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<!-- Converted by db4-upgrade version 1.1 -->
<chapter xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://docbook.org/ns/docbook" version="5.0" xml:id="using_postgis_query">
<title>Spatial Queries</title>
<para>The <emphasis>raison d'etre</emphasis> of spatial databases
is to perform queries inside the database which would
ordinarily require desktop GIS functionality. Using PostGIS effectively
requires knowing what spatial functions are available,
how to use them in queries, and ensuring that
appropriate indexes are in place to provide good performance.
</para>
<section xml:id="eval_spatial_rel">
<title>Determining Spatial Relationships</title>
<para>Spatial relationships indicate how two geometries interact with one another.
They are a fundamental capability for querying geometry.
</para>
<section xml:id="DE-9IM">
<title>Dimensionally Extended 9-Intersection Model</title>
<para>According to the <link xlink:href="http://www.opengeospatial.org/standards/sfs">OpenGIS Simple
Features Implementation Specification for SQL</link>, "the basic
approach to comparing two geometries is to make pair-wise tests of
the intersections between the Interiors, Boundaries and Exteriors of
the two geometries and to classify the relationship between the two
geometries based on the entries in the resulting 'intersection'
matrix."</para>
<para>In the theory of point-set topology,
the points in a geometry embedded in 2-dimensional space are categorized into three sets:
</para>
<glosslist>
<glossentry>
<glossterm>Boundary</glossterm>
<glossdef>
<para>The boundary of a geometry is the set of geometries of
the next lower dimension. For <varname>POINT</varname>s, which
have a dimension of 0, the boundary is the empty set. The
boundary of a <varname>LINESTRING</varname> is the two
endpoints. For <varname>POLYGON</varname>s, the boundary is
the linework of the exterior and interior
rings.</para>
</glossdef>
</glossentry>
<glossentry>
<glossterm>Interior</glossterm>
<glossdef>
<para>The interior of a geometry are those points of a
geometry that are not in the boundary. For
<varname>POINT</varname>s, the interior is the
point itself. The interior of a
<varname>LINESTRING</varname> is the set of points
between the endpoints. For <varname>POLYGON</varname>s, the
interior is the areal surface inside the polygon.</para>
</glossdef>
</glossentry>
<glossentry>
<glossterm>Exterior</glossterm>
<glossdef>
<para>The exterior of a geometry is the rest of the space
in which the geometry is embedded;
in other words, all points not in the interior or on the boundary of the geometry.
It is a 2-dimensional non-closed surface.
</para>
</glossdef>
</glossentry>
</glosslist>
<para>The <link xlink:href="http://en.wikipedia.org/wiki/DE-9IM">Dimensionally Extended 9-Intersection Model</link>
(DE-9IM) describes the spatial relationship between two geometries
by specifying the dimensions of the 9 intersections between the above sets for each geometry.
The intersection dimensions can be formally represented
in a 3x3 <emphasis role="bold">intersection matrix</emphasis>.
</para>
<para>For a geometry <emphasis>g</emphasis>
the <emphasis>Interior</emphasis>, <emphasis>Boundary</emphasis>, and <emphasis>Exterior</emphasis>
are denoted using the notation
<emphasis>I(g)</emphasis>, <emphasis>B(g)</emphasis>, and
<emphasis>E(g)</emphasis>.
