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On-line Access: 2024-08-27

Received: 2023-10-17

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

http://doi.org/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



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).

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