Abstract
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.
Highlights
Spatial data models that are designed for the purpose of analysis beyond mere visualisation need the following properties: correctness, consistency.Correctness refers here to correctness of geometry and of 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
As geometry itself has an underlying topology, it follows that, by design, CityGML does not guarantee the absence of contradictions between the topology coming from geometry and its topological model
Summary
Spatial data models that are designed for the purpose of analysis beyond mere visualisation need the following properties: correctness, consistency.Correctness refers here to correctness of geometry and of topology. Spatial data models that are designed for the purpose of analysis beyond mere visualisation need the following properties:. If data are stored redundantly, consistency issues arise. Storing data without redundancy does not guarantee consistency. CityGML has a geometry model and a separate topology model. As geometry itself has an underlying topology, it follows that, by design, CityGML does not guarantee the absence of contradictions between the topology coming from geometry and its topological model. It is the scope of this article to exhibit the carelessness with respect to this kind of topological consistency when CityGML is used for modelling spatial data
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