Curve Couples of Bézier Curves in Euclidean 2-Space

Year 2021, Volume: 4 Issue: 4, 245 - 250, 01.12.2021

Ayşe Yılmaz Ceylan

https://doi.org/10.33401/fujma.941439

Cited By: 2

Abstract

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

References

• [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.