Understanding of the earth's coordinate system and projection mode (about Beijing 54, Xi ' an 80,wgs84; Gauss, Lambert, Mercator projection)

First, the Earth model

The earth is an approximate ellipsoid, which is approximated by an ellipsoid model, called a reference ellipsoid , such as:

The equator is an approximate circle with a radius of a, and any circle meridian is an approximate circle with a radius of B. A is called the long axis radius of the ellipsoid, and B is called the short axis radius of the ellipsoid.

a ≈ 6378.137 km, b≈6356.752 km. (In fact, a is not constant, the most strengths and shortcomings of 72 meters, B of the most strengths and shortcomings of 42 meters, is very small)

Basic parameters of the Earth reference ellipsoid:

Long axis: A

Short Axis: b

Flat Rate: α= (A-B)/A

First eccentricity: e=√ (A2-B2)/A

Second eccentricity: E ' =√ (A2-B2)/b

These parameters are fixed, the mathematical model of the reference ellipsoid is determined.

What is a geodetic coordinate system?

Geodetic Coordinate system is a coordinate system established by reference ellipsoid as datum plane in geodetic survey. The position of the ground point is expressed by the longitude of Earth, the latitude of the earth and the height of the earth: (L, B, H).

The spatial Cartesian coordinate system is the origin point of the reference ellipsoid , the x-axis of the ray from the origin to the 0-degree meridian and the equator intersection, the y-axis of the origin to the 90-degree meridian and the equator intersection, and the z-axis to the north of the earth's axis of rotation: (x, Y, z)

Common denominator: Obviously, both of these coordinate systems must be based on a reference ellipsoid.

Differences: Geodetic coordinates are based on polygons, so it is also necessary to determine a standard sea level. The spatial Cartesian coordinate system is based on a single point, so a central point needs to be determined.

As long as the basic parameters of the ellipsoid are determined, the geodetic coordinate system and the spatial Cartesian coordinate system are relatively determined, but only two different expressions, the points of the two coordinate systems correspond to one by one.

Second, Beijing 54, Xi ' an 80,wgs84

Most of the explanations on the Internet are duplicated, vague, ineffective, and they are not clear about the essential difference. Why is the latitude and longitude calculated in the same 1.3 different? Do you just disagree with each other's measurement accuracy? Why WGS84 selected the Earth center of mass as the origin, and Xi ' an 80 selected a point on the surface as the origin point? What is the role of the Earth origin chosen by China? Why Choose Jingyang County Yongle Town? Since as the origin, why is latitude and longitude not 0? Here is my personal understanding.

Firstly, the three models are modeled with different reference ellipsoid, that is, the parameters of the short-and long-axis flattening ratio are different.

Beijing: Long axis 6378245m, short axis 6356863, flat rate 1/298.3

XI ' an: Long shaft 6378140m, short axis 6356755, flat rate 1/298.25722101

WGS84: Long axis 6378137.000m, short axis 6356752.314, flat rate 1/298.257223563

These parameters are different, which determines the geometric center of the ellipsoid model is different. So why is there such a big difference in the parameters of these three coordinate systems? In addition to the different measurement accuracy, there is another reason, the focus is not the same.

WGS84 is global, so it is as close as possible to the entire surface of the earth, the advantages are large range, the disadvantage is that the local is not accurate.

Beijing 54 uses the parameters of the former Soviet Union, which is for the Soviet Union, so it is as close as possible to the surface of the former Soviet region, while the rest of the country is much more or less. It takes the Soviet-based Pulkovo as the center, the farther away from that, the greater the error.

Xi ' An 80 is for China, so it is as close to the surface as possible in the Chinese region, while the rest of the country is too much. And this approximation is centered on the origin of the Earth near Xi ' an, that is to say, at the origin point of Xi ' an, the model and the true surface reference sea level coincidence, the error is 0, and the farther away from the Earth origin, the greater the error. The so-called Earth origin is so, it is artificial to set, and not must be there, it should be placed in the middle of China as far as possible, so that the total error as small and evenly distributed. Then, China's own territory in the construction, surveying, exploration and other drawings, all of this earth origin as the benchmark, to establish a variety of uses of the surface coordinate system can be unified.

So in the Chinese region, the WGS84 model is not so accurate as the XI ' an 80 model. And the XI ' an 80 model to calculate the U.S. point, it is more inaccurate. Now updated to 2000 National geodetic coordinate system, the parameters are more accurate than XI ' an 80, and the reason is the same.

All say WGS84 is the centroid coordinate system, Beijing 54, Xi ' an 80 is the heart coordinate system, what is the centroid? What is the heart of ginseng?

A good understanding of the centroid, is the center of mass of the Earth Body, WGS84 coordinate system for global positioning, so the model is the most moderate, not biased to any region, the geometric center of the ellipsoid model coincides with the Earth centroid, the model will be closest to the entire Earth.

