Using a B-Rep Structure to Query 9-Intersection Topological Relationships in 3D GIS – Reviewing the Approach and Improving Performance

A key component of a three-dimensional Geographical Information System (3D GIS) toolkit is the ability to identify binary (between two objects) topological relationships. These include adjacency (are objects next to each other), containment (is one within another) and intersection (do they interact in any way). Determining such relationships allows the GIS to answer questions such as "what is directly underneath this building?" and "if a tunnel is dug here, what rock types will be cut?" Frameworks are used to fully list the possible relationships between objects and the prevalent approach to the determination of such relationships in 3D GIS takes advantage of structures based on Boundary Representation (B-Rep). The first part of this paper thus presents a review of the 9-Intersection Framework and the use of B-Rep in 3D GIS. The second part of the paper outlines modifications to a B-Rep structure to improve binary relationship query performance, particularly relevant when the increasing size of 3D datasets is considered. An alternative structure is proposed to overcome limitations when using standard B-Rep. Tests using both structures show that the modified structure is between 11 and 15 times faster, and the paper concludes by identifying additional features of the modified structure and suggesting further research into its use.

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