Also, <emphasis>dim(s)</emphasis> denotes the dimension of
a set <emphasis>s</emphasis> with the domain of
<literal>{0,1,2,F}</literal>:
</para>
<itemizedlist spacing="compact">
<listitem>
<para><literal>0</literal> => point</para>
</listitem>
<listitem>
<para><literal>1</literal> => line</para>
</listitem>
<listitem>
<para><literal>2</literal> => area</para>
</listitem>
<listitem>
<para><literal>F</literal> => empty set</para>
</listitem>
</itemizedlist>
<para>
Using this notation, the intersection matrix
for two geometries <emphasis>a</emphasis> and <emphasis>b</emphasis> is:</para>
<informaltable tabstyle="styledtable">
<tgroup align="center" cols="4">
<thead>
<row>
<entry/>
<entry><emphasis role="bold">Interior</emphasis></entry>
<entry><emphasis role="bold">Boundary</emphasis></entry>
<entry><emphasis role="bold">Exterior</emphasis></entry>
</row>
</thead>
<tbody>
<row>
<entry><emphasis role="bold">Interior</emphasis></entry>
<entry><emphasis>dim( I(a) ∩ I(b) )</emphasis></entry>
<entry><emphasis>dim( I(a) ∩ B(b) )</emphasis></entry>
<entry><emphasis>dim( I(a) ∩ E(b) )</emphasis></entry>
</row>
<row>
<entry><emphasis role="bold">Boundary</emphasis></entry>
<entry><emphasis>dim( B(a) ∩ I(b) )</emphasis></entry>
<entry><emphasis>dim( B(a) ∩ B(b) )</emphasis></entry>
<entry><emphasis>dim( B(a) ∩ E(b) )</emphasis></entry>
</row>
<row>
<entry><emphasis role="bold">Exterior</emphasis></entry>
<entry><emphasis>dim( E(a) ∩ I(b) )</emphasis></entry>
<entry><emphasis>dim( E(a) ∩ B(b) )</emphasis></entry>
<entry><emphasis>dim( E(a) ∩ E(b) )</emphasis></entry>
</row>
</tbody>
</tgroup>
</informaltable>
<para>Visually, for two overlapping polygonal geometries, this looks like:</para>
<informaltable frame="none">
<tgroup cols="2">
<colspec colwidth="80pt"/>
<tbody>
<row>
<entry/>
<entry align="center"><para><informalfigure>
<mediaobject><imageobject><imagedata align="center" fileref="images/de9im04.png" valign="middle"/></imageobject></mediaobject>
</informalfigure></para></entry>
</row>
<row>
<entry align="center" valign="middle"><para><informalfigure>
<mediaobject><imageobject><imagedata align="center" fileref="images/de9im03.png" valign="middle"/></imageobject></mediaobject>
</informalfigure></para></entry>
<entrytbl cols="4">
<thead valign="middle">
<row>
<entry/>
<entry><emphasis role="bold">Interior</emphasis></entry>
<entry><emphasis role="bold">Boundary</emphasis></entry>
<entry><emphasis role="bold">Exterior</emphasis></entry>
</row>
</thead>
<tbody valign="middle">
<row>
<entry spanname="de9im_a">
<emphasis role="bold">Interior</emphasis>
</entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im05.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( I(a) ∩ I(b) ) =
</emphasis><emphasis role="bold">2</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im06.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( I(a) ∩ B(b) =
</emphasis><emphasis role="bold">1</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im07.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( I(a) ∩ E(b) ) =
</emphasis><emphasis role="bold">2</emphasis></para></entry>
</row>
<row>
<entry><emphasis role="bold">Boundary</emphasis></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im08.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( B(a) ∩ I(b) ) =
</emphasis><emphasis role="bold">1</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im09.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( B(a) ∩ B(b) ) =
</emphasis><emphasis role="bold">0</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im10.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( B(a) ∩ E(b) ) =
</emphasis><emphasis role="bold">1</emphasis></para></entry>
</row>
<row>
<entry><emphasis role="bold">Exterior</emphasis></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im11.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( E(a) ∩ I(b) ) =
</emphasis><emphasis role="bold">2</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im12.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( E(a) ∩ B(b) ) =
</emphasis><emphasis role="bold">1</emphasis></para></entry>
<entry><para><informalfigure>
<mediaobject><imageobject><imagedata fileref="images/de9im13.png"/></imageobject></mediaobject>
</informalfigure></para><para><emphasis>dim( E(a) ∩ E(b) =
</emphasis><emphasis role="bold">2</emphasis></para></entry>
</row>
</tbody>
</entrytbl>
</row>
</tbody>
</tgroup>
</informaltable>
<para>Reading from left to right and top to bottom, the intersection matrix is
represented as the text string '<emphasis role="bold">212101212</emphasis>'.</para>
<para>For more information, refer to:</para>
<itemizedlist spacing="compact">
<listitem>
<para><link xlink:href="http://www.opengeospatial.org/standards/sfs">OpenGIS Simple
Features Implementation Specification for SQL</link> (version 1.1, section 2.1.13.2)</para>
</listitem>
<listitem>
<para><link xlink:href="https://en.wikipedia.org/wiki/DE-9IM">Wikipedia: Dimensionally
Extended Nine-Intersection Model (DE-9IM)</link></para>
</listitem>
<listitem>
<para><link xlink:href="http://docs.geotools.org/latest/userguide/library/jts/dim9.html">GeoTools: Point Set Theory and the DE-9IM Matrix</link></para>
</listitem>
</itemizedlist>
</section>
<section xml:id="named-spatial-rel">
<title>Named Spatial Relationships</title>
<para>To make it easy to determine common spatial relationships,
the OGC SFS defines a set of <emphasis>named spatial relationship predicates</emphasis>.
