Three dimensional compact abstract cell complexes topological data structure for buildings in CityGML

Abstract

As the significance of visualising objects in three dimensional is now recognised, most city modelling approaches support 3D primitives in the construction (3D) of objects and visualisation. Although the visualisation of city models is in 3D, the topological information maintained remains in two dimensional (2D). This hinders the 3D model to serve its full potential, as the topological information that gives meaning to the objects is not preserved explicitly. The support of 3D topology is crucial for 3D spatial analysis that requires connectivity information and adjacencies in order to produce accurate output in 3D. This research investigates the implementation of a 3D topological model specifically using the Compact Abstract Cell Complexes (CACC) topological data structure for preserving the topological information of buildings in City Geographic Markup Language (CityGML). As the international standard for city modelling, the topological component of CityGML is in 2D via the simple topology-incidence. The use of the simple topology-incidence mechanism within CityGML allows only explicitly stored surfaces can be referenced. This then brings up the issue of inconsistent visualisation which is usually resolved by modelling the two buildings with two separate surfaces representing the common surface. However, the connectivity information between the two connected buildings are not preserved in CityGML as they do not share the same explicitly stored surface. Three objectives were established for the study namely to determine the specifications of a topological data structure for preserving topological information of buildings in CityGML, to implement a topological structure for buildings in CityGML that supports connectivity queries and adjacency analyses for city modelling, and to validate the proposed topological data structure in terms of geometric and topological properties in comparison to the existing CityGML topology mechanism. Several tasks were carried out to complete this research, including extraction of geometrical properties from CityGML, generation of topological links, adjacency analysis using topological information, and visualisation of 3D model and adjacency analysis results. The absence of a comprehensive topological model within CityGML made it necessary to use the geometric properties of the buildings in CityGML as a stand-in model to extract the topological properties that would subsequently be the basis for generating topological links. The CACC topological model preserves topological information by building topological links where points are connected to build alpha-0 links (1D lines), alpha-0 links are connected to build alpha-1 links (2D surfaces), alpha-1 links are connected to build alpha-2 links (3D volumes) and alpha-3 links represent the connectivity between 3D buildings. This allows connectivity between elements of different dimension as any link can be decomposed to its related lower dimension elements. Next, by implementing CACC topological model, the connectivity information for two buildings that are connected but modelled with two separate surfaces can be preserved. The support of topological information via the CACC topological model also allows the seamless execution of adjacency queries between building elements, including elements of different dimensions.