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What is Complex, Topological

Handbook of Research on Building Information Modeling and Construction Informatics: Concepts and Technologies
A topological space which has an algebraic complex associated in a straightforward manner. Then the boundary of an element is considered to “circumscribe” that element (as a cycle): For example, the surface of a body circumscribes its volume.
Published in Chapter:
Basic Topological Notions and their Relation to BIM
Norbert Paul (Technische Universität München, Germany)
DOI: 10.4018/978-1-60566-928-1.ch019
Abstract
Each building sets up a topological space in the mathematical sense. Therefore every Building Information Model (BIM) has to store topological information. Such information can be found, for example, in the IFC (Liebich et al. 2005). The volume modelling part of the IFC uses a so-called ‘IfcTopologyResource’ which is a topological model on the local scope of each single building element. At a global scope, the ‘IfcRelConnects’ class and its subclasses are used for the connectivity of the building parts. This chapter presents a generalizing concept which handles both “local” and “global” connectivity information in a common way and provides means to mutually relate them.
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