Preheating article series: “GIS History Overview and Brief Explanation of WebGis Application and Development Technology”, “GIS Coordinate system :WGS84,GCJ02,BD09, Mars coordinates, geodetic coordinates and other analysis and transformation”, “OGC Standard WMTS Service Concept and Tile Number school of Map vendors”, “GIS basic Knowledge – Coordinate system, projection, EPSG:4326, EPSG:3857 we go over the following concepts:

  • The geographic coordinate system is spherical coordinate, the reference plane is ellipsoid, and the coordinate unit is latitude and longitude.

  • The projection coordinate system is the plane coordinate system, the reference plane is the horizontal plane, the coordinate units are meters, kilometers, etc.

The process of converting a geographic coordinate system to a projection coordinate system is understood as a projection, in which the irregular surface of the earth is transformed into a plane. Under the current information technology conditions, the direct use of geographic coordinate system is not more real and accurate, like Google Earth; Projections are, after all, deformed.

At present, different combinations of ellipsoid and projection coordinate system correspond to different ID numbers. This number is called EPSG Code in EPSG, which represents specific information of ellipsoid, unit, geographic coordinate system or projection coordinate system.

Geomapping and modeling

Geoid

The natural surface of the earth is not smooth, and it is necessary to find a way to describe the surface of the earth with mathematical formulas. Only an approximate mathematical surface can be imagined.

The geoid is the shape of the surface of the ocean that extends across the land, creating a closed surface after controlling for the effects of wind, tides and other forces, but only for gravity and rotation. Although we usually speak of the Earth as a sphere or ellipsoid, the geoid is an irregular smooth surface due to the uneven distribution of the earth’s gravity (due to density differences, etc.). Although irregular, it can be approximately represented as an ellipsoid, which is called the Reference ellipsoid. The height of the geoid relative to the reference ellipsoid is called Undulation of the geoid. The fluctuation was not very large, with a maximum of 85m in Iceland and a minimum of −106m in southern India, less than 200m in total. The following figure from Wikipedia shows Undulation for different regions under EGM96 GeoID.

Reference ellipsoid

A Reference ellipsoid is a mathematically defined surface of the earth (approximated by an ellipsoid model in mapping) that approximates the geoid. Because it is a geometric model, it can be determined by the long semi-axis, the short semi-axis and the flatness. What we call longitude, latitude and altitude are based on this.

The equator is an approximate circle of radius A, and the longitude of any circle is an approximate circle of radius B. A is called the major axis radius of the ellipsoid, and b is called the minor axis radius of the ellipsoid.

A ≈6378.137 km, B ≈6356.752 km. (In fact, A is not constant. The difference between the best and the worst is 72 meters, and the difference between the best and the worst is 42 meters, which is very small.)

Basic parameters of earth reference ellipsoid:

  • Long axis: a

  • Short axis: b

  • Flatness: α=(a-b)/A

  • First eccentricity: e=√(a²-b²)/a

  • Second eccentricity: e’=√(a²-b²)/b

When these parameters are fixed, the mathematical model of the reference ellipsoid is fixed.

On the one hand, our measurements of the earth’s shape become more accurate over time. On the other hand, because the geoid is irregular, different regions of the earth often need to use different reference ellipsoids to fit the local geoid as best as possible.

Many different reference ellipsoids have appeared in history, and many are still in use. In the past, two coordinate systems “Beijing 54” and “Xi ‘an 90” have been used in China. Among them, Beijing 54 uses the reference ellipsoid of Krasovsky 1940, and Xi ‘an 80 uses the reference ellipsoid recommended by the 16th General Assembly of International Union of Geodesy and Geophysics in 1975. The reference ellipsoid defined by WGS is more commonly used in the world.

