= An example showing how to simplify a multipolygon layer, keeping topology between objects =

== What we want ==

|| Simplifying this layer: || into this: ||
|| [[Image(SPT_dept_ori.png)]] ||  [[Image(SPT_dept_sim.png)]] ||

== The data ==

French administrative subdivisions, called "départements", will be used. Data can be downloaded here: [http://http://professionnels.ign.fr/DISPLAY/000/528/175/5281750/GEOFLADept_FR_Corse_AV_L93.zip]

Data projection is Lambert-93, EPSG:2154

== Loading the data ==

{{{
#!sh
shp2pgsql -IiD -g geom -s 2154 DEPARTEMENT.SHP departement | psql
}}}

== Principle of simplification ==

Based on the technique described here [[]]:
 * we extract linestrings out of polygons, 
 * then union and simplify them
 * st_polygonize() is used to rebuild surfaces from linestrings. 
 * Finally, attributes from the initial layer are associated with simplified polygons.

== Steps ==

''Steps are divided into individual queries for the sake of clarity. One big query summarize them at the end of this page''

1. First extract the input multipolygons into polygons, keeping their departement code. This will allow us to associate attributes to each part of multipolygons at the end of the process.

{{{
#!sql
create table poly as (
    select gid, code_dept, (st_dump(geom)).* 
    from departement
);
}}} 

2. extract rings out of polygons

{{{
#!sql
create table rings as (
    select st_exteriorRing((st_dumpRings(geom)).geom) as g 
    from poly
);
}}}

3. Simplify the rings. At this step, we choose the simplification ratio we want (some trials can be made by calling st_simplifyPreserveTopology on departement table).
Here, no points further than 10km:

{{{
#!sql
create table simplerings as (
    select st_simplifyPreserveTopology(st_linemerge(st_union(g)), 10000) as g 
    from rings
);
}}}

4. extract lines as individual objects, in order to rebuild polygons from these simplified lines

{{{
#!sql
create table simplelines as (
    select (st_dump(g)).geom as g 
    from simplerings
);
}}}

5.rebuild the polygons, first by polygonizing the lines, with a distinct clause to eliminate overlaping segments that may prevent polygon to be created, then dump the collection of polygons into individual parts, in order to rebuild our layer. 
{{{
#!sql
create table simplepolys as ( 
    select (st_dump(st_polygonize(distinct g))).geom as g
    from simplelines
);
}}}

6. Add an id column to help us identify objects and a spatial index

{{{
#!sql
alter table simplepolys  add column gid serial primary key;
create index simplepolys_geom_gist on simplepolys  using gist(g);
}}}

7. attribute association between input layer and simplified polygons: First method to retrieve attribute is based on containment of a point of the surface of simplified polygons.

{{{
#!sql
create table simpledep as (
    select code_dept, g
    from departement d, simplepolys s
    where st_contains(d.geom, st_pointOnSurface(s.g))
);
}}}

It does not work: code_dept=92 is a curved polygon and fails with st_contains() test:

 [[Image(SPT_bad_attributes.png)]] 

8. Second method is based on percentage of overlaping area comparison.
{{{
#!sql
create table simpledep as (
	select distinct on (d.code_dept) d.code_dept, s.g as geom
	from departement d, simplepolys s
	where st_intersects(d.geom, s.g)
	order by d.code_dept, st_area(st_intersection(s.g, d.geom))/st_area(s.g) desc
);
}}}

 It gives better results in our testcase:

 [[Image(SPT_good_attributes.png)]] 


9. rebuild departements by grouping them by code_dept (other attributes could be re-associated here): 

{{{
#!sql
create table simple_departement as (
	select code_dept, st_collect(geom) as geom
	from simpledep
	group by code_dept
);
}}}

== Result ==

Layer now looks like this:

[[Image(SPT_simple_dept.png)]] 

Small island where collapsed during process:

[[Image(SPT_islands_removed.png)]] 

== One big query ==

{{{
#!sql
with poly as (
	select gid, code_dept, (st_dump(geom)).* 
	from departement
) select distinct on (d.code_dept) d.code_dept, qux.geom 
 from ( 
	select (st_dump(st_polygonize(distinct baz.geom))).geom as geom
	from (
		select (st_dump(geom)).geom as geom
		from (
			select st_simplifyPreserveTopology(st_linemerge(st_union(geom)), 10000) as geom
			from (
				select st_exteriorRing((st_dumpRings(geom)).geom) as geom
				from poly
			) as foo
		) as bar
	) as baz
) as qux,
poly d
where st_intersects(d.geom, qux.geom)
order by d.code_dept, st_area(st_intersection(qux.geom, d.geom))/st_area(qux.geom) desc;
}}}

Nicolas Ribot.