带形状参数的双曲多项式均匀B样条-CiteSeerX.PDF

1000-9825/2005/16(04)0625 ©2005 Journal of Software Vol.16, No.4 ∗ B + , ( , 3 10027) Hyperbolic Polynomial Uniform B-Spline with Shape Parameter + WANG Wen-Tao , WANG Guo-Zhao (Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 3 10027, China) + Corresponding author : Phn: +86-571 E-mail: wwt@zju .edu .cn Received 2004-04-08; Accepted 2004-07-06 Wang WT, Wang GZ. Hyperbolic polynomial uniform B-Spline with shape parameter. Journal of Softwar e, 2005,16(4) :625−633. DOI : 10.1360/jos160625 Abstract: The basis function of n order hyperbolic polynomial uniform B-spline with shape parameter is constructed so that the shape of the constructed curve can be adjusted by changing the parameter value. The hyperbola can be represented with this basis function accurately. With elevation of the order, feasible range of the shape parameter value is extended. Key words: uniform B-spline; basis function; CAGD; shape parameter; interpolation : n B .B , ., . : B ;;;; : TP39 1 : A ,B,,B, [1] [2,3] B ,C-B .,B zierB [4,5] ,,.B ,,B,, .[6],,, [7] [− 1,1].Barskyβ ,B ,,G2 .BC-BB ∗ Supported by the National Natural Science Foundation of China under Grant No (); the National Grand Fundamental Research 973 Program of China under Grant No.G2002CB 12101 ((973)) : (1976 ), , ,,,;(1944 ), , ,,,,. 626 Journal of Software 2005,16(4) β ,k(k≥2)B (k=3),[− 1,1].k(k≥2)B 2 k−2 ,β G (k4), C ., ,B., B. 1 B B ,h(λ ,t) , t ∈[0,