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CLC number: TP391
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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Cited: 2
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Generalized fairing algorithm of parametric cubic splines
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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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author="WANG Yuan-jun, CAO Yuan",
journal="Journal of Zhejiang University Science A",
volume="7",
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year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1572"
}
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Abstract: 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.
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[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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