A model for representing topological relations between lines considering metric details

Jingwei Shen (), Dongzhe Zhao (), Kaifang Shi () and Mingguo Ma ()
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Jingwei Shen: Southwest University
Dongzhe Zhao: Southwest University
Kaifang Shi: Southwest University
Mingguo Ma: Southwest University

Journal of Geographical Systems, 2021, vol. 23, issue 3, No 5, 407-424

Abstract: 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.

Keywords: Topological relation; Metric details; Lines; C88 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10109-021-00355-5

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