How to achieve consistency for 3D city models

Consistency is a crucial prerequisite for a large number of relevant applications of 3D city models, which have become more and more important in GIS. Users need efficient and reliable consistency checking tools in order to be able to assess the suitability of spatial data for their applications. In this paper we provide the theoretical foundations for such tools by defining an axiomatic characterization of 3D city models. These axioms are effective and efficiently supported by recent spatial database management systems and methods of Computational Geometry or Computer Graphics. They are equivalent to the topological concept of the 3D city model presented in this paper, thereby guaranteeing the reliability of the method. Hence, each error is detected by the axioms, and each violation of the axioms is in fact an error. This property, which is proven formally, is not guaranteed by existing approaches. The efficiency of the method stems from its locality: in most cases, consistency checks can safely be restricted to single components, which are defined topologically. We show how a 3D city model can be decomposed into such components which are either topologically equivalent to a disk, a sphere, or a torus, enabling the modeling of the terrain, of buildings and other constructions, and of bridges and tunnels, which are handles from a mathematical point of view. This enables a modular design of the axioms by defining axioms for each topological component and for the aggregation of the components. Finally, a sound, consistent concept for aggregating features, i.e. semantical objects like buildings or rooms, to complex features is presented.