PostGIS extension: pgRouting for calculating driving distance [Tutorial]

pgRouting is an extension of PostGIS and PostgreSQL geospatial database. It adds routing and other network analysis functionality. In this tutorial we will learn to work with pgRouting tool in estimating the driving distance from all nearby nodes which can be very useful in supply chain, logistics and transportation based applications.

This tutorial is an excerpt from a book written by Mayra Zurbaran,Pedro Wightman, Paolo Corti, Stephen Mather, Thomas Kraft and Bborie Park titled PostGIS Cookbook - Second Edition.

Driving distance is useful when user sheds are needed that give realistic driving distance estimates, for example, for all customers with five miles driving, biking, or walking distance. These estimates can be contrasted with buffering techniques, which assume no barrier to travelling and are useful for revealing the underlying structures of our transportation networks relative to individual locations.

Driving distance (pgr_drivingDistance) is a query that calculates all nodes within the specified driving distance of a starting node. This is an optional function compiled with pgRouting; so if you compile pgRouting yourself, make sure that you enable it and include the CGAL library, an optional dependency for pgr_drivingDistance.

We will start by loading a test dataset. You can get some really basic sample data from
https://docs.pgrouting.org/latest/en/sampledata.html.

In the following example, we will look at all users within a distance of three units from our starting point—that is, a proposed bike shop at node 2:

SELECT * FROM pgr_drivingDistance(
  'SELECT id, source, target, cost FROM chp06.edge_table',
  2, 3
);

The preceding command gives the following output:

As usual, we just get a list from the pgr_drivingDistance table that, in this case, comprises sequence, node, edge cost, and aggregate cost. PgRouting, like PostGIS, gives us low-level functionality; we need to reconstruct what geometries we need from that low-level functionality. We can use that node ID to extract the geometries of all of our nodes by executing the following script:

WITH DD AS (
  SELECT * FROM pgr_drivingDistance(
    'SELECT id, source, target, cost 
    FROM chp06.edge_table', 2, 3
  )
)
    
SELECT ST_AsText(the_geom)
FROM chp06.edge_table_vertices_pgr w, DD d
WHERE w.id = d.node;

The preceding command gives the following output:

But the output seen is just a cluster of points. Normally, when we think of driving distance, we visualize a polygon. Fortunately, we have the pgr_alphaShape function that provides us that functionality. This function expects id, x, and y values for input, so we will first change our previous query to convert to x and y from the geometries in edge_table_vertices_pgr:

WITH DD AS (
  SELECT * FROM pgr_drivingDistance(
    'SELECT id, source, target, cost FROM chp06.edge_table',
     2, 3
  )
)
SELECT id::integer,  ST_X(the_geom)::float AS x, ST_Y(the_geom)::float AS y 
FROM chp06.edge_table_vertices_pgr w, DD d
WHERE w.id = d.node;

The output is as follows:

Now we can wrap the preceding script up in the alphashape function:

WITH alphashape AS (
  SELECT pgr_alphaShape('
    WITH DD AS (
      SELECT * FROM pgr_drivingDistance(
        ''SELECT id, source, target, cost 
        FROM chp06.edge_table'', 2, 3
      )
    ),
    dd_points AS(
      SELECT id::integer, ST_X(the_geom)::float AS x, 
      ST_Y(the_geom)::float AS y
      FROM chp06.edge_table_vertices_pgr w, DD d
      WHERE w.id = d.node
    )
    SELECT * FROM dd_points
  ')
),

So first, we will get our cluster of points. As we did earlier, we will explicitly convert the text to geometric points:

alphapoints AS (
  SELECT ST_MakePoint((pgr_alphashape).x, (pgr_alphashape).y) FROM alphashape
),

Now that we have points, we can create a line by connecting them:

alphaline AS (
  SELECT ST_Makeline(ST_MakePoint) FROM alphapoints
)
SELECT ST_MakePolygon(ST_AddPoint(ST_Makeline, ST_StartPoint(ST_Makeline))) FROM alphaline;

Finally, we construct the line as a polygon using ST_MakePolygon. This requires adding the start point by executing ST_StartPoint in order to properly close the polygon. The complete code is as follows:

WITH alphashape AS (
  SELECT pgr_alphaShape('
    WITH DD AS (
      SELECT * FROM pgr_drivingDistance(
        ''SELECT id, source, target, cost
        FROM chp06.edge_table'', 2, 3
      )
    ),
    dd_points AS(
      SELECT id::integer, ST_X(the_geom)::float AS x,
      ST_Y(the_geom)::float AS y
      FROM chp06.edge_table_vertices_pgr w, DD d
      WHERE w.id = d.node
    )
    SELECT * FROM dd_points
  ')
),
alphapoints AS (
  SELECT ST_MakePoint((pgr_alphashape).x,
  (pgr_alphashape).y)
  FROM alphashape
),
alphaline AS (
  SELECT ST_Makeline(ST_MakePoint) FROM alphapoints
)
SELECT ST_MakePolygon(
  ST_AddPoint(ST_Makeline, ST_StartPoint(ST_Makeline))
)
FROM alphaline;

Our first driving distance calculation can be better understood in the context of the following diagram, where we can reach nodes 9, 11, 13 from node 2 with a driving distance of 3:

With this,  you can calculate the most optimistic distance route across different nodes in your transportation network. Want to explore more with PostGIS, check out PostGIS Cookbook - Second Edition and get access to complete range of PostGIS techniques and related extensions for better analytics on your spatial information.

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