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Received: 2004-11-24

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Journal of Zhejiang University SCIENCE A 2005 Vol.6 No.100 P.124~127


Shape modification of Bézier curves by constrained optimization

Author(s):  WU Qing-biao, XIA Fei-hai

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China; more

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

Key Words:  Shape modification, Bé, zier curve, Constrained optimization

WU Qing-biao, XIA Fei-hai. Shape modification of Bézier curves by constrained optimization[J]. Journal of Zhejiang University Science A, 2005, 6(100): 124~127.

@article{title="Shape modification of Bézier curves by constrained optimization",
author="WU Qing-biao, XIA Fei-hai",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Shape modification of Bézier curves by constrained optimization
%A WU Qing-biao
%A XIA Fei-hai
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 100
%P 124~127
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.AS0124

T1 - Shape modification of Bézier curves by constrained optimization
A1 - WU Qing-biao
A1 - XIA Fei-hai
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 100
SP - 124
EP - 127
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.AS0124

The ;zier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many good properties for shape design. Developing more convenient techniques for designing and modifying ;zier curve is an important problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the optimal shape modification of ;zier curves by geometric constraints. This paper presents a new method by constrained optimization based on changing the control points of the curves. By this method, the authors modify control points of the original ;zier curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Au, C.K., Yuen, M.M.F., 1995. Unified approach to NURBS curve shape modification. Computer Aided Design, 27(2):85-93.

[2] Fowler, B., Bartels, R., 1993. Constrained-based curve manipulation. IEEE Computer Graphics and Application, 13(5):43-49.

[3] Hu, S.M., Zhou, D.W., Sun, J.G., 1999. Shape Modification of NURBS Curves via Constrained Optimization. Proceedings of the CAD/Graphics

[4] Hu, S.M., Li, Y.F., Chen, J.T., 2001. Modifying the shape of NURBS surfaces with geometric constraints. Computer Aided Design, 33(12):903-912.

[5] Meek, D.S., Ong, B.H., Walton, D.J., 2003. Contrained interpolation with rational cubics. Computer Aided Geometric Design, 20:253-275.

[6] Opfer, G., Oberle, H.J., 1988. The derivation of cubic splines with obstacles by methods of optimization and optimal control. Numer. Math., 52:17-31.

[7] Piegl, L., 1989. Modifying of the shape of rational B-Spline. Part 1: Curves. Computer Aided Design, 21(8):509-518.

[8] S

[9] Xu, L., Chen, Y.J., Hu, N., 2002. Shape modification of B

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