Representing Topological Relationships Among HeterogeneousGeometry-Collection Features

Topological relationships between two spatial featuresrepresent important knowledge in Geographical Information Systems(GIS). In the last few years, many models that represent topologicalrelationships have been proposed. But these models cannot represent thetopological relationships between heterogeneous geometrycollectionfeatures, which are composed of different dimensional geometries. Inthis paper, the formal definition of regular heterogeneousgeometrycollection and regularization rules are given. Based on the spatialmodel, two methods for representing topologicalrelationships between these complex features are proposed. The first method isDimensionally Extended Nine-Intersection Model Based on Components(DE-9IMBC) that extends Dimensionally Extended Nine-Intersection Model(DE-9IM) and takes into account the topological relationships betweencomponents of these complex features. The advantage of DE-9IMBC is thata large number of different topological relationships can be checked.The second method extends the definitions of topological relationshipsin Open Geodata Interoperability Specification (OpenGIS), andredefines the seven named topological relationships: Disjoint,Touches, Within, Crosses, Overlaps, Contains and Equal, to representthe topological relationships between heterogeneous geometrycollectionfeatures. It is proven that the seven extended topologicalrelationships are complete and mutually exclusive, and they aresuitable for being embedded in spatial query languages.