In this paper, we come to understand the projection coordinate system in the coordinate system

PCS (Non-Earth Projection Coordinate System), or more simply plane Coordinate System, is used to describe the position of a point on the earth based on X and Y values

And now you might say, well, what is the relationship between the projected coordinate system and the geographic coordinate system?

In fact, the geographic coordinate system is spherical coordinate, the reference plane is ellipsoid, the coordinate unit is longitude and latitude, and the projection coordinate system is plane coordinate system, the reference plane is horizontal plane, the coordinate unit is meters, kilometers and so on

PS: Because the map is too difficult to draw, all the pictures in this article are from the Internet, if there is any infringement, please inform us and delete it immediately

What is a projection

Projection refers to the use of a group of light rays to project the shape of an object onto a plane, called a projection, which we call the projection plane, and see the picture below, and the projection we are going to study, the object to be projected is the earth

There are planes that can unfold into a plane, and a sphere will never unfold into a plane, so the only way to make a sphere into a plane is by projection, and there are many ways of projecting a sphere, which we’ll talk about later

Why we need a projection

The projection is needed because the latitude and longitude in the geographic coordinate system do not have units, and the degree minute and second is only a base system. In addition, the length of arc represented by the same degree of longitude in different latitude zones is different, which brings difficulties to the area and quantitative calculation

Traditional maps (compared with 3D platforms such as Google Earth) are presented on two-dimensional planes, so a mapping method that can transform three-dimensional coordinates on the earth sphere into two-dimensional planes is needed, which is map projection. Therefore, Map projection is a kind of mapping from latitude and longitude B,L,H to projection coordinates X,Y,Z

The essence of map projection is to establish the corresponding relation between the points on the surface of the earth ellipsoid and the points on the map plane. The longitude and latitude coordinates established in the geographic coordinate system on the sphere are converted into cartesian coordinates on the plane through a projection method

The purpose of map projection is to establish a plane coordinate system (called the projection coordinate system), a lot of calculation, business calculation on the plane compared with the calculation on the surface is easier

For example, on a sphere, two points with the same latitude and the same longitude difference will have different distances at different latitudes, which brings inconvenience to calculation. This problem does not exist on the Euclidean plane

Many classic GIS software, such as ArcMap, are based on 2D plane development for their basic framework, including rendering, editing and other functions, which is consistent with our requirements for maps

To the extent that deformation is allowed, a unified plane coordinate system is established. This point is emphasized because the scope of the map is also an important factor to be considered when designing map projections

Classification of projections

When a target on a sphere is flattened to a plane, the target will definitely be compressed or stretched. According to the nature of the deformation, map projections can be simply divided into the following categories

  • Isometric projection: after the projection, the target is deformed in all directions and the overall Angle remains unchanged

  • Isometric projection: after the projection, the overall length remains unchanged, and the area and Angle are somewhat deformed

  • Equal-area projection: If there is a differential circle on the target, if the area of the circle after the projection is unchanged, the projection is equal-area projection

  • Arbitrary projection: projection in which the area, Angle, and length of the projection are changed

The following figure

According to the way of projection, it can be divided into the following categories

  • Cylindrical projection: the projection plane is cylindrical
  • Conic projection: The projection surface is a cone
  • Azimuth projection: the projection plane is flat

A Gaussian Krueger projection is a cylindrical projection, as shown in the figure below

So according to the relationship between the principal axis of the projection plane (cylinder, cone, plane) and the earth axis (the short axis connecting the north and South Pole) relative position, projection can be divided into the following several ways

  • Orthographic projection: the central axis of the projection plane coincides with the earth axis
  • Oblique projection: the central axis of the projection plane intersects the earth axis diagonally
  • Horizontal projection: the central axis of the projection plane is perpendicular to the earth axis
  • Tangent projection: The projection plane is tangent to the ellipsoid
  • Phase cutting projection: the projection plane is phase cutting with the ellipsoid

The following figure

Common projection mode

Mercator projection -Mercator

Mercator projection (Mercator), also known as Mercator projection, positive axis equiangular cylindrical projection, by the Dutch cartographer Mercator (G.Mercator) in 1569

