Topological Spatial Relations Based on Components and Dimensions of
Set Intersections
Robert Franzosa and Max Egenhofer
Abstract
The notion of topological spatial relations is introduced.
It corresponds to the topological type of a pair of intersecting
sets in a topological space. The previously introduced
4-intersection (boundary-boundary, interior-interior,
boundary-interior, and interior-interior), a topological invariant
of topological spatial relations, is further refined by considering
the number of components and the dimension of each component in
each intersection in the 4-intersection. Properties of these
invariants are examined. We show how the topological spatial
relations between two 2-disks in the plane can be classified using
these invariants.