Common ellipsoid parameters

GRS ellipsoid WGS-84 Ellipsoid A 6 378 245.000 m 6 378 140.000 m 6 378 137.000 m b 6 356 863.019 m 6 356 755.288 m 6 356 752.314 m a 1/298.3 1/298.257 1/298.257 224 e 0.006 693 422 0.006 694 385 0.006 694 380 e 0.006 738 525 0.006 739 502 0.006 739, 497,Copy the code

Geodatum

Ellipsoid is the abstraction of earth, and cannot be completely coincide with the surface of the earth, at the time of setting reference ellipsoid inevitable in some places close to the good (reference ellipsoid and location close to the earth’s surface), have to place close to the bad problem, so this will also need a reference ellipsoid and the datum to control the relative position of the earth. There are two types of datum:

  • Geocentric datum: Derived from satellite data using the earth’s center of mass as the origin, the most widely used is WGS 1984.

  • Regional datum: the point at which the reference ellipsoid is tangent to the geoid in a particular region that coincides with the earth’s surface, e.g., Beijing-54 and Xian-80. The beijing-54 and Xian-80 coordinate systems actually refer to the two datum planes of China.

Geoid, reference ellipsoid, geodatum

  • The geoid is the first approximation of the earth’s surface. The geoid is a continuous, closed surface that extends from the sea level to the underside of all continents and is orthogonal to the direction of the earth’s gravity, when the sea is in perfect equilibrium.

  • The earth ellipsoid is the second approximation of the earth’s surface. Geoid can be approximated as a regular ellipsoid, but it is not completely regular. Its shape is similar to that of a regular ellipsoid formed by rotation of an ellipse with minimal flatness about a short axis. This ellipsoid is called the earth ellipsoid.

  • The datum is the third polar approximation of the earth’s surface.

Geodetic coordinate system and spatial rectangular coordinate system

  • Geodetic coordinate system is a coordinate system based on reference ellipsoid. The positions of ground points are indicated by geodetic longitude, geodetic latitude, and geodetic height :(L, B, H).

  • The spatial cartesian coordinate system is based on the center of the reference ellipsoid as the origin, the rays from the point of intersection of 0 degrees longitude and equator from the origin as the X-axis, the rays from the point of intersection of 90 degrees longitude and equator as the Y-axis, and the z axis north of the earth’s rotation axis :(x, y, z)

Common ground: Obviously, both coordinate systems must be based on a reference ellipsoid.

Difference: The geodetic coordinate system is based on the plane, so a standard sea level needs to be determined. The spatial cartesian coordinate system is based on a 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.

How to locate the origin of the coordinate system

Why WGS84 chose the earth’s center of mass as its origin, while Xi ‘an 80 chose a point on the earth’s surface as its origin? What is the role of the geodetic origin chosen by China? Why in Jingyang County Yongle town? If I’m at the origin, why isn’t latitude and longitude zero?

This article is very thorough “Understanding of Earth coordinate system and Projection Mode (about Beijing 54, Xi ‘an 80,WGS84; Gauss, Lambert, Mercator Projection)”

  • Beijing 54: long axis 6378245m, short axis 6356863, flatness 1/298.2997381

    In the early days after foundation, in order to carry out surveying and mapping in China rapidly, in view of the actual situation at that time, our country will be the former Soviet union in 1942 will be calculated from the coordinates of the pulkovo coordinate system data (geodetic origin in the former Soviet union pulkovo), adjustment of northeast China and eastern area, the coordinate system is chosen this biography is over 1954 Beijing coordinate system.

    The datum of elevation is the mean sea surface of the Yellow Sea calculated by Qingdao tide survey station in 1956. The anomaly of elevation was calculated from the result of geoid adjustment in 1955 in the former Soviet Union.

  • Xi ‘an 80: long axis 6378140m, short axis 6356755, flatness 1/298.25722101

    The basic parameters of the earth ellipsoid adopted in the 1980 National geodetic coordinate system were the data recommended by the sixteenth Congress of the International Union of Geodesy and Geophysics in 1975. The geodetic origin of the coordinate system is located in Yongle Town, Jingyang County, Shaanxi Province, central China, about 60 kilometers northwest of Xi ‘an city, so it is called the 1980 Xi ‘an coordinate system, also referred to as xi ‘an geodetic Origin.

    The mean sea level of the Yellow Sea determined by Qingdao Dagang Tide Survey Station from 1952 to 1979 (i.e. 1985 National Elevation datum) is adopted as datum.

