3D Spatial Queries for High-Rise Buildings Using 3D Topology Rules

3D applications and analysis for high-rise buildings require accurate 3D representation. Besides geometrical properties, topological relationships are also important in describing adjacency, containment, and connectivity information between 3D objects. Topology rules define valid topological interactions between objects. However, 2D topology rules currently implemented in spatial databases inaccurately represent 3D topological relationships due to limited 2D connectivity. This study proposes a 36IM 3D topology rule to determine 3D topological relationships between 3D objects, specifically sub-units within a high-rise building. The 36IM tested intersections between the interiors, boundaries, and exteriors of objects, whereby the highest dimension of the intersections is entered into a 3 × 3 intersection matrix. In turn, the topological relationship is determined based on logical conditions that the intersection matrix satisfies. The 36IM topology rules were implemented within an Oracle spatial database where spatial queries based on topological relationships could be executed. Five topological relationship cases were tested which includes “meets (touches)”, “disjoint”, “contains” “within (inside)” and “overlaps”. These cases are most relevant to 3D sub-units within a high-rise building as the basis for more complex spatial analysis. As a result, 3D topological relationships between 3D sub-units were able to be determined without additional storage of topological schema or data structure. The intersections could also be expressed from 0D to 3D without any object decomposition. In conclusion, 3D topological relationships provide a foundation for more complex 3D spatial analysis. These analyses are crucial especially in high-rise buildings where 3D object validity, legal boundaries, and adjacent units can be difficult to determine.