While Beijing 54 and Xi ' an 80 focus on local accuracy and abandon overall accuracy, when the ellipsoid model (XI ' an 80) is most accurate in the Chinese region, its geometric center is certainly not the centroid of the Earth, but elsewhere. So this geometric center is called the Reference Center, referred to as the heart.

On the earth a point latitude and longitude, is based on the reference ellipsoid to calculate, so, the same place, with Beijing 54, Xi ' an 80,wgs84 calculated longitude and latitude is three different values. Since GPS is WGS84, we see the latitude and longitude of the WGS84 coordinate system.

Three, the map on the plane projection

our map, must be painted on paper, on the monitor, or everywhere carrying a globe? The point on the earth is expressed by latitude and longitude, and the higher the latitude, the shorter the distance of 1 degrees of longitude. So, the problem is, the surface of the earth is a surface, and the latitude and length distance is not a simple proportional relationship, how to draw on the plane? The answer is, the projection algorithm. OK, here's the question again, which is the best projection algorithm?

1. Gauss-gram Gauss–krüger projection

Assuming that an elliptical cylinder and the Earth ellipsoid are gracefully crosscutting on a certain meridian, the longitude of the central meridian east, West 3° or 1.5° meridians are projected onto the elliptical cylinder in the isometric condition, and then the elliptical cylinder is expanded into a planar form.

Gauskruge Projection is a sub-band projection, mainly divided into 3 degrees and 6 degrees with two species. 3 degrees is longitude every 3 degrees a band, the world cut into 120 bands, 6 degrees is longitude every 6 degrees a band, the world cut into 60 bands. Each of the different bands has its own origin in the XY coordinate system, it is not possible to use the XY coordinate system to calculate the other bands, because the origin point is different. deformation analysis of Gauskruge projection:there is no deformation on the central meridian of ①, which satisfies the condition that the length ratio is invariable after projection.② except the length ratio of the central Meridian is 1, any other point length ratio is greater than 1;③ on the same parallel line, the farther away from the central meridian, the larger the deformation, and the maximum value is at the edge of the projection band. ④ on the same meridian, the lower the latitude, the greater the deformation, and the maximum value is on the equator. ⑤ conformal projection, no angular deformation , the area ratio is the square of the length ratio. the equal deformation lines of the ⑥ length ratio are parallel to the central axis meridian. Pros: The length and area deformations are minimal (compared to other projections). disadvantage: Need to be divided, adjacent to the band can not be spliced (how to connect the upper tip width?) Very difficult), resulting in a small coverage range. so the Gaussian projection is suitable for small areas of the map, a belt can be covered by the area. 2. Lambert projectionThere are two kinds:① conformal conic projection. It is envisaged to cut or cut the spherical surface with a positive cone, and apply the conformal condition to project the face of the earth onto the cone surface and then expand it into a plane along a busbar. After projection, the parallels are concentric circular arcs, and the meridians are concentric circle radii. There is no angular distortion, and the warp length is equal to the length of the parallels. It is suitable for middle and small scale map of mid-latitude region distributed along latitude. The map of China on the market should be using this projection. ② the projection of equal product azimuth. It is envisaged that the sphere and plane are tangent to a point, and the longitude is projected on the plane by the equal product condition. According to the relative position of the projection surface and the earth surface, there are 3 kinds of positive, horizontal and oblique axes. In a positive axis projection, the parallels are concentric circles, and their intervals are narrowed outward by the center of the projection, and the meridian is the concentric circle radius. In the transverse projection, the central meridian and the equator are straight lines perpendicular to each other, and the other meridians and parallels are curves symmetrical to the central meridian and the equator respectively. In oblique-axis projections, the central meridian is a straight line, and the other meridians are curves symmetrical to the central meridian. The projection has no area distortion, and the angle and length deformations increase from the center of the projection. The horizontal and oblique axes are used more often, and this projection is used in eastern and Western Hemisphere and sub-continental plots. 3. Mercator projectionAssuming that the earth is enclosed in a hollow cylinder, its reference parallels are in contact with the cylindrical tangent (equator), and then the Imaginary Earth Center has a lamp projecting the shape on the sphere onto the cylinder, and then the cylinder expands , which is the Mercator projection on the selected datum parallels "Draw out the map. advantages: No angular deformation, the length of each point to each direction is equal, its longitude are parallel lines, and intersect at right angles. disadvantage: The length and area deformation is obvious, and the weft spacing increases gradually from the datum parallels to the poles. But because it has the characteristics of equal expansion in all directions, it maintains the correct direction and the relationship between the positions. Mercator projection maps are commonly used as nautical charts and aerial maps, if the direction of the two points on the Mercator projection map is not changed, it can always reach the destination, so it has favorable conditions for the ship to locate and determine the course in the voyage, which brings great convenience to the seafaring people. Google Maps, Baidu map with the Mercator projection, and the equator as the benchmark parallels.

Understanding of the earth's coordinate system and projection mode (about Beijing 54, Xi ' an 80,wgs84; Gauss, Lambert, Mercator projection)