Abstract Topological Data Structure for 3D Spatial Objects
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 topolo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-02-01
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| Series: | ISPRS International Journal of Geo-Information |
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| Online Access: | https://www.mdpi.com/2220-9964/8/3/102 |
| _version_ | 1811298175461359616 |
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| author | Uznir Ujang Francesc Anton Castro Suhaibah Azri |
| author_facet | Uznir Ujang Francesc Anton Castro Suhaibah Azri |
| author_sort | Uznir Ujang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T06:16:43Z |
| format | Article |
| id | doaj.art-e2c51c58f72f4fd984c4f79ab8e787fc |
| institution | Directory Open Access Journal |
| issn | 2220-9964 |
| language | English |
| last_indexed | 2024-04-13T06:16:43Z |
| publishDate | 2019-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | ISPRS International Journal of Geo-Information |
| spelling | doaj.art-e2c51c58f72f4fd984c4f79ab8e787fc2022-12-22T02:58:49ZengMDPI AGISPRS International Journal of Geo-Information2220-99642019-02-018310210.3390/ijgi8030102ijgi8030102Abstract Topological Data Structure for 3D Spatial ObjectsUznir Ujang0Francesc Anton Castro1Suhaibah Azri2Faculty of Built Environment and Surveying, Universiti Teknologi Malaysia, Johor Bahru 81310, Johor, MalaysiaSchool of Mathematical Sciences and Information Technology Yachay Tech University, San Miguel de Urcuquí, Hacienda San José s/n, Imbabura, EcuadorFaculty of Built Environment and Surveying, Universiti Teknologi Malaysia, Johor Bahru 81310, Johor, MalaysiaIn 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.https://www.mdpi.com/2220-9964/8/3/102Compact Abstract Cell Complexes3D topology3D data structures3D GIS3D city modeling |
| spellingShingle | Uznir Ujang Francesc Anton Castro Suhaibah Azri Abstract Topological Data Structure for 3D Spatial Objects ISPRS International Journal of Geo-Information Compact Abstract Cell Complexes 3D topology 3D data structures 3D GIS 3D city modeling |
| title | Abstract Topological Data Structure for 3D Spatial Objects |
| title_full | Abstract Topological Data Structure for 3D Spatial Objects |
| title_fullStr | Abstract Topological Data Structure for 3D Spatial Objects |
| title_full_unstemmed | Abstract Topological Data Structure for 3D Spatial Objects |
| title_short | Abstract Topological Data Structure for 3D Spatial Objects |
| title_sort | abstract topological data structure for 3d spatial objects |
| topic | Compact Abstract Cell Complexes 3D topology 3D data structures 3D GIS 3D city modeling |
| url | https://www.mdpi.com/2220-9964/8/3/102 |
| work_keys_str_mv | AT uznirujang abstracttopologicaldatastructurefor3dspatialobjects AT francescantoncastro abstracttopologicaldatastructurefor3dspatialobjects AT suhaibahazri abstracttopologicaldatastructurefor3dspatialobjects |