Analysing Spatial Information
=============================
into four
major categories according to the type of operation they perform:
* Functions that convert geometries between various formats
* Functions that provide access to qualitative or quantitative
properties of a geometry
* Functions that describe relations between two geometries
* Functions that create new geometries from existing ones
Spatial analysis functions can be used in many contexts, such as:
* Any interactive SQL program, like `mysql' or `MySQLCC'
* Application programs written in any language that supports a MySQL
client API
Functions to Convert Geometries Between Formats
-----------------------------------------------
MySQL supports the following functions for converting geometry values
between internal format and either WKT or WKB format:
such as `PointFromText()' and
`LineFromText()'; see *Note GIS WKT Functions::.
such as `PointFromWKB()' and
`LineFromWKB()'; see *Note GIS WKB Functions::.
`AsText(g)'
Converts a value in internal geometry format to its WKT
representation and returns the resulting string.
mysql> SET @g = 'LineString(1 1,2 2,3 3)';
mysql> +--------------------------+
`AsBinary(g)'
Converts a value in internal geometry format to its WKB
representation and returns the resulting binary value.
`Geometry' Property Analysis Functions
--------------------------------------
return `NULL' if the argument is of an incorrect geometry type. For
example, `Area()' returns `NULL' if the object type is neither
`Polygon' nor `MultiPolygon'.
General Geometry Property Analysis Functions
............................................
The functions listed in this ssection do not restrict their argument and
accept a geometry value of any type.
`GeometryType(g)'
Returns as a string the name of the geometry type of which the
geometry instance `g' is a member. The name will correspond to
one of the instantiable `Geometry' subclasses.
mysql> SELECT GeometryType(GeomFromText('POINT(1 1)'));
+------------------------------------------+
| GeometryType(GeomFromText('POINT(1 1)')) |
+------------------------------------------+
| POINT |
+------------------------------------------+
`Dimension(g)'
Returns the inherent dimension of the geometry value `g'. The
result can be -1, 0, 1, or 2. (The meaning of these values is
given in *Note GIS class geometry::.)
mysql>
| 1 |
+------------------------------------------------+
`SRID(g)'
Returns an integer indicating the Spatial Reference System ID for
the geometry value `g'.
mysql> SELECT SRID(GeomFromText('LineString(1 1,2 2)',101));
+-----------------------------------------------+
| SRID(GeomFromText('LineString(1 1,2 2)',101)) |
+-----------------------------------------------+
| 101 |
+-----------------------------------------------+
`Envelope(g)'
Returns the Minimum Bounding Rectangle (MBR) for the geometry
value `g'. The result is returned as a polygon value.
mysql> SELECT AsText(Envelope(GeomFromText('LineString(1 1,2 2)')));
+-------------------------------------------------------+
| AsText(Envelope(GeomFromText('LineString(1 1,2 2)'))) |
+-------------------------------------------------------+
| POLYGON((1 1,2 1,2 2,1 2,1 1)) |
+-------------------------------------------------------+
The polygon is defined by the corner points of the bounding box:
POLYGON((MINX MINY, MAXX MINY, MAXX MAXY, MINX MAXY, MINX MINY))
The OpenGIS specification also defines the following functions, which
MySQL does not yet implement:
`Boundary(g)'
Returns a geometry that is the closure of the combinatorial
boundary of the geometry value `g'.
set.
`IsSimple(g)'
Returns 1 if the geometry value `g' has no anomalous geometric
points, such as self intersection or self tangency. `IsSimple()'
returns 0 if the argument is not simple, and -1 if it is `NULL'.
The description of each instantiable geometric class given earlier
in the chapter includes the specific conditions that cause an
instance of that class to be classified as not simple.
`Point' Property Analysis Functions
...................................
A `Point' consists of its X and Y coordinates, which may be obtained
using the following functions:
`X(p)'
Returns the X-coordinate value for the point `p' as a
double-precision number.
mysql>
| 56.7 |
+--------------------------------------+
`Y(p)'
Returns the Y-coordinate value for the point `p' as a
double-precision number.
mysql> SELECT Y(GeomFromText('Point(56.7 53.34)'));
+--------------------------------------+
| Y(GeomFromText('Point(56.7 53.34)')) |
+--------------------------------------+
| 53.34 |
+--------------------------------------+
`LineString' Property Analysis Functions
........................................
