[postgis-tickets] [SCM] PostGIS branch master updated. 3.1.0alpha3-37-g8409c6b
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- Log -----------------------------------------------------------------
commit 8409c6b71527a0b692ea3ccb479719c5a9bb858c
Author: Martin Davis <mtnclimb at gmail.com>
Date: Mon Dec 7 16:40:50 2020 -0800
Improve doc for DE-9IM and relate
diff --git a/doc/reference_relationship.xml b/doc/reference_relationship.xml
index c75bc0d..fff8479 100644
--- a/doc/reference_relationship.xml
+++ b/doc/reference_relationship.xml
@@ -1369,7 +1369,7 @@ FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 0.5)'), 3) As a,
<funcdef>text <function>ST_Relate</function></funcdef>
<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
<paramdef><type>geometry </type> <parameter>geomB</parameter></paramdef>
- <paramdef><type>integer </type> <parameter>BoundaryNodeRule</parameter></paramdef>
+ <paramdef><type>integer </type> <parameter>boundaryNodeRule</parameter></paramdef>
</funcprototype>
</funcsynopsis>
</refsynopsisdiv>
@@ -1377,80 +1377,134 @@ FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 0.5)'), 3) As a,
<refsection>
<title>Description</title>
- <para>Variant 1: Tests if two geometries are spatially related
- according to the given <varname>intersectionMatrixPattern</varname>, by testing for intersections between the
- Interior, Boundary and Exterior of the two geometries as specified
- by the values in the <ulink url="http://en.wikipedia.org/wiki/DE-9IM">DE-9IM matrix pattern</ulink>.</para>
-
- <para>This is useful for testing multiple conditions of intersection, crosses, etc in one step.
- It also allows testing spatial relationships which do not have a named pattern
- (for example, "interior-intersects" which has the pattern <code>T********</code>).
+ <para>
+ These functions allow testing and evaluating the spatial (topological) relationship between two geometries,
+ as defined by the <ulink url="http://en.wikipedia.org/wiki/DE-9IM">Dimensionally Extended 9-Intersection Model</ulink> (DE-9IM).
+ </para>
+ <para>
+ The DE-9IM is specified as a 9-element matrix indicating the dimension of the intersections between the
+ Interior, Boundary and Exterior of two geometries.
+ It is represented by a 9-character text string using the symbols 'F', '0', '1', '2'
+ (e.g. <code>'FF1FF0102'</code>).
+ </para>
+ <para>
+ A specific kind of spatial relationships is evaluated by comparing the intersection
+ matrix to an <emphasis>intersection matrix pattern</emphasis>.
+ A pattern can include the additional symbols 'T' and '*'.
+ Common spatial relationships are provided by the named functions
+ <xref linkend="ST_Contains" />, <xref linkend="ST_ContainsProperly" />,
+ <xref linkend="ST_Covers" />, <xref linkend="ST_CoveredBy" />,
+ <xref linkend="ST_Crosses" />, <xref linkend="ST_Disjoint" />, <xref linkend="ST_Equals" />,
+ <xref linkend="ST_Intersects" />, <xref linkend="ST_Overlaps" />, <xref linkend="ST_Touches" />,
+ and <xref linkend="ST_Within" />.
+ Using an explicit pattern allows testing multiple conditions of intersects, crosses, etc in one step.
+ It also allows testing spatial relationships which do not have a named spatial relationship function.
+ For example, the relationship "Interior-Intersects" has the DE-9IM pattern <code>T********</code>,
+ which is not evaluated by any named predicate.
+ </para>
+ <para>
+ For more information refer to <xref linkend="DE-9IM" />.
</para>
- <note><para>This is the "allowable" version that returns a
- boolean, not an integer. This is defined in OGC spec</para></note>
+ <para><emphasis role="bold">Variant 1:</emphasis> Tests if two geometries are spatially related
+ according to the given <varname>intersectionMatrixPattern</varname>.
+ </para>
- <note><para>This does NOT automatically include an index call.
+ <note><para>Unlike most of the named spatial relationship predicates,
+ this does NOT automatically include an index call.
The reason is that some relationships are true for geometries
- whose extents do NOT intersect (e.g. Disjoint). If you are
+ which do NOT intersect (e.g. Disjoint). If you are
using a relationship pattern that requires intersection, then include the &&
- index call.</para></note>
-
- <para>Variant 2: Returns the <xref linkend="DE-9IM" /> matrix string for the
- relationship between the two inputs</para>
-
- <para>Variant 3: same as variant 2, but allows specifying a boundary node rule (1:OGC/MOD2, 2:Endpoint, 3:MultivalentEndpoint, 4:MonovalentEndpoint)</para>
+ index call.
