Spatial Data Warehouses - Data Warehouse Systems: Design and Implementation - page 422

We describe next the topological relationships; the associated icons are
giveninFig. 11.2 and examples are shown in Fig. 11.3 .

Overlaps Contains/Within

Touches Covers/CoveredBy

Crosses

Fig. 11.3 Examples of the various topological relationships. The two objects in the
relationship are drawn in black and in gray , respectively

Intersects/Disjoint: Intersects and Disjoint are inverse relationships: When one
applies, the other does not. Two geometries are disjoint if the interior and
the boundary of one object intersects only the exterior of the other object.
Equals: A geometry equals another one if they share exactly the same set of
points.
Overlaps: Two geometries overlap if the interior of each one intersects both
the interior and the exterior of the other one.
Contains/Within: Contains and Within are symmetric relationships: a Contains
b if and only if b Within a . A geometry contains another one if the inner
object is located in the interior of the other object and the boundaries of
the two objects do not intersect.
Touches: Two geometries meet if they intersect but their interiors do not.
Covers/CoveredBy: Covers and CoveredBy are symmetric relationships: a
Covers b if and only if b CoveredBy a . A geometry covers another one
if it includes all points of the other, inner geometry. This means that the
first geometry contains the inner one, as defined previously, but without
the restriction that the boundaries of the geometries do not intersect.
Crosses: One geometry crosses another if they intersect and the dimension of
this intersection is less than the greatest dimension of the geometries.

Predicates return a Boolean value. IsEmpty determines whether a geometry
is empty. OnBorder and InInterior determine, respectively, whether a point
belongs to the boundary or the interior of another geometry.