A `LineString' consists of `Point' values. You can extract particular
points of a `LineString', count the number of points that it contains,
or obtain its length.
`EndPoint(ls)'
Returns the `Point' that is the end point of the `LineString' value
`ls'.
mysql> SELECT AsText(EndPoint(GeomFromText('LineString(1 1,2 2,3 3)')));
+------------------------------------------------------------+
| AsText(EndPoint(GeomFromText('LineString(1 1,2 2,3 3)'))) |
+------------------------------------------------------------+
| POINT(3 3) |
+------------------------------------------------------------+
`GLength(ls)'
Returns as a double-precision number the length of the `LineString'
value `ls' in its associated spatial reference.
mysql>
| 2.8284271247462 |
+--------------------------------------------------+
`IsClosed(ls)'
Returns 1 if the `LineString' value `ls' is closed (that is, it
s`StartPoint()' and `EndPoint()' values are the same). Returns 0
if `ls' is not closed, and -1 if it is `NULL'.
mysql> SELECT IsClosed(GeomFromText('LineString(1 1,2 2,3 3)'));
+---------------------------------------------------+
| IsClosed(GeomFromText('LineString(1 1,2 2,3 3)')) |
+---------------------------------------------------+
| 0 |
+---------------------------------------------------+
`NumPoints(ls)'
Returns the number of points in the `LineString' value `ls'.
mysql> SELECT NumPoints(GeomFromText('LineString(1 1,2 2,3 3)'));
+----------------------------------------------------+
| NumPoints(GeomFromText('LineString(1 1,2 2,3 3)')) |
+----------------------------------------------------+
| 3 |
+----------------------------------------------------+
`PointN(ls,n)'
Returns the `n'-th point in the `Linestring' value `ls'. Point
numbers begin at 1.
mysql> SELECT AsText(PointN(GeomFromText('LineString(1 1,2 2,3 3)'),2));
+-----------------------------------------------------------+
| AsText(PointN(GeomFromText('LineString(1 1,2 2,3 3)'),2)) |
+-----------------------------------------------------------+
| POINT(2 2) |
+-----------------------------------------------------------+
`StartPoint(ls)'
Returns the `Point' that is the start point of the `LineString'
value `ls'.
mysql> SELECT AsText(StartPoint(GeomFromText('LineString(1 1,2 2,3 3)')));
+-------------------------------------------------------------+
| AsText(StartPoint(GeomFromText('LineString(1 1,2 2,3 3)'))) |
+-------------------------------------------------------------+
| POINT(1 1) |
+-------------------------------------------------------------+
The OpenGIS specification also defines the following function, which
MySQL does not yet implement:
`IsRing(ls)'
Returns 1 if the `LineString' value `ls' is closed (thatis, its
`StartPoint()' and `EndPoint()' values are the same) and is simple
(does not pass through the same point more than once). Returns 0
if `ls' is not a ring, and -1 if it is `NULL'.
`MultiLineString' Property Analysis Functions
.............................................
`GLength(mls)'
Returns as a double-precision number the length of the
`MultiLineString' value `mls'. The length of `mls' is equal to the
sum of the lengths of its elements.
mysql> SELECT GLength(GeomFromText('MultiLineString((1 1,2 2,3 3),(4 4,5 5))'));
+-------------------------------------------------------------------+
| GLength(GeomFromText('MultiLineString((1 1,2 2,3 3),(4 4,5 5))')) |
+-------------------------------------------------------------------+
| 4.2426406871193 |
+-------------------------------------------------------------------+
`IsClosed(mls)'
Returns 1 if the `MultiLineString' value `mls' is closed (that is,
the `StartPoint()' and `EndPoint()' values are the same for each
`LineString' in `mls'). Returns 0 if `mls' is not closed, and -1
if it is `NULL'.
mysql> SELECT IsClosed(GeomFromText('MultiLineString((1 1,2 2,3 3),(4 4,5 5))'));
+--------------------------------------------------------------------+
| IsClosed(GeomFromText('MultiLineString((1 1,2 2,3 3),(4 4,5 5))')) |
+--------------------------------------------------------------------+
| 0 |
+--------------------------------------------------------------------+
`Polygon' Property Analysis Functions
.....................................
