| Computer & Information Science |
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| A class of quasi Bézier curves based on hyperbolic polynomials |
| SHEN Wan-qiang, WANG Guo-zhao |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
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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).
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Received: 23 November 2004
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