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source: trunk/workshop-foss4g/spatial_relationships.rst @ 13

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[1]1.. _spatial_relationships:
2
3Section 10: Spatial Relationships
4=================================
5
6So far we have only used spatial functions that measure (:command:`ST_Area`, :command:`ST_Length`), serialize (:command:`ST_GeomFromText`) or deserialize (:command:`ST_AsGML`) geometries. What these functions have in common is that they only work on one geometry at a time.
7
8Spatial databases are powerful because they not only store geometry, they also have the ability to compare *relationships between geometries*.
9
10Questions like “Which are the closet bike racks to a park?” or “Where are the intersections of subway lines and streets?” can only be answered by comparing geometries representing the bike racks, streets, and subway lines.
11
12The OGC standard defines the following set of methods to compare geometries.
13
14ST_Equals
15---------
16 
17:command:`ST_Equals(geometry A, geometry B)` tests the spatial equality of two geometries.
18
19.. figure:: ./spatial_relationships/st_equals.png
20   :align: center
21
22ST_Equals returns TRUE if two geometries of the same type have identical x,y coordinate values, i.e. if the secondary shape is equal (identical) to the primary shape object.
23
24First, let's retrieve a representation of a point from our ``nyc_subway_stations`` table. We'll take just the entry for 'Broad St'.
25
26.. code-block:: sql
27
28  SELECT name, the_geom, ST_AsText(the_geom)
29  FROM nyc_subway_stations
30  WHERE name = 'Broad St';             
31
32::
33
34     name   |                      the_geom                      |      st_astext
35  ----------+----------------------------------------------------+-----------------------
36   Broad St | 0101000020266900000EEBD4CF27CF2141BC17D69516315141 | POINT(583571 4506714)
37 
38Then, plug the geometry representation back into an :command:`ST_Equals` test:
39
40.. code-block:: sql
41
42  SELECT name
43  FROM nyc_subway_stations
44  WHERE ST_Equals(the_geom, '0101000020266900000EEBD4CF27CF2141BC17D69516315141');
45
46::
47
48   Broad St
49
50.. note::
51
52  The representation of the point was not very human readable (``0101000020266900000EEBD4CF27CF2141BC17D69516315141``) but it was an exact representation of the coordinate values. For a test like equality, using the exact coordinates in necessary.
53
54
55ST_Intersects, ST_Disjoint, ST_Crosses and ST_Overlaps
56------------------------------------------------------
57
58:command:`ST_Intersects`, :command:`ST_Crosses`, and :command:`ST_Overlaps` test whether the interiors of the geometries intersect.
59
60.. figure:: ./spatial_relationships/st_intersects.png
61   :align: center
62
63:command:`ST_Intersects(geometry A, geometry B)` returns t (TRUE) if the intersection does not result in an empty set. Intersects returns the exact opposite result of disjoint.
64
65.. figure:: ./spatial_relationships/st_disjoint.png
66   :align: center
67
68The opposite of ST_Intersects is :command:`ST_Disjoint(geometry A , geometry B)`. If two geometries are disjoint, they do not intersect, and vice-versa. In fact, it is often more efficient to test "not intersects" than to test "disjoint" because the intersects tests can be spatially indexed, while the disjoint test cannot.
69
70.. figure:: ./spatial_relationships/st_crosses.png 
71   :align: center
72
73For multipoint/polygon, multipoint/linestring, linestring/linestring, linestring/polygon, and linestring/multipolygon comparisons, :command:`ST_Crosses(geometry A, geometry B)` returns t (TRUE) if the intersection results in a geometry whose dimension is one less than the maximum dimension of the two source geometries and the intersection set is interior to both source geometries.
74
75.. figure:: ./spatial_relationships/st_overlaps.png
76   :align: center
77
78:command:`ST_Overlaps(geometry A, geometry B)` compares two geometries of the same dimension and returns TRUE if their intersection set results in a geometry different from both but of the same dimension.
79
80Let's take our Broad Street subway station and determine its neighborhood using the :command:`ST_Intersects` function:
81
82.. code-block:: sql
83
84  SELECT name, boroname
85  FROM nyc_neighborhoods
86  WHERE ST_Intersects(the_geom, '0101000020266900000EEBD4CF27CF2141BC17D69516315141');
87
88::
89
90          name        | boroname 
91  --------------------+-----------
92   Financial District | Manhattan
93
94
95
96ST_Touches
97----------
98
99:command:`ST_Touches` tests whether two geometries touch at their boundaries, but do not intersect in their interiors
100
101.. figure:: ./spatial_relationships/st_touches.png
102   :align: center
103
104:command:`ST_Touches(geometry A, geometry B)` returns TRUE if either of the geometries' boundaries intersect or if only one of the geometry's interiors intersects the other's boundary.