`Area(poly)'
Returns as a double-precision number the area of the `Polygon'
value `poly', as measured in its spatial reference system.
mysql> SELECT Area(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))'));
+----------------------------------------------------------------------------+
| Area(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))')) |
+----------------------------------------------------------------------------+
| 8 |
+----------------------------------------------------------------------------+
`NumInteriorRings(poly)'
Returns the number of interior rings in the `Polygon' value `poly'.
mysql> SELECT NumInteriorRings(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))'));
+----------------------------------------------------------------------------------------+
| NumInteriorRings(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))')) |
+----------------------------------------------------------------------------------------+
| 1 |
+----------------------------------------------------------------------------------------+
`ExteriorRing(poly)'
Returns the exterior ring of the `Polygon' value `poly' as a
`LineString'.
mysql> SELECT AsText(ExteriorRing(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))')));
+--------------------------------------------------------------------------------------------+
| AsText(ExteriorRing(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))'))) |
+--------------------------------------------------------------------------------------------+
| LINESTRING(0 0,0 3,3 3,3 0,0 0) |
+--------------------------------------------------------------------------------------------+
`InteriorRingN(poly,n)'
Returns the `n'-th interior ring for the `Polygon' value `poly' as
a `LineString'. Ring numbers begin at 1.
mysql> SELECT AsText(InteriorRingN(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))'),1));
+-----------------------------------------------------------------------------------------------+
| AsText(InteriorRingN(GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))'),1)) |
+-----------------------------------------------------------------------------------------------+
| LINESTRING(1 1,1 2,2 2,2 1,1 1) |
+-----------------------------------------------------------------------------------------------+
The OpenGIS specification also defines the following functions, which
MySQL does not yet implement:
`Centroid(poly)'
Returns the mathematical centroid for the `Polygon' value `poly'
as a `Point'. The result is not guaranteed to be on the polygon.
`PointOnSurface(poly)'
Returns a `Point' value that is guaranteed to be on the `Polygon'
value `poly'.
`MultiPolygon' Property Analysis Functions
..........................................
`Area(mpoly)'
Returns as a double-precision number the area of the `MultiPolygon'
value `mpoly', as measured in its spatial reference system.
mysql> Area(GeomFromText('MultiPolygon(((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1)))')) |
+-----------------------------------------------------------------------------------+
| 8 |
+-----------------------------------------------------------------------------------+
The OpenGIS specification also defines the following functions, which
MySQL does not yet implement:
`Centroid(mpoly)'
Returns the mathematical centroid for the `MultiPolygon' value
`mpoly' as a `Point'. The result is not guaranteed to be on the
`MultiPolygon'.
`PointOnSurface(mpoly)'
Returns a `Point' value that is guaranteed to be on the
`MultiPolygon' value `mpoly'.
`GeometryCollection' Property Analysis Functions
................................................
`NumGeometries(gc)'
Returns the number of geometries in the `GeometryCollection' value
`gc'.
mysql> | NumGeometries(GeomFromText('GeometryCollection(Point(1 1),LineString(2 2, 3 3))')) |
+------------------------------------------------------------------------------------+
| 2 |
+------------------------------------------------------------------------------------+
`GeometryN(gc,n)'
Returns the `n'-th geometry in the `GeometryCollection' value
`gc'. Geometry numbers begin at 1.
mysql>
| AsText(GeometryN(GeomFromText('GeometryCollection(Point(1 1),LineString(2 2, 3 3))'),1)) |
+------------------------------------------------------------------------------------------+
| POINT(1 1) |
+------------------------------------------------------------------------------------------+
Functions That Create New Geometries From Existing Ones
-------------------------------------------------------
Geometry Functions That Produce New Geometries
..............................................
In the section *Note Geometry property functions::, we've already
discussed some functions that can construct new geometries from the
existing ones:
* `Envelope(g)'
* `StartPoint(ls)'
* `EndPoint(ls)'
* `PointN(ls,n)'
* `ExteriorRing(poly)'
* `InteriorRingN(poly,n)'
* `GeometryN(gc,n)'
Spatial Operators
.................
OpenGIS proposes a number of other functions that can produce
geometries. They are designed to implement Spatial Operators.
These functions are not yet implemented in MySQL. They should appear
in future releases.
