Geometrical and topological approaches in building

SUMMARY: This paper presents concepts for dealing with topological information in building information models. On the one hand, it shows how to derive topological relationships from "traditional" building models consisting of unconnected B-Rep bodies by means of geometric processing algorithms. On the other hand, it discusses the capabilities of building modelling based on topological concepts. This approach combines relational database design principles with algebraic and point set topology and shows how complexes-in particular cw-complexes-and topological spaces can be stored in relational databases. To make complexes suitable for building modelling it is necessary to extend them by geometric properties. Finally, the paper depicts an advantageous application of cell-complex-based modelling: the separation of the building model into an abstract specification of building entities (sketch), a collection of possible concrete realizations of such sketch entities (details), and a specification of the details used by sketch entities. Then a working drawing results from the spatial version of the relational operator inner equi-join, the so-called fibre product. The first section of this paper introduces into the problem and into current modelling concepts. Section 2 discusses geometry-based modelling whereas the following sections present the topological approach. First, Section 3 takes a topological view on buildings and then Section 4 discusses the corresponding data models. At Section 5 geometry is re-introduced. Section 6 presents the above mentioned application and, together with the subsequent conclusion, advocates the topological viewpoint.