PostGIS provides these as the functions
<xref linkend="ST_Contains"/>,
<xref linkend="ST_Crosses"/>, <xref linkend="ST_Disjoint"/>, <xref linkend="ST_Equals"/>,
<xref linkend="ST_Intersects"/>, <xref linkend="ST_Overlaps"/>,
<xref linkend="ST_Touches"/>, <xref linkend="ST_Within"/>.
It also defines the non-standard relationship predicates
<xref linkend="ST_Covers"/>, <xref linkend="ST_CoveredBy"/>,
and <xref linkend="ST_ContainsProperly"/>.
</para>
<para>Spatial predicates are usually used as conditions in SQL <code>WHERE</code> or <code>JOIN</code> clauses.
The named spatial predicates automatically use a spatial index if one is available,
so there is no need to use the bounding box operator <code>&&</code> as well.
For example:
</para>
<programlisting>
SELECT city.name, state.name, city.geom
FROM city JOIN state ON ST_Intersects(city.geom, state.geom);
</programlisting>
<para>For more details and illustrations, see the
<link xlink:href="https://postgis.net/workshops/postgis-intro/spatial_relationships.html">PostGIS Workshop.</link></para>
</section>
<section xml:id="general-spatial-rel">
<title>General Spatial Relationships</title>
<para>In some cases the named spatial relationships
are insufficient to provide a desired spatial filter condition.
</para>
<informaltable frame="none">
<tgroup cols="1">
<tbody>
<row>
<entry><para><informalfigure floatstyle="right">
<mediaobject><imageobject><imagedata align="left" fileref="images/de9im01.png"/></imageobject></mediaobject>
</informalfigure></para><para>For example, consider a linear
dataset representing a road network. It may be required
to identify all road segments that cross
each other, not at a point, but in a line (perhaps to validate some business rule).
In this case <xref linkend="ST_Crosses"/> does not
provide the necessary spatial filter, since for
linear features it returns <varname>true</varname> only where they cross at a point.
