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MySQL 9.1 Reference Manual  / ...  / Functions and Operators  / Spatial Analysis Functions  / Functions That Test Spatial Relations Between Geometry Objects  /  Spatial Relation Functions That Use Minimum Bounding Rectangles

14.16.9.2 Spatial Relation Functions That Use Minimum Bounding Rectangles

MySQL provides several MySQL-specific functions that test the relationship between minimum bounding rectangles (MBRs) of two geometriesg1 andg2. The return values 1 and 0 indicate true and false, respectively.

The MBR (also known as the bounding box) for a two-dimensional geometry is the smallest rectangle which holds all points in the geometry, and so encloses the area between its greatest extents in both coordinate directions. In other words, it is the rectangle bounded by the points(min(x), min(y)),(min(x), max(y)),(max(x), max(y)), and(max(x), min(y)), wheremin() andmax() represent the geometry's minimum and maximum x-coordinate or y-coordinate, respectively.

When speaking of relationships between geometries, it is important to distinguish between containment and covering, as described here:

  • A geometryg1contains another geometryg2 if and only if all points ing2 are also ing1, and their boundaries do not intersect. That is, all points(a, b) ing2 must satisfy the conditionsmin(x) < a < max(x) andmin(y) < b < max(y). In this case,ST_Contains(g1,g2) andMBRContains(g1,g2) both return true, as doesST_Within(g2,g1).

  • We say thatg1coversg2 if all points ing2 are also ing1, including any boundary points. That is, all points(a, b) ing2 must satisfy the conditionsmin(x) <= a <= max(x) andmin(y) <= b <= max(y). In this case,MBRCovers(g1,g2) andMBRCoveredBy(g2,g1) both return true.

Let us define a rectangleg1 and pointsp1,p2, andp3 using the SQL statements shown here:

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)');

g1 contains and coversp1;p1 is entirely withing1 and does not touch any of its boundaries, as we can see from theSELECT statement shown here:

mysql> SELECT    ->   ST_Contains(@g1, @p1), ST_Within(@p1, @g1),    ->   MBRContains(@g1, @p1),    ->   MBRCovers(@g1, @p1), MBRCoveredBy(@p1, @g1),     ->   ST_Disjoint(@g1, @p1), ST_Intersects(@g1, @p1)\G*************************** 1. row ***************************  ST_Contains(@g1, @p1): 1    ST_Within(@p1, @g1): 1  MBRContains(@g1, @p1): 1    MBRCovers(@g1, @p1): 1 MBRCoveredBy(@p1, @g1): 1  ST_Disjoint(@g1, @p1): 0ST_Intersects(@g1, @p1): 11 row in set (0.01 sec)

Using the same query with@p2 in place of@p1, we can see thatg2 coversp2, but does not contain it, becausep2 is included in the boundary ofg2, but does not lie within its interior. (That is,min(x) <= a <= max(x) andmin(y) <= b <= max(y) are true, butmin(x) < a < max(x) andmin(y) < b < max(y) are not.)

mysql> SELECT    ->   ST_Contains(@g1, @p2), ST_Within(@p2, @g1),    ->   MBRContains(@g1, @p2),    ->   MBRCovers(@g1, @p2), MBRCoveredBy(@p2, @g1),     ->   ST_Disjoint(@g1, @p2), ST_Intersects(@g1, @p2)\G*************************** 1. row ***************************  ST_Contains(@g1, @p2): 0    ST_Within(@p2, @g1): 0  MBRContains(@g1, @p2): 0    MBRCovers(@g1, @p2): 1 MBRCoveredBy(@p2, @g1): 1  ST_Disjoint(@g1, @p2): 0ST_Intersects(@g1, @p2): 11 row in set (0.00 sec)

Executing the query—this time using@p3 rather than@p2 or@p1—shows us thatp3 is disjoint fromg1; the two geometries have no points in common, andg1 neither contains nor coversp3.ST_Disjoint(g1,p3) returns true;ST_Intersects(g1,p3) returns false.

mysql> SELECT    ->   ST_Contains(@g1, @p3), ST_Within(@p3, @g1),    ->   MBRContains(@g1, @p3),    ->   MBRCovers(@g1, @p3), MBRCoveredBy(@p3, @g1),     ->   ST_Disjoint(@g1, @p3), ST_Intersects(@g1, @p3)\G*************************** 1. row ***************************  ST_Contains(@g1, @p3): 0    ST_Within(@p3, @g1): 0  MBRContains(@g1, @p3): 0    MBRCovers(@g1, @p3): 0 MBRCoveredBy(@p3, @g1): 0  ST_Disjoint(@g1, @p3): 1ST_Intersects(@g1, @p3): 01 row in set (0.00 sec)

The function descriptions shown later in this section and inSection 14.16.9.1, “Spatial Relation Functions That Use Object Shapes” provide additional examples.

