| Abstract: | Topological relationships between two spatial features represent important knowledge in Geograph-
ical 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 geome-
trycollection 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 Dimension-
ally 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 topo-
logical 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. |