  • WGS84: Long axis 6378137.000m, short axis 6356752.314, oblateness 1/298.257223563, first eccentricity 0.081819790992, second eccentricity 0.082095040121

These different parameters determine that the geometric centers of the ellipsoid model are different. So why are the parameters of these three coordinate systems so different? In addition to the different measurement accuracy, there is another reason, is the focus is not the same.

  • WGS84 is globally oriented, so it tries to approximate the entire surface of the earth. The advantage is that it has a large range, but the disadvantage is that it is not accurate locally.

  • Beijing 54 uses the parameters of the former Soviet Union. It is facing the Soviet Union, so it tries to approximate the surface of the former Soviet Union as much as possible, regardless of the deviation of other countries. It’s centered on Pulkovo in the Soviet Union, and the further you go from there, the bigger the error.

  • Xi ‘an 80 is facing China, so it is as close to the surface of China as possible, and it doesn’t care how much other countries and regions are biased. Moreover, this approximation is centered on the geodetic origin near Xi ‘an, that is to say, at the Xi ‘an geodetic origin, the model coincides with the real surface reference sea level with an error of 0, while the further away from the geodetic origin, the greater the error. This is how the so-called geodetic origin comes from. It is artificially determined, not necessarily there. It should be placed in the middle of China as far as possible, so that the total error is as small as possible and the distribution is even. Then, China in its own territory in the construction, mapping, exploration of what to draw the map, with this origin as the reference, to establish a variety of uses of the surface coordinate system, can be unified.

Therefore, the WGS84 model is not as accurate as the Xi ‘an 80 model in China. Using the Xi ‘an 80 model to calculate points in the United States is even less accurate. Now updated to 2000 national geodetic coordinate system, the parameters are more accurate than Xi ‘an 80, but the principle is the same.

It is said that WGS84 is the centroid coordinate system, Beijing 54, Xi ‘an 80 is the reference center coordinate system

WGS84 coordinates, Cartesian space coordinates (the origin of cartesian space coordinates is the center of the ellipsoid) are commonly used for spatial position transformations such as translation, rotation, scaling, etc. The connection between the two is shown below

What is the center of mass? What is ginseng heart?

  • The center of mass is the center of mass of the geosphere, the center of mass

  • The reference center is the geometric center, called the reference center, referred to as the reference center

Two kinds of coordinates produced by the difference between the center of the earth ellipsoid and the center of the earth’s mass

  • Geocentric geodetic coordinate system: after positioning and orientation, the center of the earth ellipsoid coincides with the center of the earth’s mass. Such as CGCS2000 and WGS84.

  • Parameter-centered geodetic coordinate system: after positioning and orientation, the center of the earth ellipsoid does not coincide with the earth’s center of mass but approaches the earth’s center of mass. Regional geodetic coordinate system is the basis of basic mapping and conventional geodetic survey in China. Such as Beijing-54 and Xian-80.

The WGS84 coordinate system is oriented to global positioning, so the model established by it is the most neutral, without bias to any one region. When the geometric center of the ellipsoid model coincides with the earth’s center of mass, the model will be closest to the whole earth.

Beijing 54 and Xi ‘an 80 focus on local accuracy rather than overall accuracy. When the ellipsoid model (Xi ‘an 80) is most accurate in China, its geometric center is definitely not the earth’s centroid, but somewhere else.

A projection of a map onto a plane

The concept of a projection is very simple. It’s a cast shadow. Just like a light in a dark room, when it hits your big body, there will inevitably be a shadow on the wall, which is the projection of your body on the wall.

Mathematical meaning of projection

As shown in the figure above, find the shortest distance between vector y and the plane W. For the point y, along the normal direction of plane W, it intersects W at y prime, where the error z is minimal, and that’s what we’re looking for. Because the ray is perpendicular to the plane (perpendicular), it is called an orthogonal projection. In real life, it is necessary to use the least square method to fit a regular line from a large number of statistical points, which is actually the idea of orthogonal projection. The corresponding mathematical description is: when there is no solution to Ax = y in the W plane, convert it to the form Px= y so that it has a solution.

