Crosses(g1,g2)

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.

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

URL: http://dev.mysql.com/doc/refman/5.1/en/functions-that-test-spatial-relationships-between-geometries.html

