A Robustness Study for the Extraction of Watertight Volumetric Models from Boundary Representation Data

Abstract

Geometrically induced topology plays a major role in applications such as simulations, navigation, spatial or spatio-temporal analysis and many more. This article computes geometrically induced topology useful for such applications and extends previous results by presenting the unpublished used algorithms to find inner disjoint (d+1)-dimensional simplicial complexes from a set of intersecting d-dimensional simplicial complexes which partly shape their B-Reps (Boundary Representations). CityGML has been chosen as the input data format for evaluation purposes. In this case, the input data consist of planar segment complexes whose triangulated polygons serve as the set of input triangle complexes for the computation of the tetrahedral model. The creation of the volumetric model and the computation of its geometrically induced topology is partly parallelized by decomposing the input data into smaller pices. A robustness analysis of the implementations is given by varying the angular precision and the positional precision of the epsilon heuristic inaccuracy model. The results are analysed spatially and topologically, summarised and presented. It turns out that one can extract most, but not all, volumes and that the numerical issues of computational geometry produce failures as well as a variety of outcomes.