Investigating a Quadratic Bezier Curve Due to N-C-W and N-Bishop Frames

Yıl 2020, Cilt: 12 Sayı: 2, 120 - 127, 31.12.2020

Hatice Kusak Samancı Muhsin İncesu

https://doi.org/10.47000/tjmcs.704794

Cited By: 8

Öz

The purpose of our paper is to investigate N-Bishop frame of the quadratic Bezier curve which is one of the effective methods for computer-aided geometric design (CAGD). Then the N-Bishop curvatures and derivative formulas for quadratics Bezier curve are calculated and give some numeric examples.

Anahtar Kelimeler

Bezier curves, CAGD, N-C-W frame, N-Bishop frame, modified frames

Kaynakça

• Bishop, R. L. {\em There is more than one way to frame a curve}, The American Mathematical Monthly, \textbf{82}(3)(1975), 246--251.
• Farin, G., A history of curves and surfaces, Handbook of Computer Aided Geometric Design, 2002.
• Floater, M.S., {\em Derivatives of rational B\'{e}zier curves}, Computer Aided Geometric Design, \textbf{9}(3)(1991), 161--174.
• \.{I}ncesu, M., G\"{u}rsoy, O., {\em The principal forms and curvatures on Bezier curves}, XVII National Mathematics Symposium, Abant \.{I}zzet Baysal University, (2004), 146--157.
• Keskin, O., Yayli, Y., {\em An application of N-Bishop frame to spherical im-ages for direction curves}, International Journal of Geometric Methods in Modern Physics, \textbf{14}(11)(2017).
• Marsh, D., Applied geometry for computer graphics and CAD, Springer-Verlag, Berlin, 2005.
• Samanci, H. K., Celik, S., \.{I}ncesu, M. , {\em The Bishop Frame of Bezier Curves}, Life Science Journal, \textbf{12}(6)(2015).
• Sapidis, N.S., Frey, W.H., {\em Controlling the curvature of a quadratic Bezier curve}, Computer Aided Geometric Design, \textbf{9}(1992), 85--91.
• Scofield, P.D., {\em Curves of constant precession}, The American mathematical monthly, \textbf{102}(6)(1995), 531--537.
• Uzuno\u{g}lu, B., G\"{o}k, \.{I}., Yayl\i, Y., {\em A new approach to curves of constant precession}, Applied Mathematics and Computation, \textbf{275}(2016), 317--323.
• Y\i lmaz, S., Turgut, M., {\em A new version of Bishop frame and an application to spherical images}, Journal of Mathematical Analysis and Applications, \textbf{371}(2)(2010), 764--776.
• Y\i lmaz, S., \"{O}zy\i lmaz, E., Turgut, M., {\em New spherical indicatrices and their characterizations}, An. St. Univ. Ovidius Constanta, \textbf{18}(2)(2010), 337--354.