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.
Highlights
Recent developments in spatial science have heightened the need for three-dimensional (3D) city modeling
We present a new method for creating topological information called the Compact Abstract Cell Complexes (CACC) data structure for 3D spatial objects such as 3D city models
The advantages can be seen in the connectivity, the storage cost, the adjacency of neighboring entities, and the traversal between connected components
Summary
Recent developments in spatial science have heightened the need for three-dimensional (3D) city modeling. We present a new method for creating topological information called the Compact Abstract Cell Complexes (CACC) data structure for 3D spatial objects such as 3D city models. This data structure introduces new solutions for minimizing 3D topological data storage, 3D object data ordering, and 3D traversal between separated connected components, and it will improve the data retrieval time by providing 3D adjacency, 3D indexing, and nearest neighbor information This can be useful for various 3D (and more generally nD) applications. The difference with the coupling entity data structure is that the partial entity data structure kept the relationship of the objects that were connected by a vertex and, as stated by [48], this data structure saves more storage cost than the Radial Edge data structure for non-manifold cell 2-complexes. DHE is consistent in storing the duality information for a single connected component
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