Following a recent research about how to simplify a multipolygon layer while keeping topological relationships intact, here’s my take on that, using the PostGIS topological support.

### The data

French administrative subdivisions, called “départements”, will be used. Data can be downloaded here.

It is composed by **96** multipolygons for a total of **47036** vertices.

### Principle of simplification

- We convert a layer’s Geometries to TopoGeometries
- We simplify all edges of the built topology
- We convert the (now-simplified) TopoGeometries back to Geometries

### Steps

The following steps assume you loaded the shapefile into a table named “france_dept”.

-- Create a topology SELECT CreateTopology('france_dept_topo', find_srid('public', 'france_dept', 'geom')); -- Add a layer SELECT AddTopoGeometryColumn('france_dept_topo', 'public', 'france_dept', 'topogeom', 'MULTIPOLYGON'); -- Populate the layer and the topology UPDATE france_dept SET topogeom = toTopoGeom(geom, 'france_dept_topo', 1); -- 8.75 seconds -- Simplify all edges up to 10000 units SELECT SimplifyEdgeGeom('france_dept_topo', edge_id, 10000) FROM france_dept_topo.edge; -- 3.86 seconds -- Convert the TopoGeometries to Geometries for visualization ALTER TABLE france_dept ADD geomsimp GEOMETRY; UPDATE france_dept SET geomsimp = topogeom::geometry; -- 0.11 seconds

### The SimplifyEdgeGeom function

You may have noticed that the “SimplifyEdgeGeom” is not a core function. It is a function I wrote for the purpose of catching topological problems introduced by simplification.

The naive call would be:

SELECT ST_ChangeEdgeGeom('france_dept_topo', edge_id, ST_Simplify(geom, 10000)) FROM france_dept_topo.edge;

The problem with the above call is that any simplification introducing a topology error would be rejected by ST_ChangeEdgeGeom by throwing an exception and the exception would rollback the whole transaction leaving you with no edge changed. Possible topology errors introduced are: edges collapsing to points, intersecting self or other edges.

The SimplifyEdgeGeom function wraps the ST_ChangeEdgeGeom call into a subtransaction and handles exceptions by reducing the simplification factor until it succeeds. The version I used reduces simplification factor in half at each failure, dropping down to zero around 1e-8. You can roll your own with other heuristics or generalize this one to take parameters about stepping and limits.

Here’s the function:

CREATE OR REPLACE FUNCTION SimplifyEdgeGeom(atopo varchar, anedge int, maxtolerance float8) RETURNS float8 AS $$ DECLARE tol float8; sql varchar; BEGIN tol := maxtolerance; LOOP sql := 'SELECT topology.ST_ChangeEdgeGeom(' || quote_literal(atopo) || ', ' || anedge || ', ST_Simplify(geom, ' || tol || ')) FROM ' || quote_ident(atopo) || '.edge WHERE edge_id = ' || anedge; BEGIN RAISE DEBUG 'Running %', sql; EXECUTE sql; RETURN tol; EXCEPTION WHEN OTHERS THEN RAISE WARNING 'Simplification of edge % with tolerance % failed: %', anedge, tol, SQLERRM; tol := round( (tol/2.0) * 1e8 ) / 1e8; -- round to get to zero quicker IF tol = 0 THEN RAISE EXCEPTION '%', SQLERRM; END IF; END; END LOOP; END $$ LANGUAGE 'plpgsql' STABLE STRICT;

### Performance

The times shown near the “expensive” steps give you an indication of the performance you may expect. It’s about 13 seconds in total for the 3 steps outlined in the first paragraph.

A single run of the simplification step brought vertices down to **1369** (from **47036**).

