A Critical Comparison of the 4-Intersection and 9-Intersection
Models for Spatial Relations: Formal Analysis
Max Egenhofer, Jayant Sharma, and David Mark
Abstract
Two formalisms for binary topological spatial relations are
compared for their expressive power. The 4-intersection
considers the two objects' interiors and boundaries and analyzes
the intersections of these four object parts for their content
(i.e., emptiness and non-emptiness). The 9-intersection adds
to the 4-intersection the intersections with the two
objectsÕ complements. The major results are (1) for objects
with co-dimension 0, the 4-intersection and the 9-intersection with
the content invariant provide the same results; and (2) for objects
with co-dimension > 0, the 9-intersection with the content
invariant provides more details than the 4-intersection. These
additional details are crucial to determine when two objects are
equal. It is also demonstrated that the additional details can
provide crucial information when specifying the semantics of
spatial relations in GIS query languages.
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