, Volume 10, Issue 2, pp 177–196

A Quantitative Description Model for Direction Relations Based on Direction Groups



The description models for spatial relations, especially those for direction relations, have gained increasing attention in GIS and Cartography community in recent decades. In this paper, such a quantitative model for spatial direction relations is discussed. It has been suggested that people often describe directions between two objects using multiple directions but not a single one; therefore a description model for direction relations should use multiple directions, i.e. direction group. A direction group consists of two components: the azimuths of the normals of direction Voronoi edges between two objects and the corresponding weights of the azimuths. The former can be calculated by means of Delaunay triangulation of the vertices and the points of intersection of the two objects; the latter can be calculated using the common areas of the two objects or the lengths of their direction Voronoi diagram (DVD) edges.The advantages of this model exist in four aspects: (1) direction computations are converted into a 1-dimension space problem and use lines (DVDs) to solve it, therefore direction computation process is simplified; (2) once Dir(A,B), the directions from A to B, is obtained, Dir(B,A) can be got without complex computations; (3) A quantitative direction group can be transformed into a qualitative one easily; (4) quantitative direction relations between objects can be recorded in 2-dimension tables, which is very useful in spatial reasoning.


Direction relations Quantitative models Direction voronoi diagrams Direction groups 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.I. Abdelmoty and M.H. Williams. “Approaches to the representation of qualitative spatial relations for geographic databases,” Geodesy, Vol. 40:204–216, 1994.Google Scholar
  2. 2.
    T. Bittner. “On ontology and epistemology of rough location. Spatial information theory.” Cognitive and Computational Foundations of Geographic Information Science COSIT' 99, in C. Freksa and D. Mark (Eds.), Lecture Notes in Computer Science, Vol. 1661:433–448, 1999.Google Scholar
  3. 3.
    S. Cicerone and P. De Felice. “Cardinal directions between spatial objects: the pairwiseconsistency problem,” Information Science, Vol. 164(1–4):165–188, 2004.CrossRefGoogle Scholar
  4. 4.
    Clementini et al. “Qualitative representation of positional information,” Artificial Intelligence, Vol. 95:317–356, 1997.CrossRefGoogle Scholar
  5. 5.
    A. Cohn. “Calculi for qualitative spatial reasoning”. Artificial intelligence and symbolic mathematical computation, in J. Calmet, J. Campbell, and J. Pfalzgraf (Eds.), Lecture Notes in Computer Science, Vol. 1138:124–143, Springer-Verlag, New York, 1996.Google Scholar
  6. 6.
    M. Egenhofer and R. Franzosa. “Point-set topological spatial relations,” International Journal of Geographical Information System, Vol. 5(2):161–174, 1991.Google Scholar
  7. 7.
    M. Egenhofer and R. Shariff. “Metric details for natural-language spatial relations,” ACM Transactions on Information Systems, Vol. 16(4):295–321, 1998.CrossRefGoogle Scholar
  8. 8.
    A.U. Frank. “Qualitative spatial reasoning about distances and directions in geographic space,” Journal of Visual Languages and Computing, Vol. 3(2):343–371, 1992.CrossRefGoogle Scholar
  9. 9.
    A.U. Frank. “Qualitative spatial reasoning: cardinal directions as an example,” 1International Journal of Geographic Information Systems, Vol. 10(3):269–290, 1996CrossRefGoogle Scholar
  10. 10.
    C. Freksa. “Using orientation information for qualitative spatial reasoning”. Theories and methods of spatio-temporal reasoning in geographic space, in A. Frank, I. Campari, and U. Formentini (Eds.), Lecture Notes in Computer Science, Pisa, Italy, 639:162–178, 1992.Google Scholar
  11. 11.
    R.K. Goyal. “Similarity assessment for cardinal directions between extended spatial objects”. PHD Thesis. The University of Maine, 2000.Google Scholar
  12. 12.
    H. Guesgen. “Spatial reasoning based on allen's temporal logic”. Technical Report: TR-89-049, International Computer Science Institute, Berkley, CA, 1989.Google Scholar
  13. 13.
    R. Haar. “Computational models of spatial relations,” Technical Report: TR-478, MSC-72-03610, Computer Science, University of Maryland, College Park, MD, 1976.Google Scholar
  14. 14.
    D. Hernandez. “Qualitative representation of spatial knowledge,” Springer Verlag: New York, 1994.Google Scholar
  15. 15.
    J. Hong. “Qualitative distance and direction reasoning in geographic space,” PHD Thesis. University of Maine, 1994.Google Scholar
  16. 16.
    B. Kim and K. Um. “2D+ string: A spatial metadata to reason topological and direction relations,” 11th International Conference on Scientific and Statistical Database Management, 112–P122, Cleveland, Ohio, 1999.Google Scholar
