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14.16.9.1 Spatial Relation Functions That Use Object Shapes

The OpenGIS specification defines the following functions to test the relationship between two geometry valuesg1 andg2, using precise object shapes. The return values 1 and 0 indicate true and false, respectively, except that distance functions return distance values.

Functions in this section detect arguments in either Cartesian or geographic spatial reference systems (SRSs), and return results appropriate to the SRS.

Unless otherwise specified, functions in this section handle their geometry arguments as follows:

  • If any argument isNULL or any geometry argument is an empty geometry, the return value isNULL.

  • If any geometry argument is not a syntactically well-formed geometry, anER_GIS_INVALID_DATA error occurs.

  • If any geometry argument is a syntactically well-formed geometry in an undefined spatial reference system (SRS), anER_SRS_NOT_FOUND error occurs.

  • For functions that take multiple geometry arguments, if those arguments are not in the same SRS, anER_GIS_DIFFERENT_SRIDS error occurs.

  • If any geometry argument is geometrically invalid, either the result is true or false (it is undefined which), or an error occurs.

  • For geographic SRS geometry arguments, if any argument has a longitude or latitude that is out of range, an error occurs:

    Ranges shown are in degrees. If an SRS uses another unit, the range uses the corresponding values in its unit. The exact range limits deviate slightly due to floating-point arithmetic.

  • Otherwise, the return value is non-NULL.

Some functions in this section permit a unit argument that specifies the length unit for the return value. Unless otherwise specified, functions handle their unit argument as follows:

These object-shape functions are available for testing geometry relationships:

  • ST_Contains(g1,g2)

    Returns 1 or 0 to indicate whetherg1 completely containsg2 (this means thatg1 andg2 must not intersect). This relationship is the inverse of that tested byST_Within().

    ST_Contains() handles its arguments as described in the introduction to this section.

    mysql> SET @g1 = ST_GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))'),    ->     @p1 = ST_GeomFromText('Point(1 1)'),    ->     @p2 = ST_GeomFromText('Point(3 3)'),    ->     @p3 = ST_GeomFromText('Point(5 5)');Query OK, 0 rows affected (0.00 sec)mysql> SELECT    ->   ST_Contains(@g1, @p1), ST_Within(@p1, @g1),     ->   ST_Disjoint(@g1, @p1), ST_Intersects(@g1, @p1)\G*************************** 1. row ***************************  ST_Contains(@g1, @p1): 1    ST_Within(@p1, @g1): 1  ST_Disjoint(@g1, @p1): 0ST_Intersects(@g1, @p1): 11 row in set (0.00 sec)mysql> SELECT    ->   ST_Contains(@g1, @p2), ST_Within(@p2, @g1),     ->   ST_Disjoint(@g1, @p2), ST_Intersects(@g1, @p2)\G*************************** 1. row ***************************  ST_Contains(@g1, @p2): 0    ST_Within(@p2, @g1): 0  ST_Disjoint(@g1, @p2): 0ST_Intersects(@g1, @p2): 11 row in set (0.00 sec)mysql>       -> SELECT    ->   ST_Contains(@g1, @p3), ST_Within(@p3, @g1),     ->   ST_Disjoint(@g1, @p3), ST_Intersects(@g1, @p3)\G*************************** 1. row ***************************  ST_Contains(@g1, @p3): 0    ST_Within(@p3, @g1): 0  ST_Disjoint(@g1, @p3): 1ST_Intersects(@g1, @p3): 01 row in set (0.00 sec)

  • ST_Crosses(g1,g2)

    Two geometriesspatially cross if their spatial relation has the following properties:

    • Unlessg1 andg2 are both of dimension 1:g1 crossesg2 if the interior ofg2 has points in common with the interior ofg1, butg2 does not cover the entire interior ofg1.

    • If bothg1 andg2 are of dimension 1: If the lines cross each other in a finite number of points (that is, no common line segments, only single points in common).

    This function returns 1 or 0 to indicate whetherg1 spatially crossesg2.

    ST_Crosses() handles its arguments as described in the introduction to this section except that the return value isNULL for these additional conditions:

    • g1 is of dimension 2 (Polygon orMultiPolygon).

