Geometry of Neighborhood Sequences in Hexagonal Grid

  • Benedek Nagy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)


In this paper the nodes of the hexagonal grid are used as points. Three types of neighbors are used on this grid, therefore neighborhood sequences contain values 1, 2 and 3. The grid is coordinatized by three coordinates in a symmetric way. Digital circles are classified based on digital distances using neighborhood sequences. They can be triangle, hexagon, enneagon and dodecagon. The corners of the convex hulls of these polygons are computed.


Convex Hull Analyse Section Initial Part Neighborhood Relation Symmetric Pair 
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.


  1. 1.
    Rosenfeld, A., Pfaltz, J.L.: Distance functions on digital pictures. Pattern Recognition 1, 33–61 (1968)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Klette, R., Rosenfeld, A.: Digital geometry. In: Geometric methods for digital picture analysis. Morgan Kaufmann Publishers/Elsevier Science B.V, San Francisco/Amsterdam (2004)Google Scholar
  3. 3.
    Das, P.P., Chakrabarti, P.P., Chatterji, B.N.: Distance functions in digital geometry. Inform. Sci. 42, 113–136 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Das, P.P., Chatterji, B.N.: Octagonal distances for digital pictures. Inform. Sci. 50, 123–150 (1990)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Nagy, B.: A symmetric coordinate system for the hexagonal networks. In: Proceedings of Information Society 2004 – Theoretical Computer Science, ACM conference, Ljubljana, Slovenia, pp. 193–196 (2004)Google Scholar
  6. 6.
    Nagy, B.: Shortest path in triangular grids with neighbourhood sequences. Journal of Comp. and Inf. Techn. 11, 111–122 (2003)Google Scholar
  7. 7.
    Voss, K.: Discrete images, objects, and functions in ℤn. Algorithms and Combinatorics, vol. 11. Springer, Heidelberg (1993)Google Scholar
  8. 8.
    Chen, C.H., Pau, L.F., Wang, P.S.P. (eds.): Handbook of pattern recognition & computer vision. Handbooks in Science and Technology. Academic Press, Orlando (1986)Google Scholar
  9. 9.
    Gonzalez, R.C., Woods, R.E.: Digital image processing. Addison-Wesley, Reading (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Benedek Nagy
    • 1
    • 2
  1. 1.GRLMCRovira i Virgili UniversityTarragonaSpain
  2. 2.Faculty of InformaticsUniversity of DebrecenDebrecenHungary

Personalised recommendations