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Received: 2006-12-13

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.10 P.1650~1656

http://doi.org/10.1631/jzus.2007.A1650


Constrained multi-degree reduction of rational Bézier curves using reparameterization


Author(s):  CAI Hong-jie, WANG Guo-jin

Affiliation(s):  Institute of Computer Images and Graphics, State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   cai_hongjie@sina.com, wanggj@zju.edu.cn

Key Words:  Rational Bé, zier curves, Constrained multi-degree reduction, Reparameterization


CAI Hong-jie, WANG Guo-jin. Constrained multi-degree reduction of rational Bézier curves using reparameterization[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1650~1656.

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author="CAI Hong-jie, WANG Guo-jin",
journal="Journal of Zhejiang University Science A",
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number="10",
pages="1650~1656",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1650"
}

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%T Constrained multi-degree reduction of rational Bézier curves using reparameterization
%A CAI Hong-jie
%A WANG Guo-jin
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 10
%P 1650~1656
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1650

TY - JOUR
T1 - Constrained multi-degree reduction of rational Bézier curves using reparameterization
A1 - CAI Hong-jie