Hybrid polynomial approximation to higher derivatives of rational curves |
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Authors: | Jie ChenGuo-Jin Wang |
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Affiliation: | Department of Mathematics and State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China |
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Abstract: | In this paper, we extend the results published in JCAM volume 214 pp. 163-174 in 2008. Based on the bound estimates of higher derivatives of both Bernstein basis functions and rational Bézier curves, we prove that for any given rational Bézier curve, if the convergence condition of the corresponding hybrid polynomial approximation is satisfied, then not only the l-th (l=1,2,3) derivatives of its hybrid polynomial approximation curve uniformly converge to the corresponding derivatives of the rational Bézier curve, but also this conclusion is tenable in the case of any order derivative. This result can expand the area of applications of hybrid polynomial approximation to rational curves in geometric design and geometric computation. |
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Keywords: | Computer Aided Geometric Design (CAGD) Rational polynomial curve Hybrid polynomial approximation Higher derivative Convergence condition |
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