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A model for representing topological relations between lines considering metric details

Author

Listed:
  • Jingwei Shen

    (Southwest University
    Southwest University)

  • Dongzhe Zhao

    (Southwest University
    Southwest University)

  • Kaifang Shi

    (Southwest University
    Southwest University)

  • Mingguo Ma

    (Southwest University
    Southwest University)

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.

Suggested Citation

  • Jingwei Shen & Dongzhe Zhao & Kaifang Shi & Mingguo Ma, 2021. "A model for representing topological relations between lines considering metric details," Journal of Geographical Systems, Springer, vol. 23(3), pages 407-424, July.
    • Handle: RePEc:kap:jgeosy:v:23:y:2021:i:3:d:10.1007_s10109-021-00355-5
    DOI: 10.1007/s10109-021-00355-5
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    References listed on IDEAS

    as
    1. Jingwei Shen & Kaifang Shi & Min Chen, 2020. "Topological relations between directed line segments in the cyclic space," Journal of Geographical Systems, Springer, vol. 22(4), pages 497-518, October.
    2. A. Formica & M. Mazzei & E. Pourabbas & M. Rafanelli, 2017. "Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {DLP}$$ DLP -intersection matrix," Journal of Geographical Systems, Springer, vol. 19(2), pages 175-196, April.
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    1. Jingwei Shen & Kaifang Shi & Min Chen, 2020. "Topological relations between directed line segments in the cyclic space," Journal of Geographical Systems, Springer, vol. 22(4), pages 497-518, October.

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