Sure, what good would that do? Compare the difference between your body and your figure. The answer is to turn a three-dimensional problem into a two-dimensional one. This is the idea of dimensionality reduction and the value of projection. In order to simplify the problem and limit it to a certain range, necessary dimension reduction (elimination) should be carried out. If there is no solution to the problem as a result, the solution can be found through the appropriate projection matrix P.

The practical implications of projection

For a variety of reasons, a lot of times we need to abstract into two dimensions to make it easier to understand and reduce the cost. For example, how the display is flat, giving us the illusion of “depth”; The earth is clearly round, but the map looks flat.

The difference between the two is that the former uses perspective projection, which is also used by the eyes to perceive the world, so we can sense depth through the “flat” screen. While the latter uses orthogonal projection, both near and far are the same. But there is no fundamental difference in mathematical theory between them, they are both matrices P, only the elements in P are different.

Our maps have to be drawn on paper, on a monitor, or we’re carrying globes around? Points on the earth are expressed in terms of latitude and longitude, and the higher the latitude, the shorter the distance of 1 degree of longitude. So, the question is, the surface of the earth is curved, and latitude and longitude are not simply proportional to length, how do you draw it on a plane? The answer is a projection algorithm. Ok, so the question is, which algorithm is better?

Gauss-kluge projection/transverse Mercator projection

This Projection was first developed by German mathematician Gauss and later supplemented by Kruger, hence the name Gauss-Kruger Projection or Simply Gauss Projection.

It is assumed that an elliptic cylinder and the ellipsoid of the earth are crosscut on a certain longitude line, and the longitude and latitude lines within the range of 3° east and 1.5° west of the central longitude line are projected onto the elliptic cylinder according to the equiangular condition, and then the elliptic cylinder is expanded into a plane.

Gauss Krueger projection is a zonal projection, mainly divided into three degree band and six degree band. A 3-degree belt is a belt of longitude every 3 degrees, which is cut into 120 belts around the world. A 6-degree belt is a belt of longitude every 6 degrees, cut into 60 bands around the world. Each band has its own origin in the XY coordinate system, and you can’t use the xy coordinate system in this band to calculate the other bands, because the origin is different.

Gaussian projection zoning

  • In order to control deformation, the method of zoning projection is adopted, and 6° zoning is required for 1∶ 25,000-1 ∶ 500,000 topographic map. 3° zoning is used for 1∶ 10 000 and larger scale topographic maps to ensure the necessary accuracy.

  • 6° zonation method: from Greenwich 0° longitude, from west to east according to the longitude difference of every 6° for a projection belt, the world is divided into 60 projection belt, China is located between 72° ~ 136° east longitude, including 11 projection belt, namely 13 ~ 23 belt, the central longitude of each belt is 75°, 81°… And 135 °.

  • 3° zonal method: from 1°30¢, a projection belt was formed every 3° according to the longitude difference from west to east, the world was divided into 120 projection belts, China was located in belt 24 ~ 46, the central longitudes of each belt were 72°, 75°, 78°… And 135 °.

Deformation analysis of Gaussian Kluge projection:

  1. There is no deformation on the central meridian, which satisfies the condition of invariable length ratio after projection.

  2. The length ratio is greater than 1 at all points except the central meridian.

  3. On the same latitude line, the further away from the central longitude line, the greater the deformation, the maximum value is located at the edge of the projection band.

  4. In the same longitude, the lower the latitude, the greater the deformation, the maximum is located at the equator.

  5. Isometric projection, no angular distortion, area ratio is length ratio squared.

  6. The isodeformable line of length ratio is parallel to the central axis meridian.

Advantages: Length and area distortion is minimal (compared to other projections).

Disadvantages: need belt, adjacent belt can not be spliced (top tip under the width of how to connect? Difficult), resulting in a small coverage area.

So gaussian projection is good for maps of small areas, areas that can be covered by a band.

