Abstract
Directed lines are fundamental geometric elements to represent directed linear entities. The representations of their topological relations are so different from those of simple lines that they cannot be solved exactly with normal methods. In this paper, a new model based on point-set topology is defined to represent the topological relations between directed lines and simple geometries. Through the intersections between the start-points, end-points, and interiors of the directed lines and the interiors, boundaries, and exteriors of the simple geometries, this model identifies 5 cases of topological relations between directed lines and points, 39 cases of simple lines, and 26 cases of simple polygons. Another 4 cases of simple lines and one case of simple polygons are distinguished if considering the exteriors of the directed lines. All possible cases are furthermore grouped into an exclusive and complete set containing 11 named predicts. And the conceptual neighborhood graph is set up to illustrate their relationship and similarity. This model can provide a basis for natural language description and spatial query language to present the dynamic semantics of directed lines relative to the background features.
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References
Montello D R. Spatial Cognition. In: Smelser N J, Baltes P B, eds. International Encyclopedia of the Social and Behavioral Science. Oxford: Pergamon Press, 2001. 14771–14775
Kurata Y, Egenhofer M J. The Head-Body-Tail Intersection for Spatial Relations between Directed Line Segments. Berlin: Springer-Verlag, 2006. 269–286
Güting R H, Bohlen M H, Erwig M, et al. A foundation for representing and querying moving objects. ACM T Database Syst, 2000, 25(1): 1–42
Kurata Y, Egenhofer M J. Topological Relations of Arrow Symbols in Complex Diagrams. Stanford: Lecture Notes in Computer Science, 2006, 4045: 112–126
Randell D A, Cui Z, Cohn A G. A Spatial Logic Based on Regions and Connections. San Mateo: Morgan Kaufmann, 1992. 162–176
Egenhofer M J, Herring J. Categorizing binary topological relations between regins, lines and points in geographic data bases. Technical Report 91-7. Orono: University of Maine, 1991. 1–4
Renz J. A Spatial Odyssey of the Interval Algebra: Directed Intervals. Seattle: Morgan Kaufmann, 2001. 51–56
Allen J F. Maintaining knowledge about temporal intervals. Commun ACM, 1983, 26(11): 832–843
Wang S S, Liu D Y, Liu J. A new spatial algebra for road network moving objects. Int J Inf Technol, 2005, 11(12): 47–58
Egenhofer M, Franzosa R. Point-set topological spatial relations. Int J Geogr Inf Syst, 1991, 5(2): 161–174
Clementini E, di Felice P. Topological Invariants for Lines. IEEE T Knowl Data Eng, 1998, 10(1): 38–54
Clementini E, di Felice P, van Oosterom P. A Small Set of Formal Topological Relationships Suitable for End-user Interaction. Berlin: Springer-Verlag, 1993. 277–295
Freksa C. Temporal reasoning based on semi-intervals. Artif Intell, 1992, 54: 199–227
Egenhofer M, Al-Taha K. Reasoning about Gradual Changes of Topological Relationships. German: Lecture Notes in Computer Science, 1992, 639: 196–219
Egenhofer M J. Modeling conceptual neighborhoods of topological line-region relations. Int J Geogr Inf Syst, 1995, 9(5): 555–565
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Supported by the National Natural Science Foundation of China (Grant Nos. 40701134 and 40771171) and the National Hi-Tech Research and Development Program of China (Grant No. 2007AA12Z216)
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Gao, Y., Zhang, Y., Tian, Y. et al. Topological relations between directed lines and simple geometries. Sci. China Ser. E-Technol. Sci. 51 (Suppl 1), 91–101 (2008). https://doi.org/10.1007/s11431-008-5010-9
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DOI: https://doi.org/10.1007/s11431-008-5010-9