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CLC number: TP361

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Received: 2004-11-23

Revision Accepted: 2005-02-03

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.100 P.116~123

10.1631/jzus.2005.AS0116


A class of quasi Bézier curves based on hyperbolic polynomials


Author(s):  SHEN Wan-qiang, WANG Guo-zhao

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   wq_shen@163.com

Key Words:  Bernstein basis, Bé, zier curve, Hyperbolic polynomials, Extended Tchebyshev system, B-base


SHEN Wan-qiang, WANG Guo-zhao. A class of quasi Bézier curves based on hyperbolic polynomials[J]. Journal of Zhejiang University Science A, 2005, 6(100): 116~123.

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author="SHEN Wan-qiang, WANG Guo-zhao",
journal="Journal of Zhejiang University Science A",
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doi="10.1631/jzus.2005.AS0116"
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%DOI 10.1631/jzus.2005.AS0116

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T1 - A class of quasi Bézier curves based on hyperbolic polynomials
A1 - SHEN Wan-qiang
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Abstract: 
This paper presents a basis for the space of hyperbolic polynomials Γm=span{1, sht, cht, sh2t, ch2t, …, shmt, chmt} on the interval [0,α] from an extended Tchebyshev system, which is analogous to the bernstein basis for the space of polynomial used as a kind of well-known tool for free-form curves and surfaces in Computer Aided Geometry Design. Then from this basis, we construct quasi ;zier curves and discuss some of their properties. At last, we give an example and extend the range of the parameter variable t to arbitrary close interval [r, s] (r<s).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[1] Carnicer, J.M., Peña, J.M., 1994. Totally positive bases for shape preserving curve design and optimality of B-splines. Computer Aided Geometric Design, 11:635-656.

[2] Chen, Q.Y., Wang, G.Z., 2003. A class of B

[3] L

[4] Peña, J.M., 1997. Shape preserving representations for trigonometric polynomial curves. Computer Aided Geometric Design, 14:5-11.

[5] Sânchez-Reyes, J., 1998. Harmonic rational B

[6] Schumaker, L.L., 1981. Spline Functions: Basic Theory. Wiley-Interscience, New York, p.363-419.

[7] Zhang, J.W., 1996. C-curves: An extension of cubic curves. Computer Aided Geometric Design, 13:199-217.

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