Max Egenhofer Second Symposium on Large Spatial Databases, Zurich, Switzerland,
O. Gunther and H.-J. Schek (eds.), Lecture Notes in Computer Science, Vol. 525, Springer-Verlag, pp. 143-160, August 1991.
Abstract
A new formalism is presented to reason about topological relations.
It is applicable as a foundation for an algebra over topological
relations. The formalism is based upon the nine intersections of
boundaries, interiors, and complements between two objects.
Properties of topological relations are determined by analyzing the
nine intersections to detect, for instance, symmetric topological
relations and pairs of converse topological relations. Based upon
the standard rules for the transitivity of set inclusion, the
intersections are then matched with the intersections of the eight
fundamental topological relations, giving an interpretation to the
composition of topological relations. The result of this study is
the complete set of binary topological relations which result from
the composition of two topological relations between n-dimensional
point sets embedded in an n-dimensional space. While the combined
topological relations are unique for some compositions, more than
half of all possible compositions are underdetermined. Geometric
prototypes are shown for the 2-dimensional case.
Max Egenhofer