ST_Crosses(g1, g2)

The term spatially crosses denotes a spatial relation between two given
geometries that has the following properties:

o The two geometries intersect.

o Their intersection results in a geometry that has a dimension that is
  one less than the maximum dimension of the two given geometries.

o 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.

As of MySQL 5.7.5, this function returns 0 if called with an
inapplicable geometry argument type combination. For example, it
returns 0 if the first argument is a Polygon or MultiPolygon and/or the
second argument is a Point or MultiPoint.

Returns 1 if g1 spatially crosses g2. Returns NULL if g1 is a Polygon
or a MultiPolygon, or if g2 is a Point or a MultiPoint. Otherwise,
returns 0.

This function returns 0 if called with an inapplicable geometry
argument type combination. For example, it returns 0 if the first
argument is a Polygon or MultiPolygon and/or the second argument is a
Point or MultiPoint.

URL: http://dev.mysql.com/doc/refman/5.7/en/spatial-relation-functions-object-shapes.html

