Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-19T03:53:38.905Z Has data issue: false hasContentIssue false
  • English
  • Français

The minimal size of a square which includes a digital convex 2K–gon

Published online by Cambridge University Press:  17 April 2009

Dragan M. Acketa  and
Joviša D. Žunić
Dragan M. Acketa
Affiliation:
Institute of Mathematics, 21000 Novi Sad Trg Dositeja Obradovića 4 Serbia, Yugoslavia
Joviša D. Žunić
Affiliation:
Institute of Applied Basic Disciplines Faculty of Engineering, 21000 Novi Sad Velijka Vlahovića 3, Serbia, Yugoslavia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper presents a construction of a digital convex 2k–gon (for a given natural number k), which can be inscribed into a square grid of the minimal possible size F(2k). An explicit expression for the function F(2k) is also given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 3 , December 1993 , pp. 465 - 474
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Acketa, D.M. abd Žunić, J.D., ‘On the number of linear partitions of the (m, n)-grid’, Inform. Process. Lett. 38 (1991), 163–168.CrossRefGoogle Scholar
[2]Acketa, D. and Žunić, J., ‘On the maximal number of edges of digital convex polygons included into a grid square’, in Proceedings of Third Canadian Conference on Computational Geometry, 1991, pp. 215–218.Google Scholar
[3]Acketa, D. and Žunić, J., ‘A simple construction of a digital convex 2k–gon with minimal diameter’, in Proceedings of First International Conference on the Computational Graphics and Visualization Techniques, Compugraphics 1, 1991, pp. 2–9.Google Scholar
[4]Acketa, D., Matić-Kekić, S. and Žunić, J., ‘An algorithm for a simple construction of suboptimal digital convex polygons’, J. Oper. Res. Yugoslavia 2 (1992), 73–81.Google Scholar
[5]Balog, A. and Barany, I., ‘On the convex hull of the integer points in a disc’, in Proceedings of Seventh Annual ACM Symposium on Computational Geometry, 1991.CrossRefGoogle Scholar
[6]Guardina, C.R. and Dougherty, E.R., Morphological methods in image and signal processing (Prentice Hall, Englewood Cliffs, New Jersey, 1987).Google Scholar
[7]Mount, D.M., and Silverman, R., ‘Combinatorial and computational aspects of Minkowski decompositions’, Contemp. Math. 119(1991), 107–124.CrossRefGoogle Scholar
[8]Preparata, F. and Shamos, M., Computational geometry, an introduction (Springer-Verlag, Berlin, Heidelberg, New York, 1985).Google Scholar
[9]Simpson, R.J., ‘Convex lattice polygons of minimum area’, Bull. Austral. Math. Soc. 42 (1990), 353–367.CrossRefGoogle Scholar
[10]Voss, K. and Klette, R., ‘On the maximal number of edges of a convex digital polygon included into a square’, Pocitace a umela inteligencia 1 (1982), 549–558.Google Scholar