Full Text:
<2760>
CLC number: TP391
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 2
Clicked: 5086
Generalized fairing algorithm of parametric 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.
@article{title="Generalized fairing algorithm of parametric cubic splines",
author="WANG Yuan-jun, CAO Yuan",
journal="Journal of Zhejiang University Science A",
volume="7",
number="9",
pages="1572-1577",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1572"
}
%0 Journal Article
%T Generalized fairing algorithm of parametric cubic splines
%A WANG Yuan-jun
%A CAO Yuan
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 9
%P 1572-1577
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1572
TY - JOUR
T1 - Generalized fairing algorithm of parametric cubic splines
A1 - WANG Yuan-jun
A1 - CAO Yuan
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 9
SP - 1572
EP - 1577
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1572
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.
[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.
Open peer comments: Debate/Discuss/Question/Opinion
<1>