12.16.8 Spatial Operator Functions

OpenGIS proposes a number of functions that can produce geometries. They are designed to implement spatial operators.

These functions support all argument type combinations except those that are inapplicable according to the Open Geospatial Consortium specification.

In addition, Section 12.16.7, “Geometry Property Functions”, discusses several functions that construct new geometries from existing ones. See that section for descriptions of these functions:

• ST_Envelope(g)

• ST_StartPoint(ls)

• ST_EndPoint(ls)

• ST_PointN(ls, N)

• ST_ExteriorRing(poly)

• ST_InteriorRingN(poly, N)

• ST_GeometryN(gc, N)

These spatial operator functions are available:

• Buffer(g, d [, strategy1 [, strategy2 [, strategy3]]])

  ST_Buffer() and Buffer() are synonyms. For more information, see the description of ST_Buffer().

  Buffer() is deprecated; expect it to be removed in a future MySQL release. Use ST_Buffer() instead.

• ConvexHull(g)

  ST_ConvexHull() and ConvexHull() are synonyms. For more information, see the description of ST_ConvexHull().

  ConvexHull() is deprecated; expect it to be removed in a future MySQL release. Use ST_ConvexHull() instead.

• ST_Buffer(g, d [, strategy1 [, strategy2 [, strategy3]]])

  Returns a geometry that represents all points whose distance from the geometry value g is less than or equal to a distance of d, or NULL if any argument is NULL. The SRID of the geometry argument must be 0 because ST_Buffer() supports only the Cartesian coordinate system. If any geometry argument is not a syntactically well-formed geometry, an ER_GIS_INVALID_DATA error occurs.

  If the geometry argument is empty, ST_Buffer() returns an empty geometry.

  If the distance is 0, ST_Buffer() returns the geometry argument unchanged:

  mysql> SET @pt = ST_GeomFromText('POINT(0 0)');
  mysql> SELECT ST_AsText(ST_Buffer(@pt, 0));
  +------------------------------+
  | ST_AsText(ST_Buffer(@pt, 0)) |
  +------------------------------+
  | POINT(0 0)                   |
  +------------------------------+

  ST_Buffer() supports negative distances for Polygon and MultiPolygon values, and for geometry collections containing Polygon or MultiPolygon values. The result may be an empty geometry. An ER_WRONG_ARGUMENTS error occurs for ST_Buffer() with a negative distance for Point, MultiPoint, LineString, and MultiLineString values, and for geometry collections not containing any Polygon or MultiPolygon values.

  ST_Buffer() permits up to three optional strategy arguments following the distance argument. Strategies influence buffer computation. These arguments are byte string values produced by the ST_Buffer_Strategy() function, to be used for point, join, and end strategies:

  • Point strategies apply to Point and MultiPoint geometries. If no point strategy is specified, the default is ST_Buffer_Strategy('point_circle', 32).

  • Join strategies apply to LineString, MultiLineString, Polygon, and MultiPolygon geometries. If no join strategy is specified, the default is ST_Buffer_Strategy('join_round', 32).

  • End strategies apply to LineString and MultiLineString geometries. If no end strategy is specified, the default is ST_Buffer_Strategy('end_round', 32).

  Up to one strategy of each type may be specified, and they may be given in any order. If multiple strategies of a given type are specified, an ER_WRONG_ARGUMENTS error occurs.

  mysql> SET @pt = ST_GeomFromText('POINT(0 0)');
  mysql> SET @pt_strategy = ST_Buffer_Strategy('point_square');
  mysql> SELECT ST_AsText(ST_Buffer(@pt, 2, @pt_strategy));
  +--------------------------------------------+
  | ST_AsText(ST_Buffer(@pt, 2, @pt_strategy)) |
  +--------------------------------------------+
  | POLYGON((-2 -2,2 -2,2 2,-2 2,-2 -2))       |
  +--------------------------------------------+

  mysql> SET @ls = ST_GeomFromText('LINESTRING(0 0,0 5,5 5)');
  mysql> SET @end_strategy = ST_Buffer_Strategy('end_flat');
  mysql> SET @join_strategy = ST_Buffer_Strategy('join_round', 10);
  mysql> SELECT ST_AsText(ST_Buffer(@ls, 5, @end_strategy, @join_strategy))
  +---------------------------------------------------------------+
  | ST_AsText(ST_Buffer(@ls, 5, @end_strategy, @join_strategy))   |
  +---------------------------------------------------------------+
  | POLYGON((5 5,5 10,0 10,-3.5355339059327373 8.535533905932738, |
  | -5 5,-5 0,0 0,5 0,5 5))                                       |
  +---------------------------------------------------------------+

  ST_Buffer() and Buffer() are synonyms.