</para>
<para>A two-step solution
would be to first compute the actual intersection
(<xref linkend="ST_Intersection"/>) of pairs of road lines that spatially
intersect (<xref linkend="ST_Intersects"/>), and then check if the intersection's
<xref linkend="ST_GeometryType"/> is '<varname>LINESTRING</varname>' (properly
dealing with cases that return
<varname>GEOMETRYCOLLECTION</varname>s of
<varname>[MULTI]POINT</varname>s,
<varname>[MULTI]LINESTRING</varname>s, etc.).</para>
<para>Clearly, a simpler and faster solution is desirable.</para></entry>
</row>
</tbody>
</tgroup>
</informaltable>
<informaltable frame="none">
<tgroup cols="1">
<tbody>
<row>
<entry><para> <informalfigure floatstyle="right">
<mediaobject><imageobject><imagedata align="right" fileref="images/de9im02.png"/></imageobject></mediaobject>
</informalfigure></para> <para>A second
example is locating
wharves that intersect a lake's boundary on a line and
where one end of the wharf is up on shore. In other
words, where a wharf is within but not completely contained by a
lake, intersects the boundary of a lake on a line, and where
exactly one of the wharf's endpoints is within or on the
boundary of the lake. It is possible to use a
combination of spatial predicates to find the required
features:</para> <itemizedlist>
<listitem>
<para><xref linkend="ST_Contains"/>(lake, wharf) = TRUE</para>
</listitem>
<listitem>
<para><xref linkend="ST_ContainsProperly"/>(lake, wharf) = FALSE</para>
</listitem>
<listitem>
<para><xref linkend="ST_GeometryType"/>(<xref linkend="ST_Intersection"/>(wharf, lake)) =
'LINESTRING'</para>
</listitem>
<listitem>
<para><xref linkend="ST_NumGeometries"/>(<xref linkend="ST_Multi"/>(<xref linkend="ST_Intersection"/>(<xref linkend="ST_Boundary"/>(wharf),
<xref linkend="ST_Boundary"/>(lake)))) = 1</para>
<para>... but needless to say, this is quite complicated.</para>
</listitem>
</itemizedlist></entry>
</row>
</tbody>
</tgroup>
</informaltable>
<para>These requirements can be met by computing the full DE-9IM intersection matrix.
PostGIS provides the <xref linkend="ST_Relate"/> function
to do this:
</para>
<programlisting>
SELECT ST_Relate( 'LINESTRING (1 1, 5 5)',
'POLYGON ((3 3, 3 7, 7 7, 7 3, 3 3))' );
st_relate
-----------
1010F0212
</programlisting>
<para>To test a particular spatial relationship,
an <emphasis role="bold">intersection matrix pattern</emphasis> is used.
This is the matrix representation augmented with the additional symbols
<literal>{T,*}</literal>:
</para>
<itemizedlist spacing="compact">
<listitem>
<para><literal>T</literal> =>
intersection dimension is non-empty; i.e. is in <literal>{0,1,2}</literal></para>
</listitem>
<listitem>
<para><literal>*</literal> => don't care</para>
</listitem>
</itemizedlist>
<para>Using intersection matrix patterns,
specific spatial relationships can be evaluated in a more succinct way.
The <xref linkend="ST_Relate"/> and the <xref linkend="ST_RelateMatch"/>
functions can be used to test intersection matrix patterns.
For the first example above, the intersection matrix pattern specifying
two lines intersecting in a line is
'<emphasis role="bold">1*1***1**</emphasis>':</para>
<programlisting>-- Find road segments that intersect in a line
SELECT a.id
FROM roads a, roads b
WHERE a.id != b.id
AND a.geom && b.geom
AND ST_Relate(a.geom, b.geom, '1*1***1**');</programlisting>
<para>For the second example, the intersection matrix pattern
specifying a line partly inside and partly outside a polygon is
'<emphasis role="bold">102101FF2</emphasis>':</para>
<programlisting><![CDATA[
-- Find wharves partly on a lake's shoreline
SELECT a.lake_id, b.wharf_id
FROM lakes a, wharfs b
WHERE a.geom && b.geom
AND ST_Relate(a.geom, b.geom, '102101FF2');
]]></programlisting>
</section>
</section>
<section xml:id="using-query-indexes">
<title>Using Spatial Indexes</title>
<para>When constructing queries using spatial conditions,
for best performance it is important to
ensure that a spatial index is used, if one exists (see <xref linkend="build-indexes"/>).
To do this, a spatial operator or index-aware function must be used
in a <code>WHERE</code> or <code>ON</code> clause of the query.
