Araştırma Makalesi
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Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

Yıl 2019, Cilt: 22 Sayı: 4, 1075 - 1082, 01.12.2019
https://doi.org/10.2339/politeknik.542825

Öz

To tackle the geometric design in adjusting shapes of
rotation surfaces, firstly the rotation surfaces have been constructed by using
cubic Hermitian and cubic Bezier curves with two local shape parameters. It has
been seen that, the new rotational surfaces which have been constructed have a
good performance on adjusting their shapes by changing the local shape
parameters. Also, the rotational surfaces generated by cubic Hermitian and
cubic Bezier curves have provided a valuable way for the design of interesting
surfaces. In this context, some characterizations have been given for these
rotational surfaces obtaining the mean and Gaussian curvatures of them.

Kaynakça

  • 1] Arslan K., Bulca B. and Kosova D., “On Generalized Rotational Surfaces in Euclidean Spaces”, J. Korean Math. Soc., (2017). [2] Baikoussis C. and Blair D.E., “On the Gauss map of ruled surfaces”, Glasgow Math. J., 34: 355-359, (1992).
  • [3] Bobenko A. and Pinkall U., “Descrete sothermic Surfaces”, J. reine angev, Math, 475: 187-208, (1996).
  • [4] Chen B.Y., Choi M. and Kim Y.H, “Surfaces of revolution with pointwise 1-type Gauss map”, J. Korean Math. Soc., 42(3): 447-455, (2005).
  • [5] Dietz R., Hoschek J. and Juettler B., “An algebraic approach to curves and surfaces on the sphere and on other quadrics”, Computer Aided Geometric Design, 10: 211-229, (1993).
  • [6] Farin G., “Curves and Surfaces for CAGD: A Practical Guide”, Academic Press Inc, San Diego (2002).
  • [7] Kazan A. and Karadağ H. B., “A classification of Surfaces of Revolution in Lorentz-Minkowski Space”, Int. J. Contemp. Math. Sciences, 6(39): 1915-1928, (2011).
  • [8] Kazan A. and Karadağ H. B., “Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density’’, Int. J. of Analysis and Applications, 16(3): 414-426, (2018).
  • [9] Octafiatiningsih E. and Sujarwo I., “The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade”, Cauchy-Journal of Pure and Applied Mathematics, 4(2): 100-106, (2016).
  • [10] Saxena A. Saxena Sahay B., “Computer Aided Engineering Design”, Anamaya Publishers, New Delhi, India, (2005).

Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

Yıl 2019, Cilt: 22 Sayı: 4, 1075 - 1082, 01.12.2019
https://doi.org/10.2339/politeknik.542825

Öz

To
tackle the geometric design in adjusting shapes of rotation surfaces, firstly
the rotation surfaces have been constructed by using cubic Hermitian and cubic
Bezier curves with two local shape parameters. It has been seen that, the new
rotational surfaces which have been constructed have a good performance on
adjusting their shapes by changing the local shape parameters. Also, the
rotational surfaces generated by cubic Hermitian and cubic Bezier curves have provided
a valuable way for the design of interesting surfaces. In this context, some
characterizations have been given for these rotational surfaces obtaining the
mean and Gaussian curvatures of them.

Kaynakça

  • 1] Arslan K., Bulca B. and Kosova D., “On Generalized Rotational Surfaces in Euclidean Spaces”, J. Korean Math. Soc., (2017). [2] Baikoussis C. and Blair D.E., “On the Gauss map of ruled surfaces”, Glasgow Math. J., 34: 355-359, (1992).
  • [3] Bobenko A. and Pinkall U., “Descrete sothermic Surfaces”, J. reine angev, Math, 475: 187-208, (1996).
  • [4] Chen B.Y., Choi M. and Kim Y.H, “Surfaces of revolution with pointwise 1-type Gauss map”, J. Korean Math. Soc., 42(3): 447-455, (2005).
  • [5] Dietz R., Hoschek J. and Juettler B., “An algebraic approach to curves and surfaces on the sphere and on other quadrics”, Computer Aided Geometric Design, 10: 211-229, (1993).
  • [6] Farin G., “Curves and Surfaces for CAGD: A Practical Guide”, Academic Press Inc, San Diego (2002).
  • [7] Kazan A. and Karadağ H. B., “A classification of Surfaces of Revolution in Lorentz-Minkowski Space”, Int. J. Contemp. Math. Sciences, 6(39): 1915-1928, (2011).
  • [8] Kazan A. and Karadağ H. B., “Weighted Minimal and Weighted Flat Surfaces of Revolution in Galilean 3-Space with Density’’, Int. J. of Analysis and Applications, 16(3): 414-426, (2018).
  • [9] Octafiatiningsih E. and Sujarwo I., “The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade”, Cauchy-Journal of Pure and Applied Mathematics, 4(2): 100-106, (2016).
  • [10] Saxena A. Saxena Sahay B., “Computer Aided Engineering Design”, Anamaya Publishers, New Delhi, India, (2005).
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Hakan Gündüz Bu kişi benim 0000-0003-0645-5658

Ahmet Kazan Bu kişi benim 0000-0002-1959-6102

H.Bayram Karadağ 0000-0001-6474-877X

Yayımlanma Tarihi 1 Aralık 2019
Gönderilme Tarihi 21 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 22 Sayı: 4

Kaynak Göster

APA Gündüz, H., Kazan, A., & Karadağ, H. (2019). Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves. Politeknik Dergisi, 22(4), 1075-1082. https://doi.org/10.2339/politeknik.542825
AMA Gündüz H, Kazan A, Karadağ H. Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves. Politeknik Dergisi. Aralık 2019;22(4):1075-1082. doi:10.2339/politeknik.542825
Chicago Gündüz, Hakan, Ahmet Kazan, ve H.Bayram Karadağ. “Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves”. Politeknik Dergisi 22, sy. 4 (Aralık 2019): 1075-82. https://doi.org/10.2339/politeknik.542825.
EndNote Gündüz H, Kazan A, Karadağ H (01 Aralık 2019) Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves. Politeknik Dergisi 22 4 1075–1082.
IEEE H. Gündüz, A. Kazan, ve H. Karadağ, “Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves”, Politeknik Dergisi, c. 22, sy. 4, ss. 1075–1082, 2019, doi: 10.2339/politeknik.542825.
ISNAD Gündüz, Hakan vd. “Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves”. Politeknik Dergisi 22/4 (Aralık 2019), 1075-1082. https://doi.org/10.2339/politeknik.542825.
JAMA Gündüz H, Kazan A, Karadağ H. Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves. Politeknik Dergisi. 2019;22:1075–1082.
MLA Gündüz, Hakan vd. “Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves”. Politeknik Dergisi, c. 22, sy. 4, 2019, ss. 1075-82, doi:10.2339/politeknik.542825.
Vancouver Gündüz H, Kazan A, Karadağ H. Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves. Politeknik Dergisi. 2019;22(4):1075-82.
 
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