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MySQL 5.5 Reference Manual
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Excerpts from this Manual 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.

  • 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.

  • 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.