</para>
<para>Spatial operators include
the bounding box operators
(of which the most commonly used is <xref linkend="geometry_overlaps"/>;
see <xref linkend="operators-bbox"/> for the full list)
and the distance operators used in nearest-neighbor queries
(the most common being <xref linkend="geometry_distance_knn"/>;
see <xref linkend="operators-distance"/> for the full list.)
</para>
<para>Index-aware functions automatically add a bounding box operator
to the spatial condition.
Index-aware functions include the named spatial relationship predicates
<xref linkend="ST_Contains"/>,
<xref linkend="ST_ContainsProperly"/>,
<xref linkend="ST_CoveredBy"/>,
<xref linkend="ST_Covers"/>,
<xref linkend="ST_Crosses"/>,
<xref linkend="ST_Intersects"/>,
<xref linkend="ST_Overlaps"/>,
<xref linkend="ST_Touches"/>,
<xref linkend="ST_Within"/>,
<xref linkend="ST_Within"/>,
and <xref linkend="ST_3DIntersects"/>,
and the distance predicates
<xref linkend="ST_DWithin"/>,
<xref linkend="ST_DFullyWithin"/>,
<xref linkend="ST_3DDFullyWithin"/>,
and <xref linkend="ST_3DDWithin"/>
.)
</para>
<para>Functions such as
<xref linkend="ST_Distance"/> do <emphasis>not</emphasis> use indexes to optimize their
operation. For example, the following query would be quite slow on a
large table:</para>
<programlisting><![CDATA[
SELECT geom
FROM geom_table
WHERE ST_Distance( geom, 'SRID=312;POINT(100000 200000)' ) < 100
]]></programlisting>
<para>This query selects all the geometries in <code>geom_table</code> which are
within 100 units of the point (100000, 200000). It will be slow because
it is calculating the distance between each point in the table and the
specified point, ie. one <varname>ST_Distance()</varname> calculation
is computed for <emphasis role="bold">every</emphasis> row in the table.
</para>
<para>
The number of rows processed can be reduced substantially by using the
index-aware function <xref linkend="ST_DWithin"/>:</para>
<programlisting>SELECT geom
FROM geom_table
WHERE ST_DWithin( geom, 'SRID=312;POINT(100000 200000)', 100 )
</programlisting>
<para>This query selects the same geometries, but it does it in a more
efficient way.
This is enabled by <varname>ST_DWithin()</varname> using the
<varname>&&</varname> operator internally on an expanded bounding box
of the query geometry.
If there is a spatial index on <code>geom</code>, the query
planner will recognize that it can use the index to reduce the number of
rows scanned before calculating the distance.
The spatial index allows retrieving only records with geometries
whose bounding boxes overlap the expanded extent
and hence which <emphasis>might</emphasis> be within the required distance.
The actual distance is then computed to confirm whether to include the record in the result set.
</para>
<para>For more information and examples see the
<link xlink:href="https://postgis.net/workshops/postgis-intro/indexing.html">PostGIS Workshop</link>.
</para>
</section>
<section xml:id="examples_spatial_sql">
<title>Examples of Spatial SQL</title>
<para>The examples in this section make use of a table
of linear roads, and a table of polygonal municipality boundaries. The
definition of the <varname>bc_roads</varname> table is:</para>
<programlisting>Column | Type | Description
----------+-------------------+-------------------
gid | integer | Unique ID
name | character varying | Road Name
geom | geometry | Location Geometry (Linestring)</programlisting>
<para>The definition of the <varname>bc_municipality</varname>
table is:</para>
<programlisting>Column | Type | Description
---------+-------------------+-------------------
gid | integer | Unique ID
code | integer | Unique ID
name | character varying | City / Town Name
geom | geometry | Location Geometry (Polygon)</programlisting>
<qandaset>
<qandaentry xml:id="qa_total_length_roads">
<question>
<para>What is the total length of all roads, expressed in
kilometers?</para>
</question>
<answer>
<para>You can answer this question with a very simple piece of
SQL:</para>
<programlisting>SELECT sum(ST_Length(geom))/1000 AS km_roads FROM bc_roads;
km_roads
------------------
70842.1243039643
</programlisting>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>How large is the city of Prince George, in hectares?</para>
</question>
<answer>
<para>This query combines an attribute condition (on the
municipality name) with a spatial calculation (of the
polygon area):</para>
<programlisting>SELECT
ST_Area(geom)/10000 AS hectares
FROM bc_municipality
WHERE name = 'PRINCE GEORGE';
hectares
------------------
32657.9103824927
</programlisting>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>What is the largest municipality in the province, by
area?</para>
</question>
<answer>
<para>This query uses a spatial measurement as an ordering value.