+ </para></note>
+
+ <note><para>It is better to use a named relationship function if available,
+ since they automatically use a spatial index where one exists.
+ Also, they may implement performance optimizations which are not available
+ with full relate evalation.
+ </para></note>
+
+ <para><emphasis role="bold">Variant 2:</emphasis> Returns the DE-9IM matrix string for the
+ spatial relationship between the two input geometries.
+ The matrix string can be tested for matching a DE-9IM pattern using <xref linkend="ST_RelateMatch" />.
+ </para>
- <important>
- <para>Enhanced: 3.0.0 enabled support for <varname>GEOMETRYCOLLECTION</varname></para>
- </important>
+ <para><emphasis role="bold">Variant 3:</emphasis> Like variant 2,
+ but allows specifying a <emphasis role="bold">Boundary Node Rule</emphasis>.
+ A boundary node rule allows finer control over whether geometry boundary points are
+ considered to lie in the DE-9IM Interior or Boundary.
+ The <varname>boundaryNodeRule</varname> code is:
+ 1: OGC/MOD2, 2: Endpoint, 3: MultivalentEndpoint, 4: MonovalentEndpoint. </para>
- <para>not in OGC spec, but implied. see s2.1.13.2</para>
+ <para>This function is not in the OGC spec, but is implied. see s2.1.13.2</para>
<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3</para>
<para>&sqlmm_compliant; SQL-MM 3: 5.1.25</para>
<para>Performed by the GEOS module</para>
<para>Enhanced: 2.0.0 - added support for specifying boundary node rule.</para>
+ <important>
+ <para>Enhanced: 3.0.0 enabled support for <varname>GEOMETRYCOLLECTION</varname></para>
+ </important>
+
</refsection>
<refsection>
<title>Examples</title>
+
+ <para>Using the boolean-valued function to test spatial relationships.</para>
<programlisting>
---Find all compounds that intersect and not touch a poly (interior intersects)
-SELECT l.* , b.name As poly_name
- FROM polys As b
-INNER JOIN compounds As l
-ON (p.the_geom && b.the_geom
-AND ST_Relate(l.the_geom, b.the_geom,'T********'));
-
-SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2));
+SELECT ST_Relate('POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '0FFFFF212');
st_relate
-----------
-0FFFFF212
+t
-SELECT ST_Relate(ST_GeometryFromText('LINESTRING(1 2, 3 4)'), ST_GeometryFromText('LINESTRING(5 6, 7 8)'));
+SELECT ST_Relate(POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '*FF*FF212');
st_relate
-----------
-FF1FF0102
+t
+</programlisting>
+ <para>Testing a custom spatial relationship pattern as a query condition,
+ with <code>&&</code> to enable using a spatial index.</para>
+ <programlisting>
+-- Find compounds that properly intersect (not just touch) a poly (Interior Intersects)
-SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2), '0FFFFF212');
+SELECT c.* , p.name As poly_name
+ FROM polys AS p
+ INNER JOIN compounds As c
+ ON c.geom && p.geom
+ AND ST_Relate(p.geom, c.geom,'T********');
+</programlisting>
+
+ <para>Computing the intersection matrix for spatial relationships.</para>
+ <programlisting>
+SELECT ST_Relate( 'POINT(1 2)',
+ ST_Buffer( 'POINT(1 2)', 2));
st_relate
-----------
-t
+0FFFFF212
-SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2), '*FF*FF212');
+SELECT ST_Relate( 'LINESTRING(1 2, 3 4)',
+ 'LINESTRING(5 6, 7 8)' );
st_relate
-----------
-t
- </programlisting>
+FF1FF0102
+</programlisting>
+
</refsection>
<!-- Optionally add a "See Also" section -->
<refsection>
<title>See Also</title>
- <para><xref linkend="ST_Crosses" />, <xref linkend="DE-9IM" />, <xref linkend="ST_Disjoint" />, <xref linkend="ST_Intersects" />, <xref linkend="ST_Touches" /></para>
+ <para>
+ <xref linkend="DE-9IM" />, <xref linkend="ST_RelateMatch" />,
+ <xref linkend="ST_Contains" />, <xref linkend="ST_ContainsProperly" />,
+ <xref linkend="ST_Covers" />, <xref linkend="ST_CoveredBy" />,
+ <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" />
+ </para>
</refsection>
</refentry>
@@ -1458,7 +1512,8 @@ t
<refnamediv>
<refname>ST_RelateMatch</refname>
- <refpurpose>Returns true if an Intersection Matrix value matches an Intersection Matrix pattern</refpurpose>
+ <refpurpose>Returns true if a DE-9IM Intersection Matrix value matches an Intersection Matrix pattern
+ </refpurpose>
</refnamediv>
<refsynopsisdiv>
@@ -1474,10 +1529,17 @@ t
<refsection>
<title>Description</title>
- <para> Tests if an <varname>intersectionMatrix</varname> value satisfies
+ <para>
+ Tests if a <ulink url="http://en.wikipedia.org/wiki/DE-9IM">Dimensionally Extended 9-Intersection Model</ulink> (DE-9IM)
+ <varname>intersectionMatrix</varname> value satisfies
an <varname>intersectionMatrixPattern</varname>.
