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A model for representing topological relations between lines considering metric details

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Abstract

A topological relation may be described by different words, and the significance of topological relation models lies in clarifying the semantics of topological relations among different users. Metric details beyond topological relations can help enhance topological relations with qualitative metric information. Although considerable research has been conducted to study topological relation models and metric details, further work is required to consider detailed metrics for topological relation models between lines. Both simple line and nonsimple line are defined, and topological relations for both simple and nonsimple lines have been studied in this research. Metric details for line-line topological relations are elaborated. A topological relation model between lines considering metric details (TRM-MD), including the length ratio and the number-of-endpoints ratio, is proposed in this article. A total of 76 topological relations represented by the TRM-MD and corresponding geometric interpretation is shown, and the inverse relations between these topological relations are also presented. The relationships between the TRM-MD and other topological relation models are discussed. A case study is designed, and the topological relations between bus routes represented by the 9IM, DE-9IM, and TRM-MD are shown to verify the validity of the TRM-MD. The results show the following: (1) both topological relations and metric details can be distinguished by the TRM-MD, and (2) the TRM-MD can be converted to the 9IM and DE-9IM without additional calculations.

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Acknowledgements

This research was jointly supported by the Chongqing Social Science Planning Project (No. 2020PY28) and National Natural Science Foundation of China (No. 41830648). We would like to thank the editors and anonymous referees for their constructive comments.

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Authors and Affiliations

  1. Chongqing Jinfo Mountain Karst Ecosystem National Observation and Research Station, School of Geographical Sciences, Southwest University, Chongqing, 400715, China

    Jingwei Shen, Dongzhe Zhao, Kaifang Shi & Mingguo Ma

  2. Chongqing Engineering Research Centre for Remote Sensing Big Data Application, School of Geographical Sciences, Southwest University, Chongqing, 400715, China

    Jingwei Shen, Dongzhe Zhao, Kaifang Shi & Mingguo Ma

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  1. Jingwei Shen
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  2. Dongzhe Zhao
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  3. Kaifang Shi
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Correspondence to Jingwei Shen.

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Shen, J., Zhao, D., Shi, K. et al. A model for representing topological relations between lines considering metric details. J Geogr Syst 23, 407–424 (2021). https://doi.org/10.1007/s10109-021-00355-5

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  • DOI: https://doi.org/10.1007/s10109-021-00355-5

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