Timings are take on this system:

POSTGIS=”2.0.1SVN r9637″ GEOS=”3.4.0dev-CAPI-1.8.0″ PROJ=”Rel. 4.8.0, 6 March 2012″ GDAL=”GDAL 1.9.0, released 2011/12/29″ LIBXML=”2.7.6″ LIBJSON=”UNKNOWN” TOPOLOGY RASTER

PostgreSQL 8.4.10 on x86_64-pc-linux-gnu, compiled by GCC gcc-4.4.real (Ubuntu 4.4.3-4ubuntu5) 4.4.3, 64-bit

CUSTOM OPTIONS:

shared_buffers = 128MB (default is 24MB)

temp_buffers = 32MB (default is 8MB)

work_mem = 8MB (default is 1MB)

maintenance_work_mem = 32MB (default is 16MB)

max_stack_depth = 4MB (default is 2MB)

checkpoint_segments = 24 (default is 3)

CPU: Intel(R) Core(TM)2 Duo CPU P9500 @ 2.53GHz (2 x 5054.34 bogomips)

RAM: 4GB

### Considerations

The procedure described in this post is also valid for *LINESTRING* and *MULTILINESTRING* layers, using the exactly same code.

You could reuse the topology to produce multiple resolution levels w/out incurring again in the construction cost (and with a reduced input complexity at each level).

The simplification step doesn’t use TopoGeometry objects at all so you could choose to perform topology construction and attribute assignment in a different way.

Running the *SimplifyEdgeGeom* function again might give you more simplification because edges which may have intersected to the simplified version of an edge may not be intersecting anymore after their own simplification. The function can be changed to behave differently on exception to improve performance or quality.

[…] Simplifying a map layer using PostGIS topology « Strk's Blog. Publicado: 2012/04/13 Arquivado em: geo, postgis […]

awesome post. Got round to installing postgis 2 this morning and was looking to try out generalising polygons using topology. This recipe really helped.

An update: this exercise exposed a bug in ST_ChangeEdgeGeom accepting a theoretically invalid move. I figured because the move back was correctly identified as invalid (non isomorphic).

See more here: http://trac.osgeo.org/postgis/ticket/1775

The fix will be released in 2.0.1

Hello,

GeoFla files are now available with this URL: http://professionnels.ign.fr/sites/default/files/GEOFLADept_FR_Corse_AV_L93.zip (EPSG code is 2154).

Regards,

Y.

When I run the first command, I get the following error:

`ERROR: function createtopology(unknown, integer) does not exist`

LINE 1: SELECT CreateTopology('usqctsmod_topo', find_srid('public', ...

^

HINT: No function matches the given name and argument types. You might need to add explicit type casts.

********** Error **********

`ERROR: function createtopology(unknown, integer) does not exist`

SQL state: 42883

Hint: No function matches the given name and argument types. You might need to add explicit type casts.

Character: 8

Make sure you enabled topology:

`select postgis_full_version();`

should contain a TOPOLOGY label when enabled.Also make sure your search_path contains the “topology” schema (topolog.CreateTopology would work if that’s the problem).

select postgis_full_version(); returns this:

“POSTGIS=”2.0.0 r9605″ GEOS=”3.3.4-CAPI-1.7.3″ PROJ=”Rel. 4.8.0, 6 March 2012″ GDAL=”GDAL 1.9.1, released 2012/05/15″ LIBXML=”2.7.8″ LIBJSON=”UNKNOWN” TOPOLOGY RASTER”

I’m unaware as to how to check the search_path in any database. ?

Thanks for your help.

quick update: I was able to create a topology by calling topology.CreateTopology()

Use:

`SHOW search_path;`

to get the current value and`SET search_path TO x,y,z`

for setting the value.I want to reduce edges and nodes. I run “select st_remedgemodface(‘topo’, edge_id)”, I got follow error:

ERROR: TopoGeom #number in layer 1 (#table.topogeom) cannot be represented dropping edge #edge_id

The message is telling you that by dropping that edge it will be impossible for one TopoGeometry object to retain the same shape.