- For more information refer to <xref linkend="DE-9IM" />. </para>
+ Intersection matrix values can be computed by <xref linkend="ST_Relate" />.
+ </para>
+ <para>
+ For more information refer to <xref linkend="DE-9IM" />.
+ </para>
<para>Performed by the GEOS module</para>
+
<para>Availability: 2.0.0</para>
</refsection>
@@ -1488,21 +1550,38 @@ t
SELECT ST_RelateMatch('101202FFF', 'TTTTTTFFF') ;
-- result --
t
---example of common intersection matrix patterns and example matrices
--- comparing relationships of involving one invalid geometry and ( a line and polygon that intersect at interior and boundary)
-SELECT mat.name, pat.name, ST_RelateMatch(mat.val, pat.val) As satisfied
- FROM
- ( VALUES ('Equality', 'T1FF1FFF1'),
- ('Overlaps', 'T*T***T**'),
- ('Within', 'T*F**F***'),
- ('Disjoint', 'FF*FF****') As pat(name,val)
- CROSS JOIN
- ( VALUES ('Self intersections (invalid)', '111111111'),
- ('IE2_BI1_BB0_BE1_EI1_EE2', 'FF2101102'),
- ('IB1_IE1_BB0_BE0_EI2_EI1_EE2', 'F11F00212')
- ) As mat(name,val);
-
- </programlisting>
+</programlisting>
+ <para>Patterns for common spatial relationships
+matched against intersection matrix values,
+for a line in various positions relative to a polygon</para>
+ <programlisting>
+SELECT pat.name AS relationship, pat.val AS pattern,
+ mat.name AS position, mat.val AS matrix,
+ ST_RelateMatch(mat.val, pat.val) AS match
+ FROM (VALUES ( 'Equality', 'T1FF1FFF1' ),
+ ( 'Overlaps', 'T*T***T**' ),
+ ( 'Within', 'T*F**F***' ),
+ ( 'Disjoint', 'FF*FF****' )) AS pat(name,val)
+ CROSS JOIN
+ (VALUES ('non-intersecting', 'FF1FF0212'),
+ ('overlapping', '1010F0212'),
+ ('inside', '1FF0FF212')) AS mat(name,val);
+
+ relationship | pattern | position | matrix | match
+--------------+-----------+------------------+-----------+-------
+ Equality | T1FF1FFF1 | non-intersecting | FF1FF0212 | f
+ Equality | T1FF1FFF1 | overlapping | 1010F0212 | f
+ Equality | T1FF1FFF1 | inside | 1FF0FF212 | f
+ Overlaps | T*T***T** | non-intersecting | FF1FF0212 | f
+ Overlaps | T*T***T** | overlapping | 1010F0212 | t
+ Overlaps | T*T***T** | inside | 1FF0FF212 | f
+ Within | T*F**F*** | non-intersecting | FF1FF0212 | f
+ Within | T*F**F*** | overlapping | 1010F0212 | f
+ Within | T*F**F*** | inside | 1FF0FF212 | t
+ Disjoint | FF*FF**** | non-intersecting | FF1FF0212 | t
+ Disjoint | FF*FF**** | overlapping | 1010F0212 | f
+ Disjoint | FF*FF**** | inside | 1FF0FF212 | f
+</programlisting>
</refsection>
<!-- Optionally add a "See Also" section -->
diff --git a/doc/using_postgis_dataman.xml b/doc/using_postgis_dataman.xml
index 07ad721..de78a9d 100644
--- a/doc/using_postgis_dataman.xml
+++ b/doc/using_postgis_dataman.xml
@@ -6,9 +6,9 @@
<title>GIS Objects</title>
<para>The GIS objects supported by PostGIS are a superset of the "Simple
- Features" defined by the OpenGIS Consortium (OGC).
