Evaluation of Topological Consistency in CityGML

Boundary representation models are data models that represent the topology of a building or city model. This leads to an issue in combination with geometry, as the geometric model necessarily has an underlying topology. In order to allow topological queries to rely on the incidence graph only, a new notion of topological consistency is introduced that captures possible topological differences between the incidence graph and the topology coming from geometry. Intersection matrices then describe possible types of topological consistency and inconsistency. As an application, it is examined which matrices can occur as intersection matrices, and how matrices from topologically consistent data look. The analysis of CityGML data sets stored in a spatial database system then shows that many real-world data sets contain many topologically inconsistent pairs of polygons. It was observed that even if data satisfy the val3dity test, they can still be topologically inconsistent. On the other hand, it is shown that the ISO 19107 standard is equivalent to our notion of topological consistency. In the case when the intersection is a point, topological inconsistency occurs because a vertex lies on a line segment. However, the most frequent topological inconsistencies seem to arise when the intersection of two polygons is a line segment. Consequently, topological queries in present CityGML data cannot rely on the incidence graph only, but must always make costly geometric computations if correct results are to be expected.