105
106ST_Within and ST_Contains
107-------------------------
108
109:command:`ST_Within` and :command:`ST_Contains` test whether one geometry is fully within the other.
110
111.. figure:: ./spatial_relationships/st_within.png
112   :align: center
113   
114:command:`ST_Within(geometry A , geometry B)` returns TRUE if the first geometry is completely within the second geometry. ST_Within tests for the exact opposite result of ST_Contains. 
115
116:command:`ST_Contains(geometry A, geometry B)` returns TRUE if the second geometry is completely contained by the first geometry.
117
118
119ST_Distance and ST_DWithin
120--------------------------
121
122An extremely common GIS question is "find all the stuff within distance X of this other stuff".
123
124The :command:`ST_Distance(geometry A, geometry B)` calculates the *shortest* distance between two geometries and returns it as a float. This is useful for actually reporting back the distance between objects.
125
126.. code-block:: sql
127
128  SELECT ST_Distance(
129    ST_GeometryFromText('POINT(0 5)'),
130    ST_GeometryFromText('LINESTRING(-2 2, 2 2)'));
131
132::
133
134  3
135
136For testing whether two objects are within a distance of one another, the :command:`ST_DWithin` function provides an index-accelerated true/false test. This is useful for questions like "how many trees are within a 500 meter buffer of the road?". You don't have to calculate an actual buffer, you just have to test the distance relationship.
137
138  .. figure:: ./spatial_relationships/st_dwithin.png
139     :align: center
140   
141Using our Broad Street subway station again, we can find the streets nearby (within 10 meters of) the subway stop:
142
143.. code-block:: sql
144
145  SELECT name
146  FROM nyc_streets
147  WHERE ST_DWithin(
148          the_geom,
149          '0101000020266900000EEBD4CF27CF2141BC17D69516315141',
150          10
151        );
152
153:: 
154
155       name     
156  --------------
157     Wall St
158     Broad St
159     Nassau St
160
161And we can verify the answer on a map. The Broad St station is actually at the intersection of Wall, Broad and Nassau Streets.
162
163.. image:: ./spatial_relationships/broad_st.jpg
164
165Function List
166-------------
167
168`ST_Contains(geometry A, geometry B) <http://postgis.org/docs/ST_Contains.html>`_: Returns true if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.
169
170`ST_Crosses(geometry A, geometry B)  <http://postgis.org/docs/ST_Crosses.html>`_: Returns TRUE if the supplied geometries have some, but not all, interior points in common.
171
172`ST_Disjoint(geometry A , geometry B) <http://postgis.org/docs/ST_Disjoint.html>`_: Returns TRUE if the Geometries do not "spatially intersect" - if they do not share any space together.
173
174`ST_Distance(geometry A, geometry B)  <http://postgis.org/docs/ST_Distance.html>`_: Returns the 2-dimensional cartesian minimum distance (based on spatial ref) between two geometries in projected units.
175
176`ST_DWithin(geometry A, geometry B, radius) <http://postgis.org/docs/ST_DWithin.html>`_: Returns true if the geometries are within the specified distance (radius) of one another.
177
178`ST_Equals(geometry A, geometry B) <http://postgis.org/docs/ST_Equals.html>`_: Returns true if the given geometries represent the same geometry. Directionality is ignored.
179
180`ST_Intersects(geometry A, geometry B) <http://postgis.org/docs/ST_Intersects.html>`_: Returns TRUE if the Geometries/Geography "spatially intersect" - (share any portion of space) and FALSE if they don't (they are Disjoint).
181
182`ST_Overlaps(geometry A, geometry B) <http://postgis.org/docs/ST_Overlaps.html>`_: Returns TRUE if the Geometries share space, are of the same dimension, but are not completely contained by each other.
183
184`ST_Touches(geometry A, geometry B)  <http://postgis.org/docs/ST_Touches.html>`_: Returns TRUE if the geometries have at least one point in common, but their interiors do not intersect.
185
186`ST_Within(geometry A , geometry B) <http://postgis.org/docs/ST_Within.html>`_: Returns true if the geometry A is completely inside geometry B
187
188
189
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