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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2005, Vol. 6 Issue (Supplement 1): 116-123    DOI: 10.1007/BF02887226
Computer and Information Science     
A class of quasi Bézier curves based on hyperbolic polynomials
SHEN Wan-qiang, WANG Guo-zhao
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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 Bézier 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).

Key words： Bernstein basis      Bézier curve      Hyperbolic polynomials      Extended Tchebyshev system      B-base     
CLC:  TP361  
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SHEN Wan-qiang
WANG Guo-zhao
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SHEN Wan-qiang, WANG Guo-zhao. A class of quasi Bézier curves based on hyperbolic polynomials. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(Supplement 1): 116-123.

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http://www.zjujournals.com/xueshu/zjus-a/10.1007/BF02887226     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2005/V6/ISupplement 1/116

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