A generalization of rational Bernstein–Bézier curves
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This paper is concerned with a generalization of Bernstein–Bézier curves. A one parameter family of rational Bernstein–Bézier curves is introduced based on a de Casteljau type algorithm. A subdivision procedure is discussed, and matrix representation and degree elevation formulas are obtained. We also represent conic sections using rational q-Bernstein–Bézier curves.
Key wordsq-Bernstein polynomials rational Bézier curves de Casteljau algorithm subdivision degree elevation
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- 2.G. Farin, Curves and Surfaces for CAGD, a Practical Guide, 5th edn., Academic Press, San Diego USA, 2002.Google Scholar
- 3.T. N. T. Goodman, Total positivity and shape of curves, in Total Positivity and its Applications, M. Gasca and C. A. Micchelli eds., pp. 157–186, Kluwer Academic Publishers, Dordrecht, 1996.Google Scholar
- 7.H. Oruç, LU factorization of the Vandermonde matrix and its applications, Appl. Math. Lett., to appear.Google Scholar
- 11.G. M. Phillips, A de Casteljau algorithm for generalized Bernstein polynomials, BIT, 36 (1996), pp. 232–236.Google Scholar