the surface. People use the hypothetical average static sea surface to form a "" as a reference to derive an approximate elliptical body. The theory and practice prove that, the elliptical body is similar to a short axis of the Earth.
The elliptical sphere, which is rotated by the elliptical axis, can be expressed by mathematical formulas. Points on the natural surface can be reduced to the elliptical sphere for calculation. The following lists some common elliptical and parameters:
1) Sea Ford elliptical (1910) the elliptical used in China 52 years ago
A = 6378388 m B = 6356911.9461279 M α = 0.33670033670
2
A = 6378245 m B = 6356863.018773 M α = 0.33523298692
3) in 1975, I. U. g.g recommended elliptical (1975) used in the Xi'an 80 COORDINATE SYSTEM
A = 6378140 m B = 6356755.2881575 M α = 0.0033528131778
4) WGS-84 elliptical (GPS Global Positioning System elliptical, 17 international) WGS-84 coordinate system elliptical
A = 6378137 m B = 6356752.3142451 M α = 0.00335281006247
The most common geographic coordinate system is the latitude and longitude coordinate system, which can determine the location of any point on the Earth. If we regard the Earth as an elliptical body, and the net is the geographic coordinate reference system added to the Earth's surface.
Grid, longitude, and latitude are measured from the Earth's center to the Earth's surface at a specified point. Longitude is the east-west direction, while latitude is the North-South direction, and the longitude line passes through the south and north poles of the Earth, the weft is a loop line parallel to the equator. Location
Geographic coordinates can be divided into astronomical geographic coordinates and geographical coordinates: astronomical geographic coordinates are determined by astronomical measurement methods, and geographical coordinates are determined by the geological measurement methods. Geographic coordinates we use on the Earth's elliptical sphere
Is a geographical coordinate system, referred to as the geographical coordinate system.
After determining the size of the elliptic sphere, You need to perform an elliptical orientation, that is, place the rotated elliptical sphere in an appropriate location of the Earth, which is the "coordinate origin" of the geographic coordinate system ", it is the starting point for calculation of all Earth coordinates, commonly known as "Earth origin ".
It should be noted that the latitude and longitude coordinate system is not a plane coordinate system, because the degree is not a standard length unit, the length of the measurement area cannot be used; the plane coordinate system (also known as the flute coordinate system ), it has the following features:
Measure the distance between the horizontal X direction and the vertical y direction to measure the length, angle, and area. Different mathematical formulas can be used to project the earth sphere surface to a two-dimensional plane. While every plane sits
The system has a specific map projection method.
2. Map Projection
It is a geometric perspective or mathematical analysis method to solve the contradiction between the non-extensible elliptical sphere and the plane, project the points and lines on the earth to an extensible surface (plane, cylindrical, or conical surface) to generate a plane, establishes the correspondence between points and lines on the plane and points and lines on the Earth's elliptical sphere.
The process of map projection is to use a piece of paper to enclose the earth and project the Earth's objects onto the paper. The earth surface is projected on a plane, a cone surface, or a cylindrical surface.
The plane is formed after cutting along the busbar. Based on this paper, map projection can be divided into: azimuth projection, cone projection, and cylindrical projection. Based on the paper's interaction with the earth, the map projection can be divided into multiple projection types.
There is no deformation for the objects in the tangent or cut line, and the longer the deformation is from the tangent or cut line.
Many other projections are directly obtained using the parsing method. Based on the different geometric surfaces, pseudo-azimuth projection, pseudo-cone projection, and pseudo-cylindrical projection are supported.
There are two kinds of errors in map projection: Shape Change (also called angle change) or area change. A projection that can keep shape unchanged after projection is called an equal-angle projection.
Conformal Mapping (conformal mapping), which has the advantages of not only keeping the shape of the object unchanged, but also measuring the angle between the two objects on the map can also be consistent with the field, which is very important when
When sailing between two locations, the course must be accurate; or, in another example, the launch angle must be accurately measured for long-distance missiles or short-distance launch shells. Therefore, equisigned projection is the most commonly used projection.
The disadvantage of equisigned projection is that the area of the terrain in the high latitude area will be enlarged. A projection that can keep shape unchanged after projection is called equivalent mapping.
It is very important to apply product analysis. The relative area ratio of the displayed object is accurate, but the shape may change. Assume that there is a circle on the earth, and after the projection, it will become an elliptic. There is also a third projection, non-equality
Angle and other area projection, which means there are both shape changes and area changes. This type of projection is not only an angle but also a product, and the length, angle, and area are deformed. Some projection objects have a length ratio equal to 1 in a certain main direction,
It is called an offset projection.
Each projection has its own applicability. For example, mocato projection is suitable for charts. Its area deformation increases with the increase of latitude, but its direction deformation is very small. The area deformation of the horizontal mocato projection increases with the distance from the center.