Lambert projection

There are two:

Isometric conic projection

Imagine a regular cone cut on or on a sphere, using equiangular conditions to project the surface of the earth onto the cone, and then unfold it into a plane along a busbar. The projection back latitude is concentric circle arc, and the longitude is concentric circle radius. There is no angular deformation, and the longitude length ratio is equal to the latitude length ratio. Suitable for making small and medium scale map of middle latitude area distributed along the latitude line. The maps of China on the market should use this kind of projection.

Equal area azimuth projection

Imagine the sphere and plane tangent to a point, according to the equal product conditions of the longitude and latitude projection on the plane. According to the relative position of the projection plane and the earth plane, it can be divided into positive axis, horizontal axis and oblique axis. In orthoaxial projection, the latitude lines are concentric circles whose intervals gradually shrink outward from the center of the projection, and the longitude lines are concentric circles’ radii. In the transverse projection, the central longitude and equator are perpendicular to each other, while the other longitude and latitude lines are symmetrical to the central longitude and equator, respectively. In oblique projection, the central meridian is a straight line and the other longitudes are curves symmetric to the central meridian. The projection has no area deformation and the Angle and length deformation increase from the center of the projection to the surrounding area. The horizontal and oblique projections are more commonly used, and are more commonly used for east and west hemisphere maps and continent maps.

Mercator projection

Mercator projection, also known as “isometric orthoaxial cylindrical projection”, was formulated by The Dutch cartographer Mercator in 1569. It assumes that the earth is surrounded by a hollow cylinder, and its equator is in contact with the cylinder. Then, it assumes that there is a lamp at the center of the Earth, projecting the figure on the sphere onto the cylinder. Unrolled, this is a Mercator projection of the world with zero standard latitude (the equator).

Advantages: no Angle deformation, from each point to each direction of the length ratio is equal, its longitude and latitude lines are parallel straight lines, and intersect at right angles.

Disadvantages: the length and area are obviously deformed, and the latitude interval gradually increases from the reference latitude to the poles. However, because it has the characteristic of equal expansion in all directions, it maintains the correct direction and mutual position relationship.

Mercator projection map is commonly used as navigation charts and air maps. If you follow the straight line between two points on the Mercator projection map, you can always reach the destination with the same direction. Therefore, it has favorable conditions for ships to locate and determine the course during navigation, and brings great convenience to navigators.

Google Map, Baidu Map is using Mercator projection, and to the equator as a reference latitude.

Web Mercator projection

Web Mercator projection (also known as spherical Mercator projection) is a variation of Mercator projection. The input it receives is the latitude and longitude of WGS84 as Datum, but the earth is no longer treated as an ellipsoid in the projection, but as a standard sphere with a radius of 6378137 meters, so as to simplify calculation.

Web Mercator projection has two related projection standards, which are often confused:

  • EPSG4326: plane map after Web Mercator projection, but the longitude and latitude of WGS84 are still used to represent coordinates;

  • EPSG3857: Plane map after Web Mercator projection, in meters.

Summary of common map projections

  • Gauss-kriging projection: Maps for small areas

  • Lambert conformal conic projection: suitable for mid-latitude areas where east-west extension is greater than north-south extension.

  • Web Mercator: Google Maps and Microsoft Virtual Earth use web Mercator, which is a Mercator projection based on a sphere rather than an ellipsoid, simplifying calculations but sacrificing accuracy. Therefore, users must consider reprojection when using this projection to do data analysis.

Geographic coordinates and projection coordinates

Geographic coordinate System

Geographic coordinate system generally refers to the coordinate system composed of longitude, latitude and altitude, which can mark any position on the earth. As mentioned earlier, different regions may use different reference ellipsoids, and even if the same ellipsoid is used, the orientation and even size of the ellipsoid may be adjusted to better match the local geoid. This requires the use of a different Geodetic datum system for identification. Therefore, for a certain position on the earth, using different measurement systems, the resulting coordinates are not the same. When we process geographic data, we must first confirm the measurement system used for the data. As a matter of fact, as we measure the shape of the Earth more and more accurately, NAD83 datum used in North America and ETRS89 datum used in Europe are basically consistent with WGS84 datum, and even the difference between CGCS2000 and WGS84 in China is very small. However, the difference is very small and does not represent perfect uniformity. Take NAD83 for example, because it is required to maintain the uniformity in North America, the difference between IT and WGS84 is constantly changing, with a 1-2cm difference per year for most of the United States.

