Curve Couples of Bézier Curves in Euclidean 2-Space

ISSN: 2645-8845
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2018
Yayıncı: Fuat USTA

The goal of this paper is to characterize the evolute, involute and parallel curves of a Bezier curve which is applicable to computer graphics and related subjects. Especially, these curve couples are investigated at the endpoints. Moreover, the curvatures of these curve couples are given.

Keywords:

Bézier curve, Evolute, Involute Parallel,

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[1] C. Huygens, Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricæ, 1673.
[2] Ş. Kılıçoğlu, S. Şenyurt, On the involute of the cubic Bezier curve by using matrix representation in E3, Eur. J. Pure Appl. Math., (13), 216-226, 2020.
[3] Z. Duman, Involute-Evolute curve couples of Bezier curve, MSc. Thesis, Sakarya University, 2021.
[4] D. Marsh, Applied Geometry for Computer Graphics and CAD, Springer, 2006.
[5] A. Gray, E. Abbena, S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
[6] B. O’Neill, Elementary Differential Geometry, Academic Press, Rev. 2nd.ed., Elsevier, USA, 2006.
[7] J. W. Rutter, Geometry of Curves, Chapman & Hall/CRC, 2000.
[8] M. Özdemir, Diferansiyel Geometri, Altın Nokta Basın Yayın, 2020.
[9] E. Erkan, S. Yüce, Serret-Frenet frame and curvatures of Bezier curves, Mathematics, 6(12), 321, 1-20, 2018.