The increasing distance of the warp is suitable for creating map of different countries. Angular projection is often used in aerial charts, wind direction charts, ocean flow charts, and so on. Currently, many topographic maps around the world use such projections. Equal product projection is used to draw
Economic Region map and some natural maps. For most mathematical maps and small-scale general maps, the requirements for equal products should be given priority. Geographic regions, such as countries, waters, and geographic classification areas (vegetation, population, and gas)
The relative distribution range is obviously very important. Any projection is often used as a mathematical map and a map that requires a correct distance along a certain main direction. Commonly used as a map of the world, the projection includes mocato projection and height.
Er projection, Moore's projection, equidifferential weft multi-cone projection, glington projection, Sanson projection, urmayev projection, etc. Next, we will give a brief introduction to the Gaussian kerluge projection adopted by topographic maps in China.
2.1 Gaussian-kerluge Cartesian coordinates
Gauss_krivger is an angular cross-section elliptical projection. It is assumed that an Elliptical Cylinder is located horizontally outside the Earth's elliptical and is tangent to the preset central Meridian. The primary line is perpendicular to each other, and the deformation is at the intersection of the outermost meridian line between the equator and the projection band. It is often used in areas with high latitudes.
Gaussian-gram projection zoning rule: This projection is the mathematical basis of the national basic scale topographic map in China. To control deformation, this projection method is adopted at the scale. the 50 thousand-plot uses a 6 ° split band, and a 3 ° split band is used for a graph with a scale of and a scale greater.
6 ° Strip Method: From the Greenwich mean zero longitude line, each 6 ° is divided into a projection band, the world is divided into 60 projection bands, the Eastern Hemisphere from the east longitude 0 °-6 ° is the first region, the central longitude is 3 °, and so on.
The period is 1-30. The formula for calculating the projection code n and the central longitude l0 is: L0 = (6n-3) °. The Western Hemisphere projection band is calculated from 180 ° to 0 ° and numbered 31-60. The projection code
The Formula for Calculating N and the central longitude l0 is L0 = 360-(6n-3) °.
3 ° belt Partitioning Method: From the east longitude 1 ° 30', every 3 ° is a belt, the world is divided into 120 projection belts, longitude 1 ° 30'-4 ° 30 ′,... 178 ° 30'-Longitude 178 ° 30 ′,... 1 ° 30'-longitude 1 ° 30 ′.
The Eastern Hemisphere has 60 projection bands numbered 1-60. The formula for calculating the central longitude line of each band is L0 = 3 ° N, and the central longitude line is 3 °, 6 °... 180 °.
The western hemisphere has 60 projection bands numbered 1-60. The formula for calculating the central meridian of each belt is L0 = 360 °-3 ° N, and the central meridian is 177 ° ,... 3 °, 0 °.
China requires that the vertical coordinate axes of each belt be moved 500 kilometers to the west, that is, all y values plus 500 kilometers, and the coordinate values plus the belt numbers. Take the 18-belt as an example. The original coordinate value is y = 243353.5 m, the value is y = 743353.5 after the West shift, and the general coordinate of the Plus band number is y = 18743353.5.
In order to facilitate the retrieval of topographic maps at different scales, we finally briefly introduce the rules of topographic maps in China.
3. Topographic Map amplitude and number in China
The basic scale topographic maps of China are divided and numbered based on a-topographic map, extending from to, and then from. 50 thousand and.
From the equator, the latitude deviation is 4 ° to 88 °. The North and South Hemisphere is divided into 22 horizontal columns, numbered a, B ,... v; by precision 180 ° west to the east every 6 ° a column, the world's 60 columns, expressed in 1-60, such as Hainan is in the 5th million map in 49th rows, columns, its number is E-49.
In the map, according to the longitude difference 3 ° latitude difference 2 ° divided into four topographic map, A, B, C, D, such as E-49-A. Divided into 16 frames according to the longitude difference of 1 ° 30' latitude difference of 1 °
A topographic map of, [1],... [16], such as a E-49-[1]. Divided into 144 topographic maps based on the longitude difference of 30' latitude difference of 20', which are classified as 1,... 144,
Like E-49-1. That is, the last three scales are independently associated with the map number of the map.
Map on each longitude difference 15 'latitude difference 10' into four topographic map, A, B, C, D, such as E-49-1-A.
Ten thousand graph on each longitude difference 7' 30 "latitude difference 5' divided into four. 50 thousand, compiled as 1, 2, 3, 4, such as E-49-1-A-1.
On a ten-dimensional chart, each longitude difference of "latitude difference of" is divided into 64 topographic maps, edited as (1 ),... (64), such as E-49-1-A-(1 ).
On the map of every longitude difference of 1'52 "latitude difference 1' 15" divided into four topographic map, A, B, C, D, such as E-49-1-A-(1) -.