Validating a 3D topological structure of a 3D space partition

The goal of this research is to develop a 3D topological structure to represent a 3D space partition with validation functionality and support for conversions from topological to geometrical primitives. Several 3D topological structures have been presented in the past, mainly by researchers. The technical (implementation) model developed in this paper is based on the conceptual model of the ISO 19107 ‘spatial schema’ standard and consists of four topological primitives: node, edge, face, and volume, which are related to each other via their (co)boundary relationships. In our setting, only linear primitives (no curves) are supported and no isolated and dangling primitives are allowed. In our model, the rings, the shells, and the orientation play key roles within the topological structure and the functions that implement the geometrical realization. There was no formal definition of a valid 3D topological structure available and this paper presents such a definition, which is the main novel contribution. This definition is presented in three levels, where at every next level the definition is further refined such that finally a set of rules is proposed, which can be implemented unambiguously. In order to validate a 3D topological structure, the involved volumes must be valid as well as the whole structure, which means the relationships between the volumes. The rules for a valid structure have been implemented on top of Oracle Spatial and tested with artificial and real-world test data. © Springer-Verlag Berlin Heidelberg 2011 Lecture Notes in Geoinformation and Cartography 1, DOI 10.1007/978-3-642-19789-5_18, 359 S.C.M. Geertman et al. (eds.), Advancing Geoinformation Science for a Changing World, 360 Bregje Brugman, Theo Tijssen, Peter van Oosterom