You can see the shape of the TopoGeometry using:

`SELECT topogeom::geometry FROM #table WHERE id(topogeom) = #number`

I run :

SELECT st_astext(topogeom::geometry) FROM idns_link_0 WHERE id(topogeom) = #table.id

result is :

“MULTILINESTRING((14128213.2930175 4505878.66922969,14128214.0420175 4505877.92022969))”

I don’t understant this result.

I suggest subscribing to the postgis users mailing list for this kind of help

[…] saw how to get a topologically consistent simplified version of a full layer, but that method isn’t fast enough for on-demand usage. Also, we saw how to perform a fast […]

when trying to use my own data, I get the following error:

UPDATE rayons SET topogeom = toTopoGeom(geom, ‘france_dept_topo’, 1);

ERROR: lwpoly_from_lwlines: shell must be closed

CONTEXT: SQL statement “WITH ids as ( select row_number() over () as seq, edge from unnest(‘{-160,-104,45,-46,41,-44,43,-53,50,-49,47,-67,66,64,-57,55,-61,60,-84,70,-73,72,79,-76,74,-102,101,-87,85,-96,95,-112,98,-100,93,-92,90,-121,120,-125,124,-119,117,-128,113,-109,107,115,-132,-131,-115,116,-108,114,-127,129,-39,-158,159,-153,155,-137,-138,147,-141,144,-145,152,-148,149,-133,134}'::int[] ) u(edge) ), edges AS ( select CASE WHEN i.edge < 0 THEN ST_Reverse(e.geom) ELSE e.geom END as g FROM ids i left join france_dept_topo.edge_data e ON(e.edge_id = abs(i.edge)) ORDER BY seq) SELECT ST_MakePolygon(ST_MakeLine(g.g)) FROM edges g;"

PL/pgSQL function _st_addfacesplit(character varying,integer,integer,boolean) line 34 at EXECUTE statement

SQL statement "SELECT topology._ST_AddFaceSplit(atopology, -newedge.edge_id, newedge.left_face, false)"

PL/pgSQL function st_addedgemodface(character varying,integer,integer,geometry) line 513 at SQL statement

PL/pgSQL function topogeo_addlinestring(character varying,geometry,double precision) line 124 at assignment

SQL statement "SELECT array_cat(edges, array_agg(x)) FROM ( select topology.TopoGeo_addLinestring(atopology, rec.geom, tol) as x ) as foo"

PL/pgSQL function topogeo_addpolygon(character varying,geometry,double precision) line 24 at assignment

PL/pgSQL function totopogeom(geometry,character varying,integer,double precision) line 100 at FOR over SELECT rows

any ideas?

Please use the bug tracker for this: http://trac.osgeo.org/postgis

I ran into an issue with an exception being thrown using the vanilla code in the blog post. I found that it was resolved by changing the order of the lines that calculate tol and the if condition that throws an error if tol is 0. This forces the code to try tolerance 0 first, then thrown an error if that fails.

SQL/MM Spatial exception is the exception that gets thrown.

I changed the code to the following:

IF tol = 0 THEN

RAISE EXCEPTION ‘%’, SQLERRM;

END IF;

tol := round( (tol/2.0) * 1e8 ) / 1e8; — round to get to zero quicker

Needless to say simplifying with tolerance 0 is not supported.

I’m trying to run this but I get the following error

psql:topology.sql:34: ERROR: relation “topology” does not exist

Line 34 is

UPDATE my_table SET topogeom = topology.toTopoGeom(geom, ‘my_table_topo’, 1);

The other functions work by prepending “topology.” but this doesn’t seem to do the trick here.

Does the topology.topology table exist ? It should. Try \set VERBOSITY verbose

Super Post ! Merci

[…] simplifier un ensemble de polygones limitrophes (départements) […]

If you receive an error like the following:

ERROR: function createtopology(unknown, integer) does not exist

you probably haven’t created the topology extension. You’ll have to run:

create extension postgis_topology;

(I also had to restart my psql prompt for the functions to register)