Advertisement

Topological Relations of Arrow Symbols in Complex Diagrams

  • Yohei Kurata
  • Max J. Egenhofer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4045)

Abstract

Illustrating a dynamic process with an arrow-containing diagram is a widespread convention in people’s daily communications. In order to build a basis for capturing the structure and semantics of such diagrams, this paper formalizes the topological relations between two arrow symbols and discusses the influence of these topological relations on the diagram’s semantics. Topological relations of arrow symbols are established by two types of links, intersections and common references, which are further categorized into nine types based on the combination of the linked parts. The topological relations are captured by the existence/non-existence of these nine types of intersections and common references. Then, this paper demonstrates that arrow symbols with different types of intersections typically illustrate two actions with different interrelations, whereas the arrow symbols with common references illustrate a pair of semantics that may be mutually exclusive or synchronized.

Keywords

Common Reference Topological Relation Fish Catch Landing Strip Qualitative Spatial Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen, J.: Maintaining Knowledge about Temporal Intervals. Communications of the ACM 26(11), 832–843 (1983)MATHCrossRefGoogle Scholar
  2. Barraclough, G. (ed.): Collins Atlas of World History, 2nd revised edn. Borders Press, Ann Arbor (2003)Google Scholar
  3. Clementini, E., Di Felice, P.: Topological Invariants for Lines. IEEE Transactions on Knowledge and Data Engineering 10(1), 38–54 (1998)CrossRefGoogle Scholar
  4. Egenhofer, M.: Definitions of Line-Line Relations for Geographic Databases. IEEE Data Engineering Bulletin 16(3), 40–45 (1994a)Google Scholar
  5. Egenhofer, M.: Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing 5(2), 133–149 (1994b)CrossRefGoogle Scholar
  6. Egenhofer, M.: Spherical Topological Relations. Journal on Data Semantics III, 25–49 (2005)Google Scholar
  7. Egenhofer, M., Franzosa, R.: Point-Set Topological Spatial Relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)CrossRefGoogle Scholar
  8. Egenhofer, M., Herring, J.: Categorizing Binary Topological Relationships between Regions, Lines and Points in Geographic Databases. In: Egenhofer, M., Herring, J., Smith, T., Park, K. (eds.) A Framework for the Definitions of Topological Relationships and an Algebraic Approach to Spatial Reasoning within This Framework, NCGIA Technical Reports 91-7, National Center for Geographic Information and Analysis, Santa Barbara, CA (1991)Google Scholar
  9. Egenhofer, M., Mark, D.: Naive Geography. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 1–15. Springer, Heidelberg (1995)Google Scholar
  10. Horn, R.: Visual Language: Global Communication for the 21st Century. MacroVu, Inc., Bainbridge Island (1998)Google Scholar
  11. Hornsby, K., Egenhofer, M., Hayes, P.: Modeling Cyclic Change. In: Chen, P., Embley, D., Kouloumdjian, J., Liddle, S., Roddick, J. (eds.) Advances in Conceptual Modeling. LNCS, vol. 1227, pp. 98–109. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. Kurata, Y., Egenhofer, M.: Semantics of Simple Arrow Diagrams. In: Barkowsky, T., Freksa, C., Hegarty, M., Lowe, R. (eds.) AAAI Spring Symposium on Reasoning with Mental and External Diagram: Computational Modeling and Spatial Assistance, Menlo Park, CA, pp. 101–104 (2005a)Google Scholar
  13. Kurata, Y., Egenhofer, M.: Structure and Semantics of Arrow Diagrams. In: Cohn, A.G., Mark, D.M. (eds.) COSIT 2005. LNCS, vol. 3693, pp. 232–250. Springer, Heidelberg (2005b)CrossRefGoogle Scholar
  14. Moratz, R., Renz, J., Wolter, D.: Qualitative Spatial Reasoning about Line Segments. In: Horn, W. (ed.) 14th European Conference on Artificial Intelligence, Berlin, pp. 234–238 (2000)Google Scholar
  15. Nedas, K., Egenhofer, M., Wilmsen, D.: Metric Details of Topological Line-Line Relations. International Journal of Geographical Information Science (in press), http://www.spatial.maine.edu/~max/RJ53.html
  16. Renz, J.: A Spatial Odyssey of the Interval Algebra: 1. Directed Intervals. In: Nebel, B. (ed.) International Joint Conference on Artificial Intelligence 2001, Seattle, WA, pp. 51–56 (2001)Google Scholar
  17. Schlieder, C.: Reasoning about Ordering. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 341–349. Springer, Heidelberg (1995)Google Scholar
  18. Tversky, B., Heiser, J., Lozano, S., MacKenzie, R., Morrison, J.: Enriching Animations. In: Lowe, R., Schnotz, W. (eds.) Learning with animation: Research and application. Cambridge University Press, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yohei Kurata
    • 1
  • Max J. Egenhofer
    • 1
  1. 1.National Center for Geographic Information and Analysis and Department of Spatial Information Science and EngineeringUniversity of MaineOronoUSA

Personalised recommendations