    • g2 is of dimension 1 (Point orMultiPoint).

  • ST_Disjoint(g1,g2)

    Returns 1 or 0 to indicate whetherg1 is spatially disjoint from (does not intersect)g2.

    ST_Disjoint() handles its arguments as described in the introduction to this section.

  • ST_Distance(g1,g2 [,unit])

    Returns the distance betweeng1 andg2, measured in the length unit of the spatial reference system (SRS) of the geometry arguments, or in the unit of the optionalunit argument if that is specified.

    This function processes geometry collections by returning the shortest distance among all combinations of the components of the two geometry arguments.

    ST_Distance() handles its geometry arguments as described in the introduction to this section, with these exceptions:

    • ST_Distance() detects arguments in a geographic (ellipsoidal) spatial reference system and returns the geodetic distance on the ellipsoid.ST_Distance() supports distance calculations for geographic SRS arguments of all geometry types.

    • If any argument is geometrically invalid, either the result is an undefined distance (that is, it can be any number), or an error occurs.

    • If an intermediate or final result producesNaN or a negative number, anER_GIS_INVALID_DATA error occurs.

    ST_Distance() permits specifying the linear unit for the returned distance value with an optionalunit argument whichST_Distance() handles as described in the introduction to this section.

    mysql> SET @g1 = ST_GeomFromText('POINT(1 1)');mysql> SET @g2 = ST_GeomFromText('POINT(2 2)');mysql> SELECT ST_Distance(@g1, @g2);+-----------------------+| ST_Distance(@g1, @g2) |+-----------------------+|    1.4142135623730951 |+-----------------------+mysql> SET @g1 = ST_GeomFromText('POINT(1 1)', 4326);mysql> SET @g2 = ST_GeomFromText('POINT(2 2)', 4326);mysql> SELECT ST_Distance(@g1, @g2);+-----------------------+| ST_Distance(@g1, @g2) |+-----------------------+|     156874.3859490455 |+-----------------------+mysql> SELECT ST_Distance(@g1, @g2, 'metre');+--------------------------------+| ST_Distance(@g1, @g2, 'metre') |+--------------------------------+|              156874.3859490455 |+--------------------------------+mysql> SELECT ST_Distance(@g1, @g2, 'foot');+-------------------------------+| ST_Distance(@g1, @g2, 'foot') |+-------------------------------+|             514679.7439273146 |+-------------------------------+

    For the special case of distance calculations on a sphere, see theST_Distance_Sphere() function.

  • ST_Equals(g1,g2)

    Returns 1 or 0 to indicate whetherg1 is spatially equal tog2.

    ST_Equals() handles its arguments as described in the introduction to this section, except that it does not returnNULL for empty geometry arguments.

    mysql> SET @g1 = Point(1,1), @g2 = Point(2,2);mysql> SELECT ST_Equals(@g1, @g1), ST_Equals(@g1, @g2);+---------------------+---------------------+| ST_Equals(@g1, @g1) | ST_Equals(@g1, @g2) |+---------------------+---------------------+|                   1 |                   0 |+---------------------+---------------------+

  • ST_FrechetDistance(g1,g2 [,unit])

    Returns the discrete Fréchet distance between two geometries, reflecting how similar the geometries are. The result is a double-precision number measured in the length unit of the spatial reference system (SRS) of the geometry arguments, or in the length unit of theunit argument if that argument is given.

    This function implements the discrete Fréchet distance, which means it is restricted to distances between the points of the geometries. For example, given twoLineString arguments, only the points explicitly mentioned in the geometries are considered. Points on the line segments between these points are not considered.

