Abstract Topological Data Structure for 3D Spatial Objects

Abstract

In spatial science, the relationship between spatial objects is considered to be a vital element. Currently, 3D objects are often used for visual aids, improving human insight, spatial observations, and spatial planning. This scenario involves 3D geometrical data handling without the need for topological information. Nevertheless, in the near future, users will shift to more complex queries corresponding to the existing 2D spatial approaches. Therefore, having 3D spatial objects without having these relationships or topology is impractical for 3D spatial analysis queries. In this paper, we present a new method for creating topological information that we call the Compact Abstract Cell Complexes (CACC) data structure for 3D spatial objects. The idea is to express in the most compact way the topology of a model in 3D (or more generally in nD) without requiring the topological space to be discrete or geometric. This is achieved by storing all the atomic cycles through the models (null combinatorial homotopy classes). The main idea here is to store the atomic paths through the models as an ant experiences topology: each time the ant perceives a previous trace of pheromone, it knows it has completed a cycle. The main advantage of this combinatorial topological data structure over abstract simplicial complexes is that the storage size of the abstract cell cycles required to represent the geometric topology of a model is far lower than that for any of the existing topological data structures (including abstract simplicial cell cycles) required to represent the geometric decomposition of the same model into abstract simplicial cells. We provide a thorough comparative analysis of the storage sizes for the different topological data structures to sustain this.

Data Interoperability of Building Information Modeling and Geographic Information System in Construction Industry

“…The example analysis that GIS can be used to helps the construction project is in term of site selection, site layout, route planning, and others. Future integration can be extended by having more advance spatial approach such as embedding topologial information in the model (Löwner, 2013;Salleh and Ujang, 2018;Ujang et al, 2019) and implementing complex data structures to the models (Azri et al, 2020;Keling et al, 2017;Kremer et al, 2013;Ujang et al, 2013).…”

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

“…A topological data structure based on the B-Rep structure is the Complex Abstract Cell Complexes (CACC) data structure. The CACC data structure stores the topology of an object as an atomic cycle consisting of sub-parts of the cycle that can be navigated via deconstruction [14]. Geometries of each dimension is represented by α₀-cycles that connects 0D points to 1D edges, α₁-cycles that connects 1D edges to form 2D faces, α₂-cycles that connects faces to form 3D volumes and α₃-cycles that represents connectivity between volumes [14].…”

“…The CACC data structure stores the topology of an object as an atomic cycle consisting of sub-parts of the cycle that can be navigated via deconstruction [14]. Geometries of each dimension is represented by α₀-cycles that connects 0D points to 1D edges, α₁-cycles that connects 1D edges to form 2D faces, α₂-cycles that connects faces to form 3D volumes and α₃-cycles that represents connectivity between volumes [14]. This approach has also been made in further research and proven to be practical (see [15,16]).…”

Spatial Adjacency Analysis of Citygml Buildings via 3d Topological Data Structure

“…The XLinks mechanism as the topological component of CityGML supports a simple topology which is unable to directly retrieve topological relationships (Rook et al, 2016). The simple topology does not provide support for topological analysis such as 3D adjacencies and nearest neighbour (Ujang et al, 2019). Apart from that, the XLinks mechanism requires the common surfaces of related objects to be explicitly stored and represented as individual geometries (Li et al, 2016).…”