Implementing Metric Operators of a Spatial Query Language for 3D Building Models: Octree and B-Rep Approaches

Abstract

A Spatial Query Language for Building Information Models enables the spatial analysis of buildings and the extraction of partial models that fulfill certain spatial constraints. Among other features, the developed spatial query language includes metric operators, i.e. operators that reflect distance relationships between spatial objects, such as mindist, maxdist, isCloser and isFarther. The paper presents formal definitions of the semantics of these operators by using point set theory notation. It further describes two possible implementation methods: the first one is based on a discrete representation of the operands' geometry by means of the hierarchical, space-partitioning data structure octree. The octree allows for the application of recursive algorithms that successively increase the discrete resolution of the spatial objects employed and thereby enables the user to trade-off between computational effort and the required accuracy. By contrast, the second approach uses the exact boundary representation (B-Rep) of both spatial objects resulting in precise distance measurements. Here the bounding facets of each operand are indexed by a so-called axis-aligned bounding boxes tree (AABB tree). The algorithm uses the AABB-tree structure to identify candidate pairs of facets, for which an exact but expensive distance algorithm is employed.

Query Support for BIMs using Semantic and Spatial Conditions

“…The octree-based implementation of the spatial operators is discussed in detail in (Borrmann, Schraufstetter, & Rank, 2009), , and (Borrmann & Rank, 2009a). Here we will only give an overview.…”

Operations on network-based space layouts for modeling multiple space views of buildings

“…A spatial query language developed by Borrmann et al [28][29][30] supports queries on implicit topological, directional, and metric spatial relations between objects. The language is designed as an extension of SQL.…”

The PDE framework Peano applied to fluid dynamics: an efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids

“…These grids stem from k-spacetrees which are a generalisation of the well-known quad-and octree idea looking back to a long tradition in computational sciences and engineering [8,22,25] and are more and more frequently used for efficient implementations of computational methods in data management, computer graphics, engineering, and numerical simulation ( [2,3,5,17,18,32] and references therein). To construct a grid for an arbitrary computational domain, we embed the domain into a hypercube.…”