A framework for evaluating 3D topological relations based on a vector data model

3D topological relations are commonly used for testing or imposing the existence of desired properties between objects of a dataset, such as a city model. Currently available GIS systems usually provide a limited 3D support which usually includes a set of 3D spatial data types together with few operations and predicates, while limited or no support is generally provided for 3D topological relations. Therefore, an important problem to face is how such relations can be actually implemented by using the constructs already provided by the available systems. In this paper, we introduce a generic 3D vector model which includes an abstract and formal description of the 3D spatial data types and of the related basic operations and predicates that are commonly provided by GIS systems. Based on this model, we formally demonstrate how these limited sets of operations and predicates can be combined with 2D topological relations for implementing 3D topological relations.