+ Features" standard defined by the OpenGIS Consortium (OGC).
PostGIS supports all the objects and functions specified in the OGC
- "Simple Features for SQL" specification.</para>
+ "Simple Features for SQL" specification (SFS).</para>
<para>PostGIS extends the standard with support for embedded SRID information.</para>
@@ -1211,13 +1211,24 @@ gisdb=# SELECT
</sect3>
<sect3 id="DE-9IM">
- <title>Dimensionally Extended 9 Intersection Model (DE-9IM)</title>
+ <title>Evaluating Spatial Relationships with the DE-9IM</title>
- <para>It is sometimes the case that the typical spatial predicates
- (<xref linkend="ST_Intersects" />, <xref linkend="ST_Contains" />,
- <xref linkend="ST_Crosses" />, <xref linkend="ST_Touches" />, ...) are
- insufficient in and of themselves to adequately provide that desired
- spatial filter.</para>
+ <para>
+ The OGC SFS defines a set of <emphasis>named spatial relationship predicates</emphasis> to evaluate the
+ spatial relationship between pairs of geometries.
+ 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>In some cases the named spatial relationships
+ are insufficient to provide a desired spatial filter.
+ </para>
<informaltable frame="none" border="0">
<tgroup cols="1">
@@ -1226,23 +1237,23 @@ gisdb=# SELECT
<entry><para><informalfigure float="1" floatstyle="left">
<graphic align="left" fileref="images/de9im01.png" />
</informalfigure></para><para>For example, consider a linear
- dataset representing a road network. It may be the task of a
- GIS analyst to identify all road segments that cross
- each other, not at a point, but on a line, perhaps invalidating
- some business rule. In this case, <xref linkend="ST_Crosses" /> does not
- adequately provide the necessary spatial filter since, for
- linear features, it returns <varname>true</varname> only where
- they cross at a point.</para> <para>One two-step solution
- might be to first perform the actual intersection
- (<xref linkend="ST_Intersection" />) of pairs of road segments that spatially
- intersect (<xref linkend="ST_Intersects" />), and then compare the intersection's
- <xref linkend="ST_GeometryType" /> with '<varname>LINESTRING</varname>' (properly
+ 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>A
- more elegant / faster solution may indeed be
- desirable.</para></entry>
+ <varname>[MULTI]LINESTRING</varname>s, etc.).</para>
+ <para>Clearly, a simpler and faster solution is desirable.</para></entry>
</row>
</tbody>
</tgroup>
@@ -1254,15 +1265,15 @@ gisdb=# SELECT
<row>
<entry><para> <informalfigure float="1" floatstyle="right">
<graphic align="right" fileref="images/de9im02.png" />
- </informalfigure></para> <para>A second [theoretical]
- example may be that of a GIS analyst trying to locate all
- wharfs or docks that intersect a lake's boundary on a line and
- where only one end of the wharf is up on shore. In other
- words, where a wharf is within, but not completely within a
- lake, intersecting the boundary of a lake on a line, and where
- the wharf's endpoints are both completely within and on the
- boundary of the lake. The analyst may need to use a
- combination of spatial predicates to isolate the sought after
+ </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>
@@ -1281,8 +1292,7 @@ gisdb=# SELECT
<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>... (needless to say, this could get quite
- complicated)</para>
+ <para>... but needless to say, this is quite complicated.</para>
</listitem>
</itemizedlist></entry>
</row>
@@ -1290,8 +1300,8 @@ gisdb=# SELECT
</tgroup>
</informaltable>
- <para>So enters the Dimensionally Extended 9 Intersection Model, or
- DE-9IM for short.</para>
+ <para>These requirements can be met by using the
+ Dimensionally Extended 9-Intersection Model (DE-9IM for short).</para>
<sect4>
<title>Theory</title>
@@ -1305,6 +1315,11 @@ gisdb=# SELECT
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
+ can be categorized into the following sets:
+ </para>
+
<glosslist>
<glossentry>
<glossterm>Boundary</glossterm>
@@ -1313,9 +1328,9 @@ gisdb=# SELECT
<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> are the two
+ boundary of a <varname>LINESTRING</varname> is the two
endpoints. For <varname>POLYGON</varname>s, the boundary is
- the linework that make up the exterior and interior
+ the linework of the exterior and interior
rings.</para>
</glossdef>
</glossentry>
@@ -1325,10 +1340,10 @@ gisdb=# SELECT
<glossdef>
<para>The interior of a geometry are those points of a
- geometry that are left when the boundary is removed. For
+ geometry that are not in the boundary. For
