Using geometrical and topological modeling approaches in building information modeling

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 topological building modeling based on relational complexes, an approach based on Algebraic Topology and the Relational Data Model. To make these complexes suitable for building modeling it was necessary to extend them by geometric properties. Finally, the paper depicts an advantageous application of cell complex-based modeling: 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 fiber product.