T-Bezier Eğrilerin Yüzey Uygulamaları

Yıl 2023, Cilt: 26 Sayı: 4, 1563 - 1571, 01.12.2023

Hakan Gündüz , Hacı Bayram Karadağ

https://doi.org/10.2339/politeknik.1326633

Öz

Yüzey tasarımında şekilleri kontrol etmede iki şekil parametresiyle T-Bezier eğrileri kullanılarak dönel yüzeyleri oluşturuyoruz. Burada şekil parametreleri şekil tasarımında önemli bir rol oynamaktadır. Son olarak, bu dönel yüzeyleri için ortalama ve Gauss eğriliklerinin şekil parametrelerine göre karakterizasyonlarını veriyoruz.

Anahtar Kelimeler

T-Bezier baz fonksiyonları, T-Bezier eğrileri, dönel yüzeyler, şekil parametresi

Surface Applications of T-Bezier curves

Öz

In controlling the shapes in the surface design, we create the rotational surfaces using T-Bezier curves with two shape parameters. Here, shape parameters play an important role in shape design. Finally, we give the characterizations of the mean and Gaussian curvatures for these rotational surfaces according to the shape parameters.

Anahtar Kelimeler

T-Bezier basis functions, T-Bezier curves, rotational surfaces, shape parameter

Kaynakça

• [1] Arslan K., Bulca B. and Kosova D., “On Generalized Rotational Surfaces in Euclidean Spaces”, J. Korean Math. Soc., (2017).
• [2] Gündüz H., Kazan A. and Karadağ H.B., “Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves”, Politeknik Dergisi, 22(4):1075-1082, (2019).
• [3] Maqsood S., Abbas M., Hu G., Ramli A.L.A. and Miura K.T., “A Novel Generalization of Trigonometric Bezier Curve and Surface with Shape Parameters and Its Applications”, Mathematical Problems in Engineering, (2020).
• [4] 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).
• [5] Farin G., “Curves and Surfaces for CAGD: A Practical Guide”, Academic Press Inc, San Diego (2002).
• [6] 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).
• [7] 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).
• [8] 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).
• [9] Saxena A. Saxena Sahay B., “Computer Aided Engineering Design”, Anamaya Publishers, New Delhi, India, (2005).
• [10] Altın M., Kazan A. and Karadağ H.B., “Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in (L 3 , ax2 + by2)”, International Electronic Journal of Geometry, 13(2): 11-29, (2020).
• [11] Samancı H.K., Kalkan O. and Çelik S., “The timelike Bézier spline in Minkowski 3-space”, Journal of science and arts, 19 (2): 357-374, (2019).
• [12] Sarioğlugil A. and Tutar A., “On ruled surfaces in Minkowski space R31”, International Journal of Applied Mathematics, (2008).
• [13] Pressley A., “Elementary Differential Geometry”, Springer, Verlag, (2001).
• [14] Samancı H.K., Kuşçu Ç., “The Analysis of Some Spherical Mechanism Movements and Joint Design by The New SLERP Interpolations”, Politeknik Dergisi, 25(4) : 1513-1521, (2022).
• [15] Erişkin H., Yücesan A., “Bezier Curve with a Minimal Jerk Energy”, Mathematical Sciences and Applications E-Notes, Dergipark, 4(2) : 139-148, (2016).
• [16] Arslan K., Ezentaş R., Mihai I., Murathan C. and Özgür C., “Tensor Product Surfaces of a Euclidean Space Curve and a Euclidean Plane Curve”, Beiträge zur Algebra und Geometrie, 42 (2) : 523-530, (2001).
• [17] Balgetir H., Öğrenmiş A.O. and Bektaş M., “Curves on Ruled Surfaces in Minkowski 3-space”, Int. Journal of Contemp. Math. Sciences, (2006).
• [18] Yaylı Y. and Saracoglu S., “On Developable Ruled Surfaces in Minkowski Space”, Advances in Applied Clifford Algebras , 22(2) : 499-510, (2012).
• [19] Levent A. and Şahin B., “Cubic Bezier-like Transition Curves with New Basis Functions”, The Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 44(2) : 222–228, (2018).
• [20] Levent A. and Şahin B., “Beta Bézier Curves”, Applied and Computational Mathematics an International Journal, 18(1) : 79-94 (2019).
• [21] Ceylan A.Y., “The Geometry of Bézier Curves in Minkowski 3-Space”, Universal Journal of Mathematics and Applications, Dergipark, 6(1) : 7-14 (2023).
• [22] Almaz F., Külahcı M. A., “A survey on tube surfaces in Galilean 3-space”, Politeknik Dergisi, 25(3): 1033-1042, (2022).
• [23] Kılıçoğlu Ş. And Şenyurt S., “On the Bertrand Mate of Cubic Bezier Curve by Using Matrix Representation in E3”, Turkish Journal of Mathematics and Computer Science, 14(2) : 376-383, (2022).
• [24] Ayar A. and Şahin B., “Trigonometric Bézier-like Curves and Transition Curves”, Applicationes Mathematicae, 48 125-153, (2021).
• [25] Samancı H.K. and İncesu M., “Investigating a Quadratic Bezier Curve Due to N-C-W and N-Bishop Frames”, Turkish Journal of Mathematics and Computer Science, Pages 120-127, (2020).
• [26] Floater M.S., “Bézier Curves and Surfaces”, Applied and Computational Mathematics, Pages 113-115, (2015).
• [27] Samancı H.K., “Minkowski 3-Uzayında Timelike Rasyonel Bezier Eğrilerinin Eğrilikleri Üzerine”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 7(2) : 243-255, (2018).
• [28] Kılıçoglu S. and Şenyurt S., “On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3”, European Journal of Pure and Applied Mathematics, 13(2), 216-226, (2020).
• [29] Erkan E., and Yüce S., “Serret-Frenet Frame and Curvatures of Bezier Curves.” MDPI Mathematics, 6(12), 321, (2018).
• [30] Erkan E. and Yüce S., “Some Notes on Geometry of Bezier Curves in Euclidean 4-Space”, Journal of Engineering Technology and Applied Sciences, 5(3), 93-101, (2020).
• [31] Körpınar T. and Sazak A., “Binormal surfaces of adjoint curves in 3D euclidean space”, Politeknik Dergisi, Early View, (2022).