Do you really use the buffer buffer in PostGIS?

buffer - Graph buffer analysis ,GIS One of the most basic spatial analysis in .

Realization buffer There are many kinds of tools for , For example, the front-end truf.js、 Server side ArcGISserver、 On the desktop ArcMap、 Database side PosrGIS And so on .

But I've been using it lately PostGIS Point to point buffer When analyzing , What you get is an ellipse .

Why ellipse , Shouldn't it be a circle ？

To find out , I'm going to study buffer Principle .

buffer There are two ways to build ： European method and Geodesic method .

1. It's a two-dimensional method of computing on the Euclidean plane , This two-dimensional map is a map of the earth after projection , The process of projection causes the map to deform , The Euclidean method is based on the transformed map to calculate the buffer .
2. Geodesic method is to calculate on three-dimensional ellipsoid , A three-dimensional ellipsoid is a sphere very close to the shape of the earth , The geodesic method is based on the surface of this sphere for buffering , Then the calculation results are transformed by projection , Show it on the map .

The difference between the two results is , In the European method , The result of the point buffer calculation is a circle at all times , But when you put the results into the real world , But there will be errors . The size of the error , It depends on how you project 、 Buffer position and buffer distance , Take Gaud map for example , It uses a Mercator projection , In this projection , The equatorial region has the smallest deformation , The more we go to the high latitudes of the north and south poles , The more deformation , The most obvious is Greenland , Its area is only the size of the Chinese mainland 1/4 about , But on the map , It's bigger than China .

There is no error in the geodesic method , But show it on a two-dimensional map , You have to project the map , Projection causes distortion .

If there is no error in the result , And show that there is no deformation , What do I do ？

With a three-dimensional map .

Three dimensional maps do not need to be projected like two-dimensional maps , No projection transformation , There will be no deformation .

The following figure , On the left is a two-dimensional map , On the right is a three-dimensional map , It's obvious that at high latitudes , The left side has been deformed , And there's no on the right .

understand buffer After the principle of , Let's go back to the problem at the beginning .

stay postGIS In my sql The code is written like this , according to postGIS Of Official documents , This should belong to the European method .

buffer 500 The effect of rice is like this

[ Failed to transfer the external chain picture , The origin station may have anti-theft chain mechanism , It is suggested to save the pictures and upload them directly (img-0nv5XIg8-1605169096527)(http://blogimage.gisarmory.xyz/20201112122638.png)]

And then I wrote a geodesic method , Notice the difference between the red box and the above , Input v_inGeom Variable , The default is geometry type , Force it to geography after ,postGIS You'll use the geodesic method .

buffer 500 The rice effect is like this

Two at the same time

The problem is obvious , Why is the result of geodesic method round , The result of the European method is elliptic ？ This is not in line with the principle of the previous study ,

It's not supposed to be that the European method is circular , Is the geodesic method elliptical ？

I use it again truf.js do 500 The buffer of rice , The buffered result is superimposed on the graph above , The effect is this （ The little circle inside is truf.js Buffered results ）

I fell into deep thinking .

see truf.js Of Official documents , There's only one buffer , There is no specific description of what kind of .

Feeling truf.js This , That's the right European approach , What the hell is the ellipse on it ？

It seems that we need to find an authoritative one to calibrate , Use arcgis server Of buffer Interface try , See what the effect is .

Code

The effect is as follows , The big circle is the geodesic method , The small circle is the European method

So it seems ,truf.js Chinese is the European way ,postGIS The geodesic method in is correct , But the European approach is problematic .

Then study again postGIS The European method in .

Calling arcgis server Of buffer Interface , Notice that 3 Coordinate dependent parameters ,inSR Enter the coordinates of the graph ,outSR Output the coordinates of the graph ,bufferSR The coordinates used when buffering .

Mark up postGIS

The same goes for the incoming and returning wgs84 Coordinates of , What coordinates are used for buffering ？

Oh ~ Oh ~ got it

The reason why ellipses appear is because , stay geojson When you turn Geometry （ Look at the picture below ）,St_geomfromgeojson function The return is geometry type , When buffering ST_Buffer function Received geometry The type will choose to use the European method for buffering , but geojson The data in is the latitude and longitude data of spherical coordinates , The radius of the buffer also passes in radians , In spherical coordinates and radian distance units , In the plane map algorithm of Euclidean method , No wonder it turns out to be an ellipse .

Um. ~ with reason .

Turn the coordinates and try , In the red box below is the process of coordinate transformation , meanwhile , Because the projection coordinates are used to calculate ,buffer The distance parameter can be used directly in meters , There's no need to turn it into an arc .

Try again , The big circle is the geodesic method , Small circles are European methods , ha-ha , perfect ！

Finally, to verify the accuracy , Measure the distance , Which one is right .

Obviously , The following figure ,500 The distance of meters is consistent with the boundary of the big circle in the picture above , That is, geodesic method is more accurate .

Little question ：

Why is the circle buffered by the geodesic method still a regular circle , Isn't it deformed ？

answer ： The main reason is , The buffer distance in the example is only 500 rice , The range is too small . It's also Beijing , If it's a buffer 1000 Km above , You can see the obvious deformation .

summary ：

1. buffer There are two ways to build , European method and geodesic method
2. The Euclidean method is to carry out buffer calculation on the plane map after projection deformation , The advantage is that the algorithm is simple , Efficient , The disadvantage is that the result is not correct , The size of the error depends on the projection method 、 Buffer position and buffer distance .
3. Geodesic method is a buffer calculation on a three-dimensional ellipsoid , The advantage is that the results are accurate , Not affected by projection distortion , The disadvantage is that the algorithm is complex , Large amounts of data may affect efficiency .
4. truf.js Only European methods are supported .
5. arcgis server Support two ways to build .
6. postGIS Support two ways to build , The default is the European method , In the European method , If the parameter is longitude and latitude coordinates , It is necessary to convert the longitude and latitude coordinates into projection coordinates and then calculate , Otherwise, the result of the buffer will be an ellipse . Change the type of the parameter from geometry Cast to geography after ,postGIS Will use geodesic method for buffer calculation .

Example 、 Source code

This example is used in the article , It can be accessed online , Use the browser developer tool to see the code .

postGIS Buffer example

This function script , Including the European method and geodesic method mentioned in the paper , Both incoming and returning are geojson Format , The buffer radius is in meters , Control buffering by type . Direct execution creates functions .

postGIS in buffer Function script

Reference documents

http://www.postgis.net/docs/ST_Buffer.html

https://postgis.net/docs/using_postgis_dbmanagement.html#Geography_Basics

http://turfjs.org/docs/#buffer

https://desktop.arcgis.com/zh-cn/arcmap/10.3/tools/analysis-toolbox/how-buffer-analysis-works.htm

http://server.arcgisonline.com/arcgis/sdk/rest/index.html#//02ss000000nq000000

http://server.arcgisonline.com/arcgis/sdk/rest/index.html#/Buffer/02ss0000003z000000/

https://developers.arcgis.com/javascript/latest/sample-code/ge-geodesicbuffer/index.html

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