Projected coordinate Systems

The geographic coordinate system is three-dimensional, and it needs to be transformed into two dimensions to be displayed on a Map or screen, which is called Map projection. Obviously, when you go from three to two dimensions, you’re going to have distortion and distortion, and distortion is inevitable, but different projections have different distortions, and that gives us a choice. Commonly used projections are Platte Carre and Mercator. The following figure is from Mercator vs. Well… Not Mercator (Platte Carre), vividly illustrates the distortion under these two projections:

The image on the left shows a circle of the same size on the sphere of the Earth. The Mercator projection on the upper right is still a circle, but the object is greatly magnified at high latitudes. On the lower right is an isometric projection, where the size of the object does not change significantly, but the image is stretched out. Platte Carre projection is not suitable for navigation and other activities because of its distortion in projection. However, because the correspondence between coordinates and pixels is very simple, it is very suitable for the display of raster graphs. Platte Carre projection is the default projection of many GIS software.

It should be noted that for Mercator projections, the greater the size distortion, the greater the latitude, the greater the size distortion will be at the poles, so the Mercator projection will not show the polar regions. The image below, from Wikipedia, shows the difference in size between the Mercator projection and the actual size of each country. However, the two characteristics of conformality and straight Rhumb lines make it very suitable for sea navigation.

By Jakub Nowosad-own work, CC by-SA 4.0, Link

EPSG, SRID, WKT concepts

EPSG

EPSG: European Petroleum Survey Group (EPSG) www.epsg.org, which was founded in 1986 and reorganized into OGP(Internation Association of Oil & Gas Producers) in 2005, It is responsible for maintaining and publishing the data set parameters of the coordinate reference system, as well as coordinate transformation descriptions, which are widely accepted and used.

EPSG has maps for every part of the world, but they vary from place to place due to different coordinates.

For China, for example, a map centered on the geometric spherical center of the Earth would be EPSG:4479, centered on the ellipsoid focal point of the Earth would be EPSG:4480, and EPSG:4490, because the choice of different coordinate systems is critical to the cost of oil and gas exploration, there are different coordinate systems.

EPSG:3857 (Pseudo-Mercator)

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. We already know that WGS84 is based on an ellipsoid, but the pseudo-Mercator projection projects coordinates onto a sphere, which leads to greater distortion at the poles, but is easier to calculate. Maybe that’s why it’s called a “fake” Mercator. In addition, the pseudo-Mercator projection also cuts out areas above the latitude of 85.051129° to ensure that the entire projection is square. Because of conformal features such as Mercator projection, where the shape of objects remains the same on different layers, a square can be continuously divided into more and smaller squares to show clearer details. Obviously, the pseudo Mercator coordinate system is very good for displaying data, but it is not suitable for storing data. Usually we use WGS84 to store data and use pseudo Mercator to display data.

Web Mercator was first proposed by Google and has now become the de facto standard for Web Maps. But perhaps due to the above “bogus” reasons, Web Mercator was initially denied the assignment of EPSG code. The unofficial code EPSG:900913 (a Google number variant) is widely used to represent it. It was not until 2008 that the code EPSG:3785 was assigned, but later that year it was abandoned and the official code EPSG:3857 was reassigned, which is in use today. Today it is the coordinate system used by Google Maps and almost every other Web charting application.

Most familiar to Web Map developers are EPSG:4326 (WGS84) and EPSG:3857(pseudo-mercator).

EPSG:4326 (WGS84)

Internationally, each coordinate system is assigned an EPSG code. EPSG:4326 is the code for WGS84. GPS is based on WGS84, so we usually get coordinate data from WGS84. Generally, when we store data, we still press WGS84 for storage.

EPSG:3785

This is the WKID set up by EPSG for Web Mercator in 2008, but the reference plane of this coordinate system is a regular sphere, not WGS 1984(pseudo-Mercator projection -> Spherical Mercator). It existed for some time and then was abandoned.