  17. 17.
    L.J. Latecki, and R. Rőhrig. “Orientation and qualitative angle for spatial reasoning,” International Joint Conference on Artificial Intelligence, Chambëry, France, 1993.Google Scholar
  18. 18.
    Z. Li, R. Zhao, and J. Chen. “A voronoi-based spatial algebra for spatial relations,” Progress in Natural Science, Vol. 12(6):43–51, 2002.Google Scholar
  19. 19.
    G. Ligozat. “Reasoning about cardinal directions,” Journal of Visual Languages and Computing, Vol. 9(1):23– 44, 1998.CrossRefGoogle Scholar
  20. 20.
    S.L. Liu and X. Chen. “Measuring distance between spatial objects in 2D GIS,” 2nd international symposium on spatial data quality. Hongkong, China, in W.Z. Shi, M.F. Goodchild, and P.F., Fisher (Eds.), 51–60, 2003.Google Scholar
  21. 21.
    D. Mitra. “A class of star-algebras for point-based qualitative reasoning in two dimension space,” in D. Mitra (Ed.), Proceedings of the FLAIRS-2002, Pendacola Beach, Florida, 2002.Google Scholar
  22. 22.
    D. Mitra. “Qualitative reasoning with arbitrary angular directions,” Spatial and temporal reasoning workshop note, AAAI, Edmonton, Canada, 2002.Google Scholar
  23. 23.
    M. Nabil, et al. “2D projection interval relations: A symbolic representation of spatial relations,” Advances in Spatial Databases-4th International Symposium, Portland, in M. Egenhofer and J. Herring (Eds.), Lecture Notes in Computer Science, Vol. 951:292–309, Springer-Verlag: Berlin, 1995.Google Scholar
  24. 24.
    D. Papadias, Y. Theodoridis, and T. Sellis. “The retrieval of direction relations using R-Trees,” Database and Expert Systems Applications-5th International Conference, DEXA '94. Athens, Greece. in D. Karagiannis (Ed.), Lecture Notes in Computer Science, Vol. 856:173–182, Springer-Verlag: New York, 1994.Google Scholar
  25. 25.
    D. Peuquet and C.X. Zhan. “An algorithm to determine the directional relation between arbitrarily-shaped polygons in the plane,” Pattern Recognition, Vol. 201:65–74, 1987.CrossRefGoogle Scholar
  26. 26.
    S. Pigot. “A topological model for 3D spatial information system,” Auto Carto, 10:368–392, 1992.Google Scholar
  27. 27.
    N. Pissinou, I. Radev, K. Macki, and W.G. Campbell. “A topological-directional model for the spatio-temporal composition of the video objects,” Eighth international workshop on research issues on data engineering. in A. Silberschatz, A. Zhang, and S. Mehrotra (Eds.), Continuous-Media Databases and Applications, 17–24, Orlando, FL, 1998.Google Scholar
  28. 28.
    M. Safar and C. Shahabi. “2D topological and direction relations in the World of Minimum Bounding Circles,” in Proceedings of the 1999 International Database Engineering and Applications Symposium, 1999.Google Scholar
  29. 29.
    C. Schlieder. “Reasoning about ordering [A],” A Theoretical Basis for GIS International Conference COSIT'95 Semmering, 314–349, Springer-Verlag: Berlin, 1995.Google Scholar
  30. 30.
    J. Sharma. “Integrated spatial reasoning in geographic information systems: Combining topology and direction,” PHD Thesis, University of Maine, 1996.Google Scholar
  31. 31.
    S. Shekhar and X. Liu. “Direction as a spatial object: A summary of results,” The Sixth International Symposium on Advances in Geographic Information Systems, 69–75, Washington, 1998.Google Scholar
  32. 32.
    R. Weibel. “A topology of constraints to line simplification,” in M.J. Kraak and M. Molenaar (Eds.), Advances on GIS II, 9A.1–9A.14, London, Taylor & Francis, 1996.Google Scholar
  33. 33.
    M. Wertheimer. “Law of organization in perceptual forms.” in W. D. Ellis (Kegan Paul, Trench, Trubner) (Ed.), A Source Book of Gestalt Psychology, 71–88, 1923.Google Scholar
  34. 34.
    H.W. Yan and R.Z. Guo. “Research on a formal description model for direction relations based on voronoi diagrams,” Geoinformatics and Information Science of Wuhan University, Vol. 28(4):468–472, 2003.Google Scholar
  35. 35.
    H.W. Yan and R.Z. Guo. “Theorization of directional relation description based on voronoi diagram,” Geoinformatics and Information Science of Wuhan University, Vol. 27(3):306–310, 2002.Google Scholar
  36. 36.
    K. Zimmermann and C. Freksa. “Qualitative spatial reasoning using orientation, distance, and path knowledge,” Applied Intelligence, Vol. 6(1):49–58, 2003.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Haowen Yan
    • 1
  • Yandong Chu
    • 1
  • Zhilin Li
    • 2
  • Renzhong Guo
    • 3
  1. 1.School of Math-Physics and Software EngineeringLanzhou Jiaotong UniversityLanzhouP.R. China
  2. 2.Land Surveying and Geo-informatics Department of Hongkong Polytechnical UniversityHongkongChina
  3. 3.Shenzhen Bureau of Municipal Planning and Land ResourceShenzhenChina

Personalised recommendations