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Received: 2006-05-20

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.9 P.1572-1577


Generalized fairing algorithm of parametric cubic splines

Author(s):  WANG Yuan-jun, CAO Yuan

Affiliation(s):  School of Mathematical Science, Fudan University, Shanghai 200433, China

Corresponding email(s):   wyj803@yahoo.com.cn, caoy@fudan.edu.cn

Key Words:  Curve fairing, Tangent vector, Energy optimization, Cubic splines

WANG Yuan-jun, CAO Yuan. Generalized fairing algorithm of parametric cubic splines[J]. Journal of Zhejiang University Science A, 2006, 7(9): 1572-1577.

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Kjellander has reported an algorithm for fairing uniform parametric cubic splines. Poliakoff extended Kjellander’s algorithm to non-uniform case. However, they merely changed the bad point’s position, and neglected the smoothing of tangent at bad point. In this paper, we present a fairing algorithm that both changed point’s position and its corresponding tangent vector. The new algorithm possesses the minimum property of energy. We also proved Poliakoff’s fairing algorithm is a deduction of our fairing algorithm. Several fairing examples are given in this paper.

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


[1] Farin, G., Sapides, N., 1989. Curvature and the fairness of curves and surfaces. IEEE Computer Graphics and Applications, 9(2):52-57.

[2] Kjellander, J.A.P., 1983. Smoothing of cubic parametric splines. Computer-Aided Design, 15(3):175-179.

[3] Lee, E.T.Y., 1990. Energy, fairness, and a counterexample. Computer-Aided Design, 22(1):37-40.

[4] Li, W., Xu, S., Zheng, J., Zhao, G., 2004. Target curvature driven fairing algorithm for planar B-spline curves. Computer Aided Geometric Design, 21:499-513.

[5] Poliakoff, J.F., 1996. An improved algorithm for automatic fairing of non-uniform parametric cubic splines. Computer-Aided Design, 28(1):59-66.

[6] Wang, X., Cheng, F., Barsky, B.A., 1997. Energy and B-spline interproximation. Computer-Aided Design, 29(7):485-496.

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