There are several ways of approaching this problem, but
the most efficient is below:</para>
<programlisting>SELECT
name,
ST_Area(geom)/10000 AS hectares
FROM bc_municipality
ORDER BY hectares DESC
LIMIT 1;
name | hectares
---------------+-----------------
TUMBLER RIDGE | 155020.02556131
</programlisting>
<para>Note that in order to answer this query we have to calculate
the area of every polygon. If we were doing this a lot it would
make sense to add an area column to the table that could
be indexed for performance. By ordering the results in a
descending direction, and them using the PostgreSQL "LIMIT"
command we can easily select just the largest value without using an
aggregate function like MAX().</para>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>What is the length of roads fully contained within each
municipality?</para>
</question>
<answer>
<para>This is an example of a "spatial join",
which brings together data from two tables (with a join) using a
spatial interaction ("contained") as the join condition
(rather than the usual relational approach of joining on a common
key):</para>
<programlisting>SELECT
m.name,
sum(ST_Length(r.geom))/1000 as roads_km
FROM bc_roads AS r
JOIN bc_municipality AS m
ON ST_Contains(m.geom, r.geom)
GROUP BY m.name
ORDER BY roads_km;
name | roads_km
----------------------------+------------------
SURREY | 1539.47553551242
VANCOUVER | 1450.33093486576
LANGLEY DISTRICT | 833.793392535662
BURNABY | 773.769091404338
PRINCE GEORGE | 694.37554369147
...</programlisting>
<para>This query takes a while, because every road in the table is
summarized into the final result (about 250K roads for the
example table). For smaller datasets (several thousand
records on several hundred) the response can be very fast.</para>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>Create a new table with all the roads within the city of
Prince George.</para>
</question>
<answer>
<para>This is an example of an "overlay", which takes in two
tables and outputs a new table that consists of spatially clipped
or cut resultants. Unlike the "spatial join" demonstrated above,
this query creates new geometries. An overlay is like a
turbo-charged spatial join, and is useful for more exact analysis
work:</para>
<programlisting>CREATE TABLE pg_roads as
SELECT
ST_Intersection(r.geom, m.geom) AS intersection_geom,
ST_Length(r.geom) AS rd_orig_length,
r.*
FROM bc_roads AS r
JOIN bc_municipality AS m
ON ST_Intersects(r.geom, m.geom)
WHERE
m.name = 'PRINCE GEORGE';
</programlisting>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>What is the length in kilometers of "Douglas St" in
Victoria?</para>
</question>
<answer>
<programlisting>SELECT
sum(ST_Length(r.geom))/1000 AS kilometers
FROM bc_roads r
JOIN bc_municipality m
ON ST_Intersects(m.geom, r.geom
WHERE
r.name = 'Douglas St'
AND m.name = 'VICTORIA';
kilometers
------------------
4.89151904172838
</programlisting>
</answer>
</qandaentry>
<qandaentry>
<question>
<para>What is the largest municipality polygon that has a
hole?</para>
</question>
<answer>
<programlisting><![CDATA[
SELECT gid, name, ST_Area(geom) AS area
FROM bc_municipality
WHERE ST_NRings(geom) > 1
ORDER BY area DESC LIMIT 1;
gid | name | area
-----+--------------+------------------
12 | SPALLUMCHEEN | 257374619.430216
]]></programlisting>
</answer>
</qandaentry>
</qandaset>
</section>
</chapter>
|
