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Hybrid polynomial approximation to higher derivatives of rational curves

✍ Scribed by Jie Chen; Guo-Jin Wang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
1010 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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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