The bounding box of a point is interpreted as a point that is both boundary and interior.

The bounding box of a straight horizontal or vertical line is interpreted as a line where the interior of the line is also boundary. The endpoints are boundary points.

If any of the parameters are geometry collections, the interior, boundary, and exterior of those parameters are those of the union of all elements in the collection.

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 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 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.

These MBR functions are available for testing geometry relationships:

  • MBRContains(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangle ofg1 contains the minimum bounding rectangle ofg2. This tests the opposite relationship asMBRWithin().

    MBRContains() 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))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @g3 = ST_GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))'),    ->   @g4 = ST_GeomFromText('Polygon((5 5,5 10,10 10,10 5,5 5))'),    ->   @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    ->   MBRContains(@g1, @g2), MBRContains(@g1, @g4),    ->   MBRContains(@g2, @g1), MBRContains(@g2, @g4),    ->   MBRContains(@g2, @g3), MBRContains(@g3, @g4),    ->   MBRContains(@g3, @g1), MBRContains(@g1, @g3),    ->   MBRContains(@g1, @p1), MBRContains(@p1, @g1),    ->   MBRContains(@g1, @p1), MBRContains(@p1, @g1),    ->   MBRContains(@g2, @p2), MBRContains(@g2, @p3),    ->   MBRContains(@g3, @p1), MBRContains(@g3, @p2),    ->   MBRContains(@g3, @p3), MBRContains(@g4, @p1),    ->   MBRContains(@g4, @p2), MBRContains(@g4, @p3)\G*************************** 1. row ***************************MBRContains(@g1, @g2): 1MBRContains(@g1, @g4): 0MBRContains(@g2, @g1): 0MBRContains(@g2, @g4): 0MBRContains(@g2, @g3): 0MBRContains(@g3, @g4): 0MBRContains(@g3, @g1): 1MBRContains(@g1, @g3): 0MBRContains(@g1, @p1): 1MBRContains(@p1, @g1): 0MBRContains(@g1, @p1): 1MBRContains(@p1, @g1): 0MBRContains(@g2, @p2): 0MBRContains(@g2, @p3): 0MBRContains(@g3, @p1): 1MBRContains(@g3, @p2): 1MBRContains(@g3, @p3): 0MBRContains(@g4, @p1): 0MBRContains(@g4, @p2): 0MBRContains(@g4, @p3): 01 row in set (0.00 sec)

  • MBRCoveredBy(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangle ofg1 is covered by the minimum bounding rectangle ofg2. This tests the opposite relationship asMBRCovers().

    MBRCoveredBy() 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))');mysql> SET @g2 = ST_GeomFromText('Point(1 1)');mysql> SELECT MBRCovers(@g1,@g2), MBRCoveredby(@g1,@g2);+--------------------+-----------------------+| MBRCovers(@g1,@g2) | MBRCoveredby(@g1,@g2) |+--------------------+-----------------------+|                  1 |                     0 |+--------------------+-----------------------+mysql> SELECT MBRCovers(@g2,@g1), MBRCoveredby(@g2,@g1);+--------------------+-----------------------+| MBRCovers(@g2,@g1) | MBRCoveredby(@g2,@g1) |+--------------------+-----------------------+|                  0 |                     1 |+--------------------+-----------------------+

    See the description of theMBRCovers() function for additional examples.

  • MBRCovers(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangle ofg1 covers the minimum bounding rectangle ofg2. This tests the opposite relationship asMBRCoveredBy(). See the description ofMBRCoveredBy() for additional examples.

    MBRCovers() 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))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @p1 = ST_GeomFromText('Point(1 1)'),    ->   @p2 = ST_GeomFromText('Point(3 3)'),    ->   @p3 = ST_GeomFromText('Point(5 5)');Query OK, 0 rows affected (0.02 sec)mysql> SELECT     ->   MBRCovers(@g1, @p1), MBRCovers(@g1, @p2),     ->   MBRCovers(@g1, @g2), MBRCovers(@g1, @p3)\G*************************** 1. row ***************************MBRCovers(@g1, @p1): 1MBRCovers(@g1, @p2): 1MBRCovers(@g1, @g2): 1MBRCovers(@g1, @p3): 01 row in set (0.00 sec)

  • MBRDisjoint(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangles of the two geometriesg1 andg2 are disjoint (do not intersect).

