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.

一个拓扑关系可以用不同的词来描述，拓扑关系模型的意义在于阐明了不同用户之间拓扑关系的语义。拓扑关系之外的度量细节可以帮助增强具有定性度量信息的拓扑关系。尽管已经进行了大量研究来研究拓扑关系模型和度量细节，但还需要进一步的工作来考虑线之间拓扑关系模型的详细度量。定义了单线和非单线，研究了单线和非单线的拓扑关系。详细阐述了线-线拓扑关系的度量细节。考虑度量细节的线之间的拓扑关系模型（TRM-MD），包括长度比和端点数比，本文提出。共显示了由 TRM-MD 表示的 76 种拓扑关系和相应的几何解释，并给出了这些拓扑关系之间的逆关系。讨论了 TRM-MD 和其他拓扑关系模型之间的关系。设计了一个案例研究，并展示了以 9IM、DE-9IM 和 TRM-MD 为代表的公交路线之间的拓扑关系，以验证 TRM-MD 的有效性。结果表明：（1）TRM-MD可以区分拓扑关系和度量细节，（2）TRM-MD可以转换为9IM和DE-9IM而无需额外计算。共显示了由 TRM-MD 表示的 76 种拓扑关系和相应的几何解释，并给出了这些拓扑关系之间的逆关系。讨论了 TRM-MD 和其他拓扑关系模型之间的关系。设计了一个案例研究，并展示了以 9IM、DE-9IM 和 TRM-MD 为代表的公交路线之间的拓扑关系，以验证 TRM-MD 的有效性。结果表明：（1）TRM-MD可以区分拓扑关系和度量细节，（2）TRM-MD可以转换为9IM和DE-9IM而无需额外计算。共显示了由 TRM-MD 表示的 76 种拓扑关系和相应的几何解释，并给出了这些拓扑关系之间的逆关系。讨论了 TRM-MD 和其他拓扑关系模型之间的关系。设计了一个案例研究，并展示了以 9IM、DE-9IM 和 TRM-MD 为代表的公交路线之间的拓扑关系，以验证 TRM-MD 的有效性。结果表明：（1）TRM-MD可以区分拓扑关系和度量细节，（2）TRM-MD可以转换为9IM和DE-9IM而无需额外计算。讨论了 TRM-MD 和其他拓扑关系模型之间的关系。设计了一个案例研究，并展示了以 9IM、DE-9IM 和 TRM-MD 为代表的公交路线之间的拓扑关系，以验证 TRM-MD 的有效性。结果表明：（1）TRM-MD可以区分拓扑关系和度量细节，（2）TRM-MD可以转换为9IM和DE-9IM而无需额外计算。讨论了 TRM-MD 和其他拓扑关系模型之间的关系。设计了一个案例研究，并展示了以 9IM、DE-9IM 和 TRM-MD 为代表的公交路线之间的拓扑关系，以验证 TRM-MD 的有效性。结果表明：（1）TRM-MD可以区分拓扑关系和度量细节，（2）TRM-MD可以转换为9IM和DE-9IM而无需额外计算。