Enabling 3D Topological Analysis for Building Models with Boundary Representation

Abstract

D topological analysis for building models can remarkably facilitate construction planning in detecting construction activity interferences and deriving partial building models based on topological and locational constraints to meet the demands from team collaboration and task distribution. A widely used 3D topology framework is the 9-Intersection-Model (9-IM) that describes two spatial objects' topological relationship by identifying intersects between their exterior, boundary, and interior. However, some existing building models using Boundary representation (B-rep) (i.e. CAD) do not naturally carry information about each 3D object's exterior, boundary, and interior and thus, challenge arises in topological analysis for building models. Most collision detection algorithms only detect whether two 3D objects intersect with each other, but do not support the analysis of detailed topological relationships. This study presents a Vertex Examination Method (VEM) that enables a full range of 3D topological analyses for building models with boundary representation, using the Minkowski-sum calculation. Each vertex of a 3D object is examined by conducting Minkowski-sum with the volume of another 3D object to identify their vertex-volume relationship. The topological relationship between two 3D objects can be determined based on the vertex-volume relationship pattern. This method complements the 3D collision detection by enabling 3D topological analysis between any 3D objects with boundary representation. It is expected to benefits many construction planning tasks, such as site layout, workspace management, and scheduling, by facilitating analytical reasoning and operation on building models. At last, the method limitations and the potential to extend to 4D topological analysis are discussed.