Topological analysis of 3D building models using a spatial query language
The paper presents parts of the development of a spatial query language for building information models. Such a query language enables the spatial analysis of building information models and the extraction of partial models that fulfill certain spatial constraints. Among other features, it includes topological operators, i.e. operators that reflect the topological relationships between 3D spatial objects. The paper presents definitions of the semantics of the topological operators within, contain, touch, overlap, disjoint and equal in 3D space by using the 9-intersection model. It further describes a possible implementation of the topological operators by means of an octree-based algorithm. The recursive algorithm presented in this article relies on a breadth-first traversal of the operands’ octree representations and the application of rules that are based on the color of the octants under examination. Because it successively increases the discrete resolution of the spatial objects employed, the algorithm enables the user on the one hand to handle topological relationships in a fuzzy manner and on the other hand to trade-off between computational effort and the required accuracy. The article also presents detailed investigations on the runtime performance of the developed algorithm.