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Thu Oct 30 09:20:08 2014

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Catchment Areas with pgRouting driving_distance()

In a previous post, I’ve described how to create catchment areas with pgRouting shortest_path() function. The solution described there calculates costs from the starting node (aka vertex) to all other nodes in the network. Depending on the network size, this can take a long time. Especially, if you are only interested in relatively small catchment areas (e.g. 50 km around a node in a network covering 10,000 km) there is a lot of unnecessary calculation going on. This is where you might want to use driving_distance() instead.

Driving_distance() offers a parameter for maximum distance/cost and will stop calculations when the costs exceed this limit. But let’s start at the beginning: installing the necessary functions.

Installation

If you have followed my guide to installing pgRouting, you already have some routing functions installed – but not driving_distance(). Weirdly, the necessary SQL scripts are not shipped with the .zip file available on pgRouting’s download page. You need:

routing_dd.sql
routing_dd_wrappers.sql

Both are available through the project repository at Github. Get them and execute them in your pgRouting-enabled database. Now, you should be ready.

Calculating driving distances

To calculate driving distances, we need a query very similar to shortest_path():

CREATE OR REPLACE FUNCTION driving_distance(
sql text,
source_id integer,
distance float8,
directed boolean,
has_reverse_cost boolean)
RETURNS SETOF path_result

The only new value is “distance”. That’s the maximum distance/cost you want to be contained in the result set. “distance” has to be specified in the same units as the cost attribute (which is specified in the “sql” text parameter).

Note: In my opinion, the name “(driving) distance” is misleading. While you can use distance as a cost attribute, you’re not limited to distances. You can use any cost attribute you like, e.g. travel time, fuel consumption, co2 emissions, …

The actual query for a catchment area of 100 km around node # 2000 looks like this:

SELECT * FROM driving_distance('
      SELECT gid AS id,
          start_id::int4 AS source,
          end_id::int4 AS target,
          shape_leng::float8 AS cost
      FROM network',
      2000,
      100000,
      false,
      false)

Interpreting the result

These are the first lines of the result set:

vertex_id;edge_id;cost
294;7262;97400.433506144
297;7236;98012.620979231
335;1095;96849.456306244
347;7263;93617.693852324
364;7098;93573.849081386
366;2551;92702.443434779
378;7263;91994.328368081

The cost attribute contains the total cost of travel from the starting node to the vertex_id node.
We will only be using vertex_id and cost. The use of edge_id is a mystery to me.

Visualizing the result

The easiest way to visualize driving_distance() results is using RT Sql Layer plugin. We need to join the results of driving_distance() with the table containing node geometries:

SELECT *
   FROM node
   JOIN
   (SELECT * FROM driving_distance('
      SELECT gid AS id,
          start_id::int4 AS source,
          end_id::int4 AS target,
          shape_leng::float8 AS cost
      FROM network',
      2000,
      100000,
      false,
      false)) AS route
   ON
   node.id = route.vertex_id

If you color the nodes based on the cost attribute, it will look something like this:

result of pgRouting driving_distance() visualized in QGIS


A Beginner’s Guide to pgRouting

The aim of this post is to describe the steps necessary to calculate routes with pgRouting. In the end, we’ll visualize the results in QGIS.

This guide assumes that you have the following installed and running:

  • Postgres with PostGIS and pgAdmin
  • QGIS with PostGIS Manager and RT Sql Layer plugins

Installing pgRouting

pgRouting can be downloaded from www.pgrouting.org.

Building from source is covered by pgRouting documentation. If you’re using Windows, download the binaries and copy the .dlls into PostGIS’ lib folder, e.g. C:\Program Files (x86)\PostgreSQL\8.4\lib.

Start pgAdmin and create a new database based on your PostGIS template. (I called mine ‘routing_template’.) Open a Query dialog, load and execute the three .sql files located in your pgRouting download (routing_core.sql, routing_core_wrappers.sql, routing_topology.sql). Congratulations, you now have a pgRouting-enabled database.

Creating a routable road network

The following description is based on the free road network published by National Land Survey of Finland (NLS). All you get is one Shapefile containing line geometries, a road type attribute and further attributes unrelated to routing.

pgRouting requires each road entry to have a start and an end node id. We’ll create those now:

First step is to load roads.shp into PostGIS. This is easy using PostGIS Manager – Data – Load Data from Shapefile.

Next, we create start and end point geometries. I used a view:

CREATE OR REPLACE VIEW road_ext AS
   SELECT *, startpoint(the_geom), endpoint(the_geom)
   FROM road;

Now, we create a table containing all the unique network nodes (start and end points) and we’ll also give them an id:

CREATE TABLE node AS
   SELECT row_number() OVER (ORDER BY foo.p)::integer AS id,
          foo.p AS the_geom
   FROM (
      SELECT DISTINCT road_ext.startpoint AS p FROM road_ext
      UNION
      SELECT DISTINCT road_ext.endpoint AS p FROM road_ext
   ) foo
   GROUP BY foo.p;

Finally, we can combine our road_ext view and node table to create the routable network table:

CREATE TABLE network AS
   SELECT a.*, b.id as start_id, c.id as end_id
   FROM road_ext AS a
      JOIN node AS b ON a.startpoint = b.the_geom
      JOIN node AS c ON a.endpoint = c.the_geom

(This can take a while.)

I recommend adding a spatial index to the resulting table.

Calculating shortest routes

Let’s try pgRouting’s Shortest Path Dijkstra method. The following query returns the route from node #1 to node #5110:

SELECT * FROM shortest_path('
   SELECT gid AS id,
          start_id::int4 AS source,
          end_id::int4 AS target,
          shape_leng::float8 AS cost
   FROM network',
1,
5110,
false,
false)

Final step: Visualization

With RT Sql Layer plugin, we can visualize the results of a query. The results will be loaded as a new layer. The query has to contain both geometry and a unique id. Therefore, we’ll join the results of the previous query with the network table containing the necessary geometries.

SELECT *
   FROM network
   JOIN
   (SELECT * FROM shortest_path('
      SELECT gid AS id,
          start_id::int4 AS source,
          end_id::int4 AS target,
          shape_leng::float8 AS cost
      FROM network',
      1,
      5110,
      false,
      false)) AS route
   ON
   network.gid = route.edge_id

In my case, this is how the result looks like:

Route from node #1 to node #5110


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