Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

Year 2019, Volume: 22 Issue: 4, 1075 - 1082, 01.12.2019

Hakan Gündüz Ahmet Kazan H.Bayram Karadağ

https://doi.org/10.2339/politeknik.542825

Cited By: 3

Abstract

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.

Keywords

Hermitian curves, Bezier curves, rotational surfaces, shape parameter

Rotational Surfaces Generated by Cubic Hermitian and Cubic Bezier Curves

Abstract

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.

Keywords

Hermitian curves, Bezier curves, rotational surfaces, shape parameter

References

• 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).