Impact of data representation rules on the robustness of topological relation evaluation

A spatial object is characterized not only by its geometric extents, but also by the spatial relations existing with its surrounding objects. An important kind of spatial relations is represented by topological relations. Many models have been defined in literature for formalizing the semantics of topological relations between spatial objects in the Euclidean 2D and 3D space [3, 4, 7]. Nevertheless, when these relations are evaluated in available systems many robustness problems can arise, which are essentially related to the discrete representations adopted by such systems. In a Spatial Data Infrastructure (SDI) the perturbations introduced by the exchange of data between different systems can increase the robustness problems. This paper deals with a set of rules for the representation of spatial datasets which allow to evaluate topological relations in a robust way using existing systems. These rules are well-known and described in literature and are based on a few basic assumptions on the system behavior which are fulfilled by today's systems. The main contribution of this paper is to determine in detail which rules are sufficient in order to make each topological relation robust; it turns out that the rules depend not only on the topological relation being considered, but also on the geometric types of the involved geometries and on the dimension of the space in which they are embedded, thus giving rise to a very large number of possible combinations. The paper analyses the topological relations and a significant subset of the geometric types defined in the most recent version of the Simple Feature Access (SFA) model published by OGC, considering both a 2D and a 3D space. The extension of the work to the types which have been left out can be done using the same concepts and methodology.