Author: Demons

After the introduction of maps and map services, this article introduces coordinate systems. The earth is an irregular ellipsoid like sphere. In order to represent the position of each point on the map, a coordinate system needs to be established. So the coordinate system is a reference for geospatial data. Without a coordinate system, maps are prone to misalignment. Coordinate system is divided into geographic coordinate system and projection coordinate system, so how to understand geographic coordinate system and projection coordinate system? Longitude and latitude → Geographic coordinate system ← Actual measured geographic data X and Y coordinates → Projection coordinate system ← Actual geographic data projected data The two coordinate systems are connected by projection.

projection

The process of projection is the transformation from the surface of the earth to a plane. The geographic coordinate system is three dimensional, and if we want to display it on a map or on a screen, we need to convert it to two dimensions, which is called projection.



Why do we do a projection

  • Spherical coordinates are not convenient for the calculation of distance, azimuth, area and other parameters and various spatial analysis
  • Projection map for the plane, in line with the visual psychology
  • The earth ellipsoid is an unextendable surface

Coordinate system

The coordinate system consists of the origin and the coordinate system. There are many kinds of coordinate systems, and we will introduce some common coordinate systems below.

Geocentric coordinate system

The origin coincides with the earth’s centroid, and the space rectangular coordinate system is established with the earth’s centroid as the origin, or the earth’s ellipsoid with the center of the reference ellipsoid coincides with the earth’s centroid as the geodetic coordinate system established by the datum.

  • The reference ellipsoid fits the geoid best on a global scale
  • Global coordinate system
  • A global measurement benchmark

Parameter-centered coordinate system (obsolete)

The origin coincides with the center of the reference ellipsoid adopted for a region or country, usually not with the earth’s center of mass. The regional geodetic coordinate system is only suitable for use in local areas of the earth.

  • The reference ellipsoid corresponds best to the geoid in a certain country or region
  • Local coordinate system
  • It is suitable for local measurement and calculation

WKID and EPSG

WKID is a Well Known ID. One organization that manages these IDS is EPSG. The website is EPSG.io. In general, a coordinate system in GIS must have a WKID, except for some special ones. For example, WKID=4326, which is the ID of the geographic coordinate system WGS84. This definition is used in both geographic coordinate systems and projected coordinate systems, but it is not repeated, and there is no rule about which segment of the number is a geographic coordinate system and which segment is a projected coordinate system. Commonly used EPSG:

The coordinate system EPSG
WGS64 4326
CGCS2000 4490
Web Mercator 3857

Geographic Coordinate System (GCS)

Geographic coordinate system is a reference system for the location of space elements on the earth surface. Defined by longitude and latitude. For a particular location on the earth, different measurement systems give different coordinates. When we process geographic data, we must first confirm the measurement system used for the data.

Geodetic datum

Since the earth is an irregular ellipsoid, the first step in the measurement of longitude and latitude is to establish a model of the earth ellipsoid, that is, geodetic datum.

Using different geodetic datum at the same point, the coordinate values obtained are different.

For example:



Using different geodetic datum at different locations will result in different coordinate values.

The geographic coordinate system commonly used in our country

The coordinate system The benchmark ellipsoid Coordinate system wkid
Beijing 54 coordinate system (BZJ54) Beijing 54 geodetic datum Krasovsky Ellipsoid (1954) And the heart 4214
Xi ‘an 80 coordinate system (GDZ80) Xi ‘an 80 geodetic datum 1975 international ellipsoid (IAG75 recommended by the international geodesy association) And the heart 4610
The WGS – 84 coordinate system Wgs-80 geodetic reference WGS84 Ellipsoid (1984) The center of the earth 4326
CGCS2000

(Starting from July 2018, the whole country is required to start using 2000 coordinates)		 CGCS2000 geodetic datum And the ellipsoid of our country’s terrain approximation The center of the earth 4490


EPSG: 3857: Pseudo Mercator projection, also known as sphere Mercator, Web Mercator. It is based on the Mercator projection, projecting the WGS84 coordinate system onto the square. Usually we use WGS84 to store data and pseudo Mercator to display data.