SRS

SRS: Spatial Reference System. In the context of a spatial database, the defined space used to describe geometry is called a spatial reference frame. A spatial reference frame defines at least the following:

  • The unit of measurement (degree, meter, etc.) in the base coordinate system

  • Maximum and minimum coordinates (also called boundaries)

  • Default linear unit of measurement

  • Is the data plane data or ellipsoid data

  • Projection information used to convert data into other SRS

Each Spatial Reference frame has an Identifier, called the Spatial Reference Identifier (SRID).

SRID

**SRID: **Spatial Reference Identifiers The parameter SRID in OGC standard also refers to the ID of the spatial reference system, which is consistent with EPSG, namely:

The SPATIAL reference system SRID in OGC standard is consistent with the spatial reference system ID in EPSG.

  1. Each spatial instance has a spatial reference identifier (SRID)

  2. SRID corresponds to a spatial reference system based on a specific ellipsoid and can be used for flat sphere mapping or round sphere mapping

  3. The result of any spatial method derived from two instances of spatial data is valid only if the two instances have the same SRID based on the same units of measure, data, and projection used to determine instance coordinates.

  4. The SRID is most commonly measured in meters or square meters.

For details, see Microsoft SQL Server 2019 “Space Reference Identifiers” and MapTalks “tile-system”.

WKT

WKT: Well-known binary (WKT) is a text markup language used to represent vector geometric objects, space-referenced systems, and transformations between space-referenced systems. Its binary representation, known as WKB, is better than storing the same information in transport and ina database. The format was developed by the Open Geospatial Consortium(OGC).

WKT/ geometric object

Geometric objects that WKT can represent include points, lines, polygons, TIN (irregular triangulation network) and polyhedra. Geometric objects of different dimensions can be represented by geometric sets.

The coordinates of a geometric object can be 2D(x,y),3D(x,y,z),4D(x,y,z,m), plus an M value belonging to a linear reference system.

POINT(6 10)

LINESTRING 50 (3, 4, 10, 20, 25)

POLYGON(1,5,5, 5,1,5),(2,2, 3,3, 3,3,2,2,2)

MULTIPOINT (3.5, 5.6, 4.8, 10.5)

MULTILINESTRING (50 (3, 4, 10, 20, 25), (8-5-8-10 -, 15-4))

MULTIPOLYGON (((1, 1, 1, 5 5, 1, 1, 1), (2, 2, 2, 3, 3, 3, 3, 2, 2)), ((6, 3, 9, 9, 4, 6 2 3)))

WKT/ Space reference system

A WKT string representing a spatial reference system describes geodesic datum, geoid, coordinate system and map projection of a space object. WKT is widely used in many GIS programs.

No matter the reference ellipsoid, datum, projection mode, coordinate unit, etc., all have corresponding EPSG values, as shown in the following table:

Reference article:

Understanding of Earth coordinate system and Projection Mode (about Beijing 54, Xi ‘an 80,WGS84; Gauss, lambert, Mercator projection) www.cnblogs.com/xieqianli/p…

What is EPSG? What is WKT? What is SRID? EPSG, WKT, SRID concept blog.csdn.net/gis0911178/…

The difference between the geographic coordinates and projection coordinates blog.csdn.net/aganliang/a…

Basic knowledge of GIS – coordinate system, projection, EPSG: 4326, EPSG: 3857 www.cnblogs.com/E7868A/p/11…

EPSG 4326 vs EPSG 3857 (projections, datums, coordinate systems, and more!)

Mercator vs. Well… not Mercator (Platte Carre)

Spatial reference system (SRS) and the spatial reference identifier (SRID) dcx.sap.com/1201/zh/dbspatial/spatial-reference-identifier.html

Projection mathematical meaning of www.cnblogs.com/fuckgiser/p…

Reprint the home station article GIS coordinate mapping principle: geoid/datum reference ellipsoid/EPSG/SRI/WKT “, please indicate the source: www.zhoulujun.cn/html/GIS/GI…