    MBRDisjoint() 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))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @g3 = ST_GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))'),    ->   @g4 = ST_GeomFromText('Polygon((5 5,5 10,10 10,10 5,5 5))'),    ->   @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    ->   MBRDisjoint(@g1, @g4), MBRDisjoint(@g2, @g4),    ->   MBRDisjoint(@g3, @g4), MBRDisjoint(@g4, @g4),    ->   MBRDisjoint(@g1, @p1), MBRDisjoint(@g1, @p2),     ->   MBRDisjoint(@g1, @p3)\G*************************** 1. row ***************************MBRDisjoint(@g1, @g4): 1MBRDisjoint(@g2, @g4): 1MBRDisjoint(@g3, @g4): 0MBRDisjoint(@g4, @g4): 0MBRDisjoint(@g1, @p1): 0MBRDisjoint(@g1, @p2): 0MBRDisjoint(@g1, @p3): 11 row in set (0.00 sec)

  • MBREquals(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangles of the two geometriesg1 andg2 are the same.

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

    mysql> SET    ->   @g1 = ST_GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @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     ->   MBREquals(@g1, @g1), MBREquals(@g1, @g2),     ->   MBREquals(@g1, @p1), MBREquals(@g1, @p2), MBREquals(@g2, @g2),     ->   MBREquals(@p1, @p1), MBREquals(@p1, @p2), MBREquals(@p2, @p2)\G*************************** 1. row ***************************MBREquals(@g1, @g1): 1MBREquals(@g1, @g2): 0MBREquals(@g1, @p1): 0MBREquals(@g1, @p2): 0MBREquals(@g2, @g2): 1MBREquals(@p1, @p1): 1MBREquals(@p1, @p2): 0MBREquals(@p2, @p2): 11 row in set (0.00 sec)

  • MBRIntersects(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangles of the two geometriesg1 andg2 intersect.

    MBRIntersects() 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))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @g3 = ST_GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))'),    ->   @g4 = ST_GeomFromText('Polygon((5 5,5 10,10 10,10 5,5 5))'),    ->   @g5 = ST_GeomFromText('Polygon((2 2,2 8,8 8,8 2,2 2))'),    ->   @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    ->   MBRIntersects(@g1, @g1), MBRIntersects(@g1, @g2),    ->   MBRIntersects(@g1, @g3), MBRIntersects(@g1, @g4), MBRIntersects(@g1, @g5),     ->   MBRIntersects(@g1, @p1), MBRIntersects(@g1, @p2), MBRIntersects(@g1, @p3),     ->   MBRIntersects(@g2, @p1), MBRIntersects(@g2, @p2), MBRIntersects(@g2, @p3)\G*************************** 1. row ***************************MBRIntersects(@g1, @g1): 1MBRIntersects(@g1, @g2): 1MBRIntersects(@g1, @g3): 1MBRIntersects(@g1, @g4): 0MBRIntersects(@g1, @g5): 1MBRIntersects(@g1, @p1): 1MBRIntersects(@g1, @p2): 1MBRIntersects(@g1, @p3): 0MBRIntersects(@g2, @p1): 1MBRIntersects(@g2, @p2): 0MBRIntersects(@g2, @p3): 01 row in set (0.00 sec)

  • MBROverlaps(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 whether the minimum bounding rectangles of the two geometriesg1 andg2 overlap.

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

  • MBRTouches(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 whether the minimum bounding rectangles of the two geometriesg1 andg2 touch.

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

  • MBRWithin(g1,g2)

    Returns 1 or 0 to indicate whether the minimum bounding rectangle ofg1 is within the minimum bounding rectangle ofg2. This tests the opposite relationship asMBRContains().

    MBRWithin() 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))'),    ->   @g2 = ST_GeomFromText('Polygon((1 1,1 2,2 2,2 1,1 1))'),    ->   @g3 = ST_GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))'),    ->   @g4 = ST_GeomFromText('Polygon((5 5,5 10,10 10,10 5,5 5))'),    ->   @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    ->   MBRWithin(@g1, @g2), MBRWithin(@g1, @g4),    ->   MBRWithin(@g2, @g1), MBRWithin(@g2, @g4),    ->   MBRWithin(@g2, @g3), MBRWithin(@g3, @g4),    ->   MBRWithin(@g1, @p1), MBRWithin(@p1, @g1),    ->   MBRWithin(@g1, @p1), MBRWithin(@p1, @g1),    ->   MBRWithin(@g2, @p2), MBRWithin(@g2, @p3)\G*************************** 1. row ***************************MBRWithin(@g1, @g2): 0MBRWithin(@g1, @g4): 0MBRWithin(@g2, @g1): 1MBRWithin(@g2, @g4): 0MBRWithin(@g2, @g3): 1MBRWithin(@g3, @g4): 0MBRWithin(@g1, @p1): 0MBRWithin(@p1, @g1): 1MBRWithin(@g1, @p1): 0MBRWithin(@p1, @g1): 1MBRWithin(@g2, @p2): 0MBRWithin(@g2, @p3): 01 row in set (0.00 sec)