    ST_FrechetDistance() handles its geometry arguments as described in the introduction to this section, with these exceptions:

    ST_FrechetDistance() handles its optionalunit argument as described in the introduction to this section.

    mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0,0 5,5 5)');mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 1,0 6,3 3,5 6)');mysql> SELECT ST_FrechetDistance(@ls1, @ls2);+--------------------------------+| ST_FrechetDistance(@ls1, @ls2) |+--------------------------------+|             2.8284271247461903 |+--------------------------------+mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0,0 5,5 5)', 4326);mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 1,0 6,3 3,5 6)', 4326);mysql> SELECT ST_FrechetDistance(@ls1, @ls2);+--------------------------------+| ST_FrechetDistance(@ls1, @ls2) |+--------------------------------+|              313421.1999416798 |+--------------------------------+mysql> SELECT ST_FrechetDistance(@ls1, @ls2, 'foot');+----------------------------------------+| ST_FrechetDistance(@ls1, @ls2, 'foot') |+----------------------------------------+|                     1028284.7767115477 |+----------------------------------------+

  • ST_HausdorffDistance(g1,g2 [,unit])

    Returns the discrete Hausdorff distance between two geometries, reflecting how similar the geometries are. The result is a double-precision number measured in the length unit of the spatial reference system (SRS) of the geometry arguments, or in the length unit of theunit argument if that argument is given.

    This function implements the discrete Hausdorff distance, which means it is restricted to distances between the points of the geometries. For example, given twoLineString arguments, only the points explicitly mentioned in the geometries are considered. Points on the line segments between these points are not considered.

    ST_HausdorffDistance() handles its geometry arguments as described in the introduction to this section, with these exceptions:

    • If the geometry arguments are in the same Cartesian or geographic SRS, but are not in a supported combination, anER_NOT_IMPLEMENTED_FOR_CARTESIAN_SRS orER_NOT_IMPLEMENTED_FOR_GEOGRAPHIC_SRS error occurs, depending on the SRS type. These combinations are supported:

      • LineString andLineString

      • Point andMultiPoint

      • LineString andMultiLineString

      • MultiPoint andMultiPoint

      • MultiLineString andMultiLineString

    ST_HausdorffDistance() handles its optionalunit argument as described in the introduction to this section.

    mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0,0 5,5 5)');mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 1,0 6,3 3,5 6)');mysql> SELECT ST_HausdorffDistance(@ls1, @ls2);+----------------------------------+| ST_HausdorffDistance(@ls1, @ls2) |+----------------------------------+|                                1 |+----------------------------------+mysql> SET @ls1 = ST_GeomFromText('LINESTRING(0 0,0 5,5 5)', 4326);mysql> SET @ls2 = ST_GeomFromText('LINESTRING(0 1,0 6,3 3,5 6)', 4326);mysql> SELECT ST_HausdorffDistance(@ls1, @ls2);+----------------------------------+| ST_HausdorffDistance(@ls1, @ls2) |+----------------------------------+|               111319.49079326246 |+----------------------------------+mysql> SELECT ST_HausdorffDistance(@ls1, @ls2, 'foot');+------------------------------------------+| ST_HausdorffDistance(@ls1, @ls2, 'foot') |+------------------------------------------+|                        365221.4264870815 |+------------------------------------------+

  • ST_Intersects(g1,g2)

    Returns 1 or 0 to indicate whetherg1 spatially intersectsg2.

    ST_Intersects() handles its arguments as described in the introduction to this section.

  • ST_Overlaps(g1,g2)

    Two geometriesspatially overlap if they intersect and their intersection results in a geometry of the same dimension but not equal to either of the given geometries.

    This function returns 1 or 0 to indicate whetherg1 spatially overlapsg2.

    ST_Overlaps() handles its arguments as described in the introduction to this section except that the return value isNULL for the additional condition that the dimensions of the two geometries are not equal.

  • ST_Touches(g1,g2)

    Two geometriesspatially touch if their interiors do not intersect, but the boundary of one of the geometries intersects either the boundary or the interior of the other.

    This function returns 1 or 0 to indicate whetherg1 spatially touchesg2.

    ST_Touches() handles its arguments as described in the introduction to this section except that the return value isNULL for the additional condition that both geometries are of dimension 0 (Point orMultiPoint).

  • ST_Within(g1,g2)

    Returns 1 or 0 to indicate whetherg1 is spatially withing2. This tests the opposite relationship asST_Contains().

    ST_Within() handles its arguments as described in the introduction to this section.