`Intersection(g1,g2)'
Returns a geometry that represents the point set intersection of
the geometry values `g1' with `g2'.
`Union(g1,g2)'
Returns a geometry that represents the point set union of the
geometry values `g1' and `g2'.
`Difference(g1,g2)'
Returns a geometry that represents the point set difference of the
geometry value `g1' with `g2'.
`SymDifference(g1,g2)'
Returns a geometry that represents the point set symmetric
difference of the geometry value `g1' with `g2'.
`Buffer(g,d)'
Returns a geometry that represents all points whose distance from
the geometry value `g' is less than or equal to a distance of `d'.
`ConvexHull(g)'
Returns a geometry that represents the convex hull of the geometry
value `g'.
Functions For Testing Spatial Relations Between Geometric Objects
-----------------------------------------------------------------
The functions described in these sections take two geometries as input
parameters and return a qualitive or quantitive relation between them.
Relations On Geometry Minimal Bounding Rectangles (MBRs)
--------------------------------------------------------
MySQL provides some functions that can test relations between mininal
bounding rectangles of two geometries `g1' and `g2'. They include:
`MBRContains(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangle of `g1' contains the Minimum Bounding Rectangle of `g2'.
mysql> SET @g1 = GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))');
mysql> SET @g2 = GeomFromText('Point(1 1)');
mysql>
| 1 | 0 |
+----------------------+----------------------+
`MBRWithin(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangle of `g1' is within the Minimum Bounding Rectangle of `g2'.
mysql> SET @g1 = GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))');
mysql> SET @g2 = GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))');
mysql> SELECT MBRWithin(@g1,@g2), MBRWithin(@g2,@g1);
+--------------------+--------------------+
| MBRWithin(@g1,@g2) | MBRWithin(@g2,@g1) |
+--------------------+--------------------+
| 1 | 0 |
+--------------------+--------------------+
`MBRDisjoint(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangles of the two geometries `g1' and `g2' are disjoint (do
not intersect).
`MBREquals(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangles of the two geometries `g1' and `g2' are the same.
`MBRIntersects(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangles of the two geometries `g1' and `g2' intersect.
`MBROverlaps(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangles of the two geometries `g1' and `g2' overlap.
`MBRTouches(g1,g2)'
Returns 1 or 0 to indicate whether or not the Minimum Bounding
Rectangles of the two geometries `g1' and `g2' touch.
Functions That Test Spatial Relationships Between Geometries
------------------------------------------------------------
The OpenGIS specification defines the following functions, which MySQL
does not yet implement. They should appear in future releases. When
implemented, they will provide full support for spatial analysis, not
just MBR-based support.
The functions operate on two geometry values `g1' and `g2'.
`Contains(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' completely contains
`g2'.
`Crosses(g1,g2)'
Returns 1 if `g1' spatially crosses `g2'. Returns `NULL' if `g1'
is a `Polygon' or a `MultiPolygon', or if `g2' is a `Point' or a
`MultiPoint'. Otherwise, returns 0.
The term *spatially crosses* denotes a spatial relation between
two given geometries that has the following properties:
* The two geometries intersect
* Their intersection results in a geometry that has a dimension
that is one less than the maximum dimension of the two given
geometries
* Their intersection is not equal to either of the two given
geometries
`Disjoint(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' is spatially
disjoint from (does not intersect) `g2'.
`Equals(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' is spatially equal
to `g2'.
`Intersects(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' spatially intersects
`g2'.
in a geometry of the same
dimension but not equal to either of the given geometries.
`Touches(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' spatially touches
`g2'. Two geometries *spatially touch* if the interiors of the
geometries do not intersect, but the boundary of one of the
geometries intersects either the boundary or the interior of the
other.
`Within(g1,g2)'
Returns 1 or 0 to indicate whether or not `g1' is spatially within
`g2'.
`Distance(g1,g2)'
Returns as a double-precision number the shortest distance between
any two points in the two geometries.
`Related(g1,g2,pattern_matrix)'
Returns 1 or 0 to indicate whether or not the spatial relationship
specified by `pattern_matrix' exists between `g1' and `g2'.
Returns -1 if the arguments are `NULL'. The pattern matrix is a
string. Its specification will be noted here when this function is
implemented.
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