To put it simply, it is assumed that the earth is enclosed in a cylinder, and the equator is tangent to the cylinder. Then, a lamp is placed in the center of the earth, and the figure on the sphere is projected onto the cylinder. Then, the cylinder is expanded to form a Mercator projection world map, as shown in the following figure

Because it can display the correct position between two points, the purpose of the navigation chart, most of the route map drawing all this way, the projection of the linear scale around any point in the picture remains constant, which can keep the mainland after the contour projection Angle and shape unchanged (isometric), but the Mercator projection area causes deformation, The proportion of poles (that is, the north and South regions) reaches infinity

Therefore, it does not show the whole world completely. The highest latitude on the map is 85.05 degrees. In order to simplify the calculation, a spherical map is used instead of an ellipsoid shape

Gauss-kruger projection

This projection is by the German mathematician, physicist, astronomer Gauss in the 1820s drafted, after the German geodetic kluge in 1912 to supplement the projection formula, so called Gauss Kluge projection

You can imagine an ellipsoid cylinder lying horizontally on the ellipsoid of the earth (tangent to the coil), rotating around the earth’s axis, projecting the earth’s surface onto the elliptic cylinder, then cutting and spreading the surface along the height of the elliptic cylinder into a plane, as shown below

This is called zonation. Rotate the projection plane of Gaussian Krueger to get the projection of the next zonation, which is suitable for all parts of the world, as shown below

Gaussian Kluge projection, also known as equiangular transverse elliptic cylindrical projection, is known as the transverse Mercator projection in The United States and Britain. The global/universal transverse Mercator projection (UTM) used by the United States in compiling military maps and earth resources satellite images around the world is a variant of the transverse Mercator projection

Universal transverse Mercator projection (UTM)

Universal Transverse Mercator is similar to gaussian Kluge projection except that it cuts the earth ellipsoid for Transverse normal axis of elliptic cylinder. The center line of the ellipsoid is located on the equator plane of the ellipsoid. And through the points of the ellipsoid constitution, the points on the ellipsoid are projected onto the ellipsoid cylinder, as shown below

This projection was proposed by the US Army Corps of Engineers Surveying and Mapping Bureau in 1940s. Clarke 1866 ellipsoid is used in the US mainland, and WGS84 ellipsoid is used in other parts of the world. At present, most remote sensing images use UTM projection coordinate system

WebMercator projection

Popular Visualization Pseudo Mercator (PVPM) is not a Mercator projection, but a pseudo-Mercator projection method first proposed by Google Map

Its imprudence lies in the fact that the ellipsoid representing the earth is treated as a regular sphere in the projection process

Legend has it that Google programmers were too lazy to program with ellipsoids to calculate screen coordinates. I don’t know

It takes the whole world equator as the standard latitude, the prime meridian as the central longitude, the intersection of the two as the origin of coordinates, east to north is positive, west to south is negative

We said Mercator projection method above, then you can know, when the latitude near the poles, y value tends to infinity, and the lazy engineer is restricting the scope of y axis between [20037508.3427892, 20037508.3427892]

The longitude range of the Mercator projection coordinates is [-180,180]. The latitude range is [-85.05112877980659, 85.05112877980659]. What about the rest of the region? No one knows. We don’t need it

In addition, we also need to know that WebMercator projection also adopts WGS84 datum plane. Please refer to geographic coordinate system above for datum plane correlation

The last

In China, there are only Beijing 54, Xi ‘an 80 and China 2000 geographic coordinate systems, which can be selected according to the central longitude as required

The PCS family based on UTM projection is similar to the Family of Gaussian Krueger projection coordinate systems, except that it is based on WGS84 and can be selected according to the central longitude as needed

China’s gold, baidu, tencent maps, Google maps, OSM the network Mercator maps are used to show complanation, but domestic gold tencent, baidu and Google maps of the geographic coordinate system is encrypted, and while a map world with 2000 national geographic coordinate system, but also provides a Mercator projection method to planar maps, ArcGIS Earth is similar to Google Earth in that it directly uses 3857 coordinate system

The resources

Introduction to Geographic Information Systems – 9th edition

Talk about GIS in the coordinate system | reprint

Interesting projection methods you didn’t know about