12.17.9.1 Spatial Relation Functions That Use Object Shapes

The OpenGIS specification defines the following functions to test the relationship between two geometry values g1 and g2, using precise object shapes. The return values 1 and 0 indicate true and false, respectively, except for ST_Distance(), which returns distance values.

ST_Contains(g1, g2)
Returns 1 or 0 to indicate whether g1 completely contains g2. This tests the opposite relationship as ST_Within().
Crosses(g1, g2)
ST_Crosses() and Crosses() are synonyms. For more information, see the description of ST_Crosses().
ST_Crosses(g1, g2)
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.
This function returns 1 or 0 to indicate whether g1 spatially crosses g2. If g1 is a Polygon or a MultiPolygon, or if g2 is a Point or a MultiPoint, the return value is NULL.
ST_Crosses() and Crosses() are synonyms.
ST_Disjoint(g1, g2)
Returns 1 or 0 to indicate whether g1 is spatially disjoint from (does not intersect) g2.

ST_Distance(g1, g2)

Returns the distance between g1 and g2.

mysql> SET @g1 = Point(1,1);
mysql> SET @g2 = Point(2,2);
mysql> SELECT ST_Distance(@g1, @g2);
+-----------------------+
| ST_Distance(@g1, @g2) |
+-----------------------+
|    1.4142135623730951 |
+-----------------------+

ST_Equals(g1, g2)

Returns 1 or 0 to indicate whether g1 is spatially equal to g2.

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_Intersects(g1, g2)
Returns 1 or 0 to indicate whether g1 spatially intersects g2.
ST_Overlaps(g1, g2)
Two geometries spatially 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 g1 spatially overlaps g2.
ST_Touches(g1, g2)
Two geometries spatially 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 g1 spatially touches g2.
ST_Touches() and Touches() are synonyms.
ST_Within(g1, g2)
Returns 1 or 0 to indicate whether g1 is spatially within g2. This tests the opposite relationship as ST_Contains().
Touches(g1, g2)
ST_Touches() and Touches() are synonyms. For more information, see the description of ST_Touches().