<varname>POINT</varname>s, the interior is the
- <varname>POINT</varname> itself. The interior of a
- <varname>LINESTRING</varname> are the set of real points
+ 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>
@@ -1338,29 +1353,63 @@ gisdb=# SELECT
<glossterm>Exterior</glossterm>
<glossdef>
- <para>The exterior of a geometry is the universe, an areal
- surface, not on the interior or boundary of the
- geometry.</para>
+ <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>Given geometry <emphasis>a</emphasis>, where the
- <emphasis>I(a)</emphasis>, <emphasis>B(a)</emphasis>, and
- <emphasis>E(a)</emphasis> are the <emphasis>Interior</emphasis>,
- <emphasis>Boundary</emphasis>, and <emphasis>Exterior</emphasis> of
- a, the mathematical representation of the matrix is:</para>
+ <para>The <ulink url="http://en.wikipedia.org/wiki/DE-9IM">Dimensionally Extended 9-Intersection Model</ulink>
+ (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(g)</emphasis> denotes the dimension of
+ <emphasis>g</emphasis> with the domain of
+ <literal>{0,1,2,F}</literal>
+ (as computed by <xref linkend="ST_Dimension" />)
+ </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>
-
<entry><emphasis role="bold">Interior</emphasis></entry>
-
<entry><emphasis role="bold">Boundary</emphasis></entry>
-
<entry><emphasis role="bold">Exterior</emphasis></entry>
</row>
</thead>
@@ -1389,40 +1438,7 @@ gisdb=# SELECT
</tgroup>
</informaltable>
- <para>Where <emphasis>dim(a)</emphasis> is the dimension of
- <emphasis>a</emphasis> as specified by
- <xref linkend="ST_Dimension" /> but has the domain of
- <literal>{0,1,2,T,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>T</literal> =>
- <literal>{0,1,2}</literal></para>
- </listitem>
-
- <listitem>
- <para><literal>F</literal> => empty set</para>
- </listitem>
-
- <listitem>
- <para><literal>*</literal> => don't care</para>
- </listitem>
- </itemizedlist>
-
- <para>Visually, for two overlapping polygonal geometries, this looks
- like:</para>
+ <para>Visually, for two overlapping polygonal geometries, this looks like:</para>
<informaltable frame="none" border="0">
<tgroup cols="2">
@@ -1538,31 +1554,64 @@ gisdb=# SELECT
</tgroup>
</informaltable>
- <para>Read from left to right and from top to bottom, the dimensional matrix is
- represented, '<emphasis role="bold">212101212</emphasis>'.</para>
+ <para>Reading from left to right and from top to bottom, the intersection matrix is
+ represented as '<emphasis role="bold">212101212</emphasis>'.</para>
+
+ <para>
+ PostGIS provides the <xref linkend="ST_Relate" /> function
+ to compute the intersection matrix for two geometries:
+ </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 specify more general spatial relationships,
+ an <emphasis role="bold">intersection matrix pattern</emphasis> is used.
+ This is a matrix represention 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>A relate matrix that would therefore represent our first
- example of two lines that intersect on a line would be: '<emphasis
- role="bold">1*1***1**</emphasis>'</para>
+ <para>Using intersection matrix patterns and the 3-parameter variant of <xref linkend="ST_Relate" />,
+ specific spatial relationships can be evaluated in a more succinct way.
+ For the first example above, an intersection matrix pattern specifying
+ two lines intersecting in a line is
+ '<emphasis role="bold">1*1***1**</emphasis>':</para>
- <programlisting>-- Identify road segments that cross on a line
+ <programlisting>-- Find road segments that cross on 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>A relate matrix that represents the second example of wharfs
- partly on the lake's shoreline would be '<emphasis
- role="bold">102101FF2</emphasis>'</para>
+ <para>For the second example, an intersection matrix pattern
+ specifying a line partly inside and partly outside a polygon is
+ '<emphasis role="bold">102101FF2</emphasis>':</para>
- <programlisting>-- Identify wharfs partly on a lake's shoreline
+ <programlisting>-- 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>
- <para>For more information or reading, see:</para>
+ <para>For more information, refer to:</para>
<itemizedlist spacing="compact">
<listitem>
-----------------------------------------------------------------------
Summary of changes:
doc/reference_relationship.xml | 195 +++++++++++++++++++++++----------
doc/using_postgis_dataman.xml | 241 +++++++++++++++++++++++++----------------
2 files changed, 282 insertions(+), 154 deletions(-)
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