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

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

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.

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  • 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.
  • İncesu, 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.
  • Uzunou{g}lu, B., G"{o}k, .{I}., Yayli, Y., {em A new approach to curves of constant precession}, Applied Mathematics and Computation, textbf{275}(2016), 317--323.
  • Yi 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.
  • Yi lmaz, S., "{O}zyi lmaz, E., Turgut, M., {em New spherical indicatrices and their characterizations}, An. St. Univ. Ovidius Constanta, textbf{18}(2)(2010), 337--354.