Representing Topological Relationships for 3-Dimensional Spatial Features

One of the fundamental components important to the analysis of spatial objects is to represent topological relationships between spatial features. Users of geographic information systems retrieve a lot of objects from spatial database and analyze their condition by means of topological relationships. The existing methods that represent these relationships have the disadvantage that they have limited information in $R^2$. In this paper, we represent and define the topological relationships between 3-dimensional spatial objects using the several representing methods of 2-dimensional features. We use the diverse representing methods, which include the 4-, 9-intersection, dimension extended and calculus-based method. Furthermore, we discuss OGC's topological relationships and operators for 3-dimensional spatial data.