Welcome to Francis Academic Press

Academic Journal of Engineering and Technology Science, 2024, 7(1); doi: 10.25236/AJETS.2024.070101.

Metric specification and improvement of intersection models


Qilun Xu1, Yuan Liu2

Corresponding Author:
Qilun Xu

1School of Computer Science and Engineering, Hunan University of Science and Technology, Xiangtan, 411201, China

2Mathematics Teaching and Research Group, Leiyang No. 1 Middle School, Leiyang, 421899, China


Egenhofer's intersection model for describing topological relations has a normative problem in metrics, and the inner, outer and boundary boundaries of different dimensional online objects do not conform to the definition of inner, outer and boundary based on metric-neighborhood language pairs in point set topology. Therefore, by establishing a mapping from the dimension to the lower dimension, the boundary, exterior and interior of the line object are inversely mapped in one dimension, so that the line object in the two-dimensional space still conforms to the three-part division of the metric specification. This process allows the new node degree to be used, and the resulting topological formal model is more distinguishable than other models.


GIS, Topological Relations, 9-Intersection Model, Metric Specification

Cite This Paper

Qilun Xu, Yuan Liu. Metric specification and improvement of intersection models. Academic Journal of Engineering and Technology Science (2024) Vol. 7, Issue 1: 1-7. https://doi.org/10.25236/AJETS.2024.070101.


[1] Egenhofer M, Franzosa R .Point Set Topological Spatial Relations[J]. 1991.DOI: 10. 1080/2693799108927841dx.doi.org.

[2] David M. Mark & Max J. Egenhofer (1994) Modeling Spatial Relations Between Lines and Regions: Combining Formal Mathematical Models and Human Subjects Testing, Cartography and Geographic Information Systems, 21:4, 195-212, DOI: 10.1559/152304094782540637.

[3] Deng Min, Feng Xue-zhi, Liu Wen-bao. Fundamental Problems and Research Progress in Formal Description of Topological Relations[J]. Computer Engineering and Applications, 2004, 40(1):5. DOI:10.3321/j.issn:1002-8331.2004.01.003.

[4] Deng M ,Cheng T ,Chen X ,et al.Multi-level Topological Relations Between Spatial Regions Based Upon Topological Invariants[J].Geoinformatica, 2007, 11(2):239-267.DOI:10.1007/s10707-006-0004-x.

[5] Zheng Heng, Zhou Xiaoguang. Conflict Detection of OSM Data Based on E-WID Line/Line Subdivision Topological Relationship[J]. Geoinformation World, 2020, 27(1):6. DOI:CNKI:SUN: CHRK. 0.2020-01-004.

[6] Cheng Jishu. Point-set Topology [M]. Science Press, 2008.

[7] Deng Min, Feng Xuezhao, Chen Xiaoyong. Hierarchical Model for Formalized Description of Topological Relationships between Face Targets [J]. Journal of Surveying and Mapping, 2005, 34(2):6. DOI:10.3321/j.issn:1001-1595.2005.02.010.

[8] Deng Min, Li Zhilin, Li Yongli, etc. 4-Cross Model for Describing Topological Relationships between GIS Line Targets [J]. Journal of Wuhan University (Information Science Edition), 2006. DOI:CNKI: SUN: WHCH.0.2006-11-001.

[9] Li, Jian. Research on the Topological Relationship Model Between Multiple Spatial Regions [D]. Jilin University, 2013.

[10] Chen Jun , Li Chengming , Li Zhilin & Gold CM (2000) Improving 9-intersection model by replacing the complement with voronoi region, Geo-spatial Information Science, 3:1, 1-10, DOI: 10.1007/BF02826800.

[11] Liu W , Chen J , Yan C ,et al.Model for calculating topology stable area of the plane discrete points[J].Acta Geodaetica et Cartographica Sinica[2023-12-08].DOI:10.1007/s11783-011-0280-z.

[12] Zhou Xiaoguang, Chen Fei, Chen Jun. Line/Area Topology Relationship Subdivision Method and Application Introducing Node Degree[J]. Journal of Surveying and Mapping, 2015, 44(04):445-452. , 2020, 37(10):57-63.

[13] Ivo, Düntsch, Gunther,et al.A Necessary Relation Algebra for Mereotopology[J].Studia Logica, 2001.DOI:10.1023/A:1013892110192.

[14] Clementini, E., Felice, P.D., & Oosterom, P.V. (1993). A Small Set of Formal Topological Relationships Suitable for End-User Interaction. International Multi-Conference on Systems, Signals & Devices.

[15] Peipei Li. Research on fitting, parameterization and shape optimization problems in curve modeling [D]. Shandong University, 2012. DOI: CNKI: CDMD: 1.1012.461424.

[16] Jingwei Shen. Research on Description, Calculation, and Inference of Three-Dimensional Topological Relationships [D]. Nanjing Normal University, 2011. DOI: 10.7666/d.y1924372.

[17] Min Deng. Extended model of topological relationship in vector GIS: theory and method [J]. Journal of Surveying and Mapping, 2004, 33(002):188-188. DOI:10.3321/j.issn:1001-1595.2004. 02.019.