PCS (Projected Coordinate System)

Since the earth is an irregular sphere, it must be deformed or cracked before it can be converted to a flat surface, so no map with no distortion error exists. The projection coordinate system is a plane rectangular coordinate system (x, Y) to represent the distance between the ground point and the origin of coordinates. Since plane cartesian coordinates are converted from geographic coordinates, coordinate values are also related to geodetic Datum. Deformation caused by map projection:

  • The length of the deformation
  • Area of the deformation
  • Angle deformation



Map projection category

Classification according to deformation

  • Isometric projection: Angular deformation is zero. After projection, the Angle remains unchanged, and the length in each direction is fixed at the same point.
  • Equal area projection: area deformation is zero.
  • Arbitrary projection: deformation of length, Angle and area.

Geometric projection

It is obtained by projecting the longitude and latitude network of the ellipsoid onto a geometric surface and then expanding the geometric surface into a plane. It can be divided into cylindrical projection, conic projection and azimuth projection according to the projection plane. According to the different position of the geometrical surface and sphere, it can be divided into positive axis, horizontal axis and oblique axis projection.

  1. Conic projection: projection using a cone as a projection surface

  1. Cylindrical projection: Projection on a cylindrical surface

  1. Azimuth projection: projection on a plane.

Common map projection

Mercator projection

  • Also known as orthoaxial equiangular cylindrical projection.
  • Projection method: Assume that the earth is surrounded by a hollow cylinder, and its standard latitude line is in tangent contact with the cylinder. Then imagine that there is a lamp in the center of the earth, and project the figure on the sphere onto the cylinder, and then expand the cylinder. This is a map drawn by the Mercator projection on the selected standard latitude line.
  • The Mercator projection has no angular deformation, and the length ratio from each point to each direction is equal. Its longitude and latitude lines are parallel straight lines, and intersect at right angles. The longitude and latitude lines are equally spaced, and the latitude line spacing gradually increases from the standard latitude line to two steps.
  • On the map of Mercator projection, the deformation of length and area is obvious, but there is no deformation of the standard latitude line. The deformation gradually increases from the standard latitude line to the two steps, but because it has the characteristic of equal expansion in all directions, it maintains the correct direction and mutual position relationship.



Gauss-kruger projection

  • Also known as transverse Mercator projection, gauss projection for short. It belongs to the transverse equiangular cylindrical projection.
  • After projection, there is no angular deformation, and no length deformation of the central longitude. On the same longitude, the lower the latitude, the greater the deformation, and the largest at the equator. On the same latitude, the further away from the central longitude, the greater the deformation.
  • In order to control the length deformation, the strip projection method is adopted. The ellipse of the earth is divided into several zones according to a certain longitude, which is called the projection zone. The bandwidth is generally 6° and 3°, which are called the 6° zone and 3° zone respectively.



     

Universal Transverse Mercator Projection

  • The universal transverse Mercator projection is the transverse equiangular elliptic cylindrical projection.
  • According to the equiangular condition, the region within a certain range on both sides of the central meridian is projected onto the elliptic cylinder, and then it is expanded into a plane.
  • The central meridian of a Gauss-Kluge projection keeps its length unchanged after projection, that is, its scaling coefficient is 1, while that of a UTM projection is 0.9996. That is UTM projection =0.9996 Gaussian projection.
  • Common projection of remote sensing images in China.



Lambert projection

  • Also known as normal axis isometric secant conic projection.
  • Projection method: imagine using a regular cone cut on the sphere, using equiangular conditions to project the earth surface onto the cone surface, and then expand along a bus, namely, the Lamberto projection plane.
  • The projection back latitude is concentric arc and the longitude is concentric radius.
  • It can be used to compile medium and small scale maps. Suitable for maps less than 1:1,000,000.
  • A projection most suitable for mid-latitude. It describes shape more accurately than area.

Albers projection

  • Also known as “normal axis equal-area conic projection”, “double standard weft equal-area conic projection”.

Map projection options

Large scale topographic map, high precision requirements, should use small deformation projection, such as zoning projection. Medium and small scale map has large scope, high generalization degree and low positioning accuracy, and can be selected by equiangle, equiproduct and arbitrary projection.

Map projection used by the main types of maps in China

The map type The projection
Map of China Oblique axis equal area (or equal Angle) azimuth projection
Map of Provinces in China Normal axis equal Angle (or equal area) secant conic projection (Albers projection)
1:1 million topographic maps Normal axis equiangular secant conic projection (Lambert projection)
1:5-1:500,000 topographic map Gauss-kluge projection (6 degree zoning)
1:5000-1:25,000 Gauss-kluge projection (3 degree zoning)
1:500-1:5000 Gaussian projection of local coordinates