Title: Geometry of contrapedal curves of Bézier curves
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00072; Volume 4 / Issue 2 / Year 2022, Pages 11-17
Document Type: Research Paper
aDepartment of Mathematics, Faculty of Science, Akdeniz University, 07058 Antalya, Turkey
Received: 29 November 2021, Accepted: 4 March 2022, Published: 29 April 2022.
Corresponding Author: Ayşe Yılmaz Ceylan (Email address: email@example.com)
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The scope of this paper is to study the geometric structures of contrapedal curves of Bézier curves which has many applications in computer graphics and related areas. Especially, the curvature of a contrapedal curve of a planar Bézier curve are examined. Moreover, the curvature of this curve couple is handled with the origin pedal point. In addition, the curvatures are investigated at the end points.
Keywords: Bézier curve, curvature, contrapedal curveReferences:
- A. Y. Ceylan, Curve couples of Bézier curves in Euclidean 2-space, Fundam. J. Math. Appl. 4 (4), 245–250, 2021.
- A. Y. Ceylan and M. Kara, On pedal and contrapedal curves of Bézier curves, Konuralp J. Math. 9 (2), 217–221, 2021.
- Z. Duman, Bézier eğrilerinin involüt-evolüt eğri çiftleri, Master Thesis, Sakarya University, Sakarya, 2021.
- G. Farin, A history of curves and surfaces, In: Handbook of Computer Aided Geometric Design (Ed. by G. Farin, J. Hoschek and M.-S. Kim), North Holland, 1–21, 2002.
- G. H. Georgiev, Shapes of plane Bézier curves, In: Curve and Surface Design-Avignon 2006 (Ed. by P. Chenin, T. Lyche and L. L. Schumaker), Nashboro Prees, Brentwood, 143–152, 2006.
- G. H. Georgiev, On the shape of the cubic Bézier curve, Proc. of International Congress Pure and Applied Differential Geometry-Brussels (Ed. by F. Dillen and I. Van de Woestyne), Shaker Verlag, Aachen, 98–106, 2007.
- A. Gray, E. Abbena and S. Salamon, Modern differential geometry of curves and surfaces with mathematica, Chapman and Hall/CRC, Boca Raton, FL, USA, 2016.
- M. Incesu and O. Gürsoy, Bézier eğrilerinde esas formlar ve eğrilikler, XVII Ulusal Matematik Sempozyumu, Bildiriler, Abant İzzet Baysal Üniversitesi, 146–157, 2004.
- Ş. Kiliçoğlu and S. Şenyurt, On the involute of the cubic Bézier curve by using matrix representation in E3, Eur. J. Pure Appl. Math. 13 (2), 216–226, 2020.
- Y. Li and D. Pei, Pedal curves of frontals in the Euclidean plane, Math. Methods Appl. Sci. 41, 1988–1997, 2018.
- D. Marsh, Applied geometry for computer graphics and CAD, Springer, 2006.
- J. Sánchez-Reyes, p-Bézier curves, spirals, and sectrix curves, Comput. Aided Geom. Des. 19 (6), 445–464, 2002.
- O. O. Tuncer, H. Ceyhan, İ. Gök and F. N. Ekmekci, Notes on pedal and contrapedal curves of fronts in the Euclidean plane, Math. Methods Appl. Sci. 41, 5096–5111, 2018.
- K. Ueda, A sequence of Bézier curves generated by successive pedal-point constructions, In: Curves and Surfaces with Applications in CAGD (Ed. by A. Le Méhauté, C. Rabut and L. Schumaker), Vanderbilt University Press, 427–434, 1997.
- K. Ueda, Pedal curves and surfaces, In: Mathematical Methods for Curves and Surfaces–Oslo 2000 (Ed. by T. Lyche and L. L. Schumaker), Vanderbilt University Press, 497–507, 2001.