Representing Topological Relationships Among Heterogeneous Geometry-Collection Features

Topological relationships between two spatial features represent important knowledge in Geographical Information Systems (GIS). In the last few years, many models that represent topological relationships have been proposed. But these models cannot represent the topological relationships between heterogeneous geometrycollection features, which are composed of different dimensional geometries. In this paper, the formal definition of regular heterogeneous geometrycollection and regularization rules are given. Based on the spatial model, two methods for representing topological relationships between these complex features are proposed. The first method is Dimensionally 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 between components of these complex features. The advantage of DE-9IMBC is that a large number of different topological relationships can be checked. The second method extends the definitions of topological relationships in Open Geodata Interoperability Specification (OpenGIS), and redefines the seven named topological relationships: {Disjoint, Touches, Within, Crosses, Overlaps, Contains and Equal}, to represent the topological relationships between heterogeneous geometrycollection features. It is proven that the seven extended topological relationships are complete and mutually exclusive, and they are suitable for being embedded in spatial query languages.