• ST_Buffer_Strategy(strategy [, points_per_circle])

  This function returns a strategy byte string for use with ST_Buffer() to influence buffer computation. If any argument is NULL, the return value is NULL. If any argument is invalid, an ER_WRONG_ARGUMENTS error occurs.

  Information about strategies is available at Boost.org.

  The first argument must be a string indicating a strategy option:

  • For point strategies, permitted values are 'point_circle' and 'point_square'.

  • For join strategies, permitted values are 'join_round' and 'join_miter'.

  • For end strategies, permitted values are 'end_round' and 'end_flat'.

  If the first argument is 'point_circle', 'join_round', 'join_miter', or 'end_round', the points_per_circle argument must be given as a positive numeric value. The maximum points_per_circle value is the value of the max_points_in_geometry system variable. If the first argument is 'point_square' or 'end_flat', the points_per_circle argument must not be given or an ER_WRONG_ARGUMENTS error occurs.

  For examples, see the description of ST_Buffer().

• ST_ConvexHull(g)

  Returns a geometry that represents the convex hull of the geometry value g. If the argument is NULL, the return value is NULL.

  This function computes a geometry's convex hull by first checking whether its vertex points are colinear. The function returns a linear hull if so, a polygon hull otherwise. This function processes geometry collections by extracting all vertex points of all components of the collection, creating a MultiPoint value from them, and computing its convex hull. If the argument is an empty geometry collection, the return value is NULL.

  mysql> SET @g = 'MULTIPOINT(5 0,25 0,15 10,15 25)';
  mysql> SELECT ST_AsText(ST_ConvexHull(ST_GeomFromText(@g)));
  +-----------------------------------------------+
  | ST_AsText(ST_ConvexHull(ST_GeomFromText(@g))) |
  +-----------------------------------------------+
  | POLYGON((5 0,25 0,15 25,5 0))                 |
  +-----------------------------------------------+

  ST_ConvexHull() and ConvexHull() are synonyms.

• ST_Difference(g1, g2)

  Returns a geometry that represents the point set difference of the geometry values g1 and g2. If any argument is NULL, the return value is NULL.

  mysql> SET @g1 = Point(1,1), @g2 = Point(2,2);
  mysql> SELECT ST_AsText(ST_Difference(@g1, @g2));
  +------------------------------------+
  | ST_AsText(ST_Difference(@g1, @g2)) |
  +------------------------------------+
  | POINT(1 1)                         |
  +------------------------------------+

• ST_Intersection(g1, g2)

  Returns a geometry that represents the point set intersection of the geometry values g1 and g2. If any argument is NULL, the return value is NULL.

  mysql> SET @g1 = ST_GeomFromText('LineString(1 1, 3 3)');
  mysql> SET @g2 = ST_GeomFromText('LineString(1 3, 3 1)');
  mysql> SELECT ST_AsText(ST_Intersection(@g1, @g2));
  +--------------------------------------+
  | ST_AsText(ST_Intersection(@g1, @g2)) |
  +--------------------------------------+
  | POINT(2 2)                           |
  +--------------------------------------+

• ST_SymDifference(g1, g2)

  Returns a geometry that represents the point set symmetric difference of the geometry values g1 and g2, which is defined as:

  g1 symdifference g2 := (g1 union g2) difference (g1 intersection g2)

  Or, in function call notation:

  ST_SymDifference(g1, g2) = ST_Difference(ST_Union(g1, g2), ST_Intersection(g1, g2))

  If any argument is NULL, the return value is NULL.

  mysql> SET @g1 = ST_GeomFromText('MULTIPOINT(5 0,15 10,15 25)');
  mysql> SET @g2 = ST_GeomFromText('MULTIPOINT(1 1,15 10,15 25)');
  mysql> SELECT ST_AsText(ST_SymDifference(@g1, @g2));
  +---------------------------------------+
  | ST_AsText(ST_SymDifference(@g1, @g2)) |
  +---------------------------------------+
  | MULTIPOINT((1 1),(5 0))               |
  +---------------------------------------+

• ST_Union(g1, g2)

  Returns a geometry that represents the point set union of the geometry values g1 and g2. If any argument is NULL, the return value is NULL.

  mysql> SET @g1 = ST_GeomFromText('LineString(1 1, 3 3)');
  mysql> SET @g2 = ST_GeomFromText('LineString(1 3, 3 1)');
  mysql> SELECT ST_AsText(ST_Union(@g1, @g2));
  +--------------------------------------+
  | ST_AsText(ST_Union(@g1, @g2))        |
  +--------------------------------------+
  | MULTILINESTRING((1 1,3 3),(1 3,3 1)) |
  +--------------------------------------+