Research Article
BibTex RIS Cite

Voronoi Diyagramı ve Taksi Düzlemi Üzerine

Year 2021, Volume: 14 Issue: 1, 175 - 181, 31.03.2021

Ziya Akça Ceyda Çalış

https://doi.org/10.18185/erzifbed.699158
Cited By: 2

Abstract

Bu çalışmada, Voronoi diyagramları, Fortune Algoritması ve Taksi düzlemde Voronoi diyagramları incelenmiştir.

Keywords

Voronoi diagramları Taksi düzlem geometri Fortune algoritması

References

  • [1] Akça Z, Kaya R, On the taxicab trigonometry, J. of Inst. Math. Comput. Sci. Math. Ser., vol. 10, no. 3, pp. 151--159, Apr. 1997.
  • [2] Bayar A., Ekmekçi, S, On Complex Numbers and Taxicab Plane, Mathematical Sciences & Applications E-Notes, vol. 3, no. 1, pp. 58--64, 2015.
  • [3] Bayar A., Kaya R., On the Taxicab Distance On a Sphere, Missouri Journal of Mathematical Sciences, pp. 41-51, 2005.
  • [4] Çalış C., Taksi Düzlemde Voronoi Diyagramları Üzerine, Yüksek Lisans Tezi. Esk. Osmangazi Üni. Fen Bil. Ens., p. 60, 2019.
  • [5] Ekici C., , Kocayusufoğlu İ., Akça Z, The norm in taxicab geometry, Turkish J. Math., vol. 22, no. 3, pp. 295--307, 1998.
  • [6] Ekmekçi, S. Taksi çemberleriyle ilgili özellikler, Doktora Tezi. Esk. Osmangazi Üni. Fen Bil. Ens., pp. 5-11, 2001.
  • [7] Fortune Steven, A sweepline algorithm for Voronoi diagrams, Algorithmica 2:153-174, 1987.
  • [8] Horn, M. ve J. Weber, Computational Geometry Lecture Notes Voronoi Diagrams. URL: cs.princeton.edu, 2004.
  • [9] Kaya R, Akça Z, Özcan M., Günaltılı İ., General equation for taxicab conics and their classification, Mitt. Math. Ges. Hamburg , vol. 19, no. 0, pp. 135--148, 2000.
  • [10] Miu, A. Computatonal Geometry, Lecture 7: Voronoi Diagrams, 2001.
  • [11] Özcan M., Ekmekçi, S, Bayar A., The Taxicab Lengths under Rotations, The Pi Mu Epsilon Journal, pp. 381--384, 2002.
  • [12] Özbek, B., İki ve Üç Boyutlu Cisimlerin Voronoi Diyagramlarının Çıkarılması ve Delaunay Mozaiklemesinin Gerçekleştirilmesi. YL. Ankara Üniversitesi Fen Bilimleri Enstitüsü, 2010.
  • [13] Toma.L. Computational Geometry. Bowdin College, 2010.
  • [14] Vassilev, S. ve B. Eades, Generalions of the Voronoi Diagram. American Journal of Computational and Applied Mathematics, pp. 91-96, 2013.

On The Voronoi Diagram and Taxicab Plane

Year 2021, Volume: 14 Issue: 1, 175 - 181, 31.03.2021

Ziya Akça Ceyda Çalış

https://doi.org/10.18185/erzifbed.699158
Cited By: 2

Abstract


In this work, Voronoi diagrams, Fortune algorithm and Voronoi diagrams in the Taxicab plane are investigated.

Keywords

Voronoi diagrams, Taxicab geomtry, Fortune algorithm Taxicab geomtry Fortune algorithm

References

  • [1] Akça Z, Kaya R, On the taxicab trigonometry, J. of Inst. Math. Comput. Sci. Math. Ser., vol. 10, no. 3, pp. 151--159, Apr. 1997.
  • [2] Bayar A., Ekmekçi, S, On Complex Numbers and Taxicab Plane, Mathematical Sciences & Applications E-Notes, vol. 3, no. 1, pp. 58--64, 2015.
  • [3] Bayar A., Kaya R., On the Taxicab Distance On a Sphere, Missouri Journal of Mathematical Sciences, pp. 41-51, 2005.
  • [4] Çalış C., Taksi Düzlemde Voronoi Diyagramları Üzerine, Yüksek Lisans Tezi. Esk. Osmangazi Üni. Fen Bil. Ens., p. 60, 2019.
  • [5] Ekici C., , Kocayusufoğlu İ., Akça Z, The norm in taxicab geometry, Turkish J. Math., vol. 22, no. 3, pp. 295--307, 1998.
  • [6] Ekmekçi, S. Taksi çemberleriyle ilgili özellikler, Doktora Tezi. Esk. Osmangazi Üni. Fen Bil. Ens., pp. 5-11, 2001.
  • [7] Fortune Steven, A sweepline algorithm for Voronoi diagrams, Algorithmica 2:153-174, 1987.
  • [8] Horn, M. ve J. Weber, Computational Geometry Lecture Notes Voronoi Diagrams. URL: cs.princeton.edu, 2004.
  • [9] Kaya R, Akça Z, Özcan M., Günaltılı İ., General equation for taxicab conics and their classification, Mitt. Math. Ges. Hamburg , vol. 19, no. 0, pp. 135--148, 2000.
  • [10] Miu, A. Computatonal Geometry, Lecture 7: Voronoi Diagrams, 2001.
  • [11] Özcan M., Ekmekçi, S, Bayar A., The Taxicab Lengths under Rotations, The Pi Mu Epsilon Journal, pp. 381--384, 2002.
  • [12] Özbek, B., İki ve Üç Boyutlu Cisimlerin Voronoi Diyagramlarının Çıkarılması ve Delaunay Mozaiklemesinin Gerçekleştirilmesi. YL. Ankara Üniversitesi Fen Bilimleri Enstitüsü, 2010.
  • [13] Toma.L. Computational Geometry. Bowdin College, 2010.
  • [14] Vassilev, S. ve B. Eades, Generalions of the Voronoi Diagram. American Journal of Computational and Applied Mathematics, pp. 91-96, 2013.
There are 14 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Makaleler
Authors

Ziya Akça 0000-0001-6379-0546

Ceyda Çalış 0000-0001-5267-4400

Publication Date March 31, 2021
Published in Issue Year 2021 Volume: 14 Issue: 1

Cite

APA Akça, Z., & Çalış, C. (2021). On The Voronoi Diagram and Taxicab Plane. Erzincan University Journal of Science and Technology, 14(1), 175-181. https://doi.org/10.18185/erzifbed.699158

Cited By

ON THE MAXIMUM CIRCULAR INVERSES OF MAXIMUM CIRCLES
Eskişehir Technical University Journal of Science and Technology A - Applied Sciences and Engineering
https://doi.org/10.18038/estubtda.1370728
A Note on the Maximum Circle Inverses of Lines in the Maximum Plane
Ikonion Journal of Mathematics
https://doi.org/10.54286/ikjm.1319223