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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.6 P.497-501


Bézier curves with shape parameter

Author(s):  WANG Wen-tao, WANG Guo-zhao

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

Corresponding email(s):   wwt@zju.edu.cn

Key Words:  Bé, zier curve, Bé, zier basis with shape parameter, Bernstein basis

WANG Wen-tao, WANG Guo-zhao. Bézier curves with shape parameter[J]. Journal of Zhejiang University Science A, 2005, 6(6): 497-501.

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In this paper, %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier curves with shape parameter. The %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier basis curves with shape parameter have most properties of bernstein basis and the %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier curves. Moreover the shape parameter can adjust the curves’ shape with the same control polygon. As the increase of the shape parameter, the %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier curves with shape parameter approximate to the control polygon. In the last, the %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier surface with shape parameter is also constructed and it has most properties of %29&ck%5B%5D=abstract&ck%5B%5D=keyword'>;zier surface.

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[1] Chen, Q.Y., Wang, G.Z., 2003. A class of Bézier-like curves. Computer Aided Geometric Design, 20:29-39.

[2] Goodman, T.N.T., Said, H.B., 1991. Properties of generalized Ball curves and surfaces. Computer Aided Design, 23(8):554-560.

[3] Mainar, E., Peńa, J.N., Sânchez-Reys, J., 2001. Shape preserving alternatives to the rational Bézier model. Computer Aided Geometric Design, 15:909-923.

[4] Said, H.B., 1989. Generalized Ball curve and its recursive algorithm. ACM Transaction on Graphics, 8(4):360-371.

[5] Wang, W.T., Wang, G.Z., 2004. Uniform B Spline with Shape Parameter. Journal of Computer-Aided Design & Computer Graphics, 16(6):783-788.

Open peer comments: Debate/Discuss/Question/Opinion


reenu@Rani Durgawati University<reenusharma6@rediff.com>

2012-01-12 13:24:34

I am doing Ph.D. on the topic spline curves.

This paper entitled "Bézier curves with shape parameter" will defenitly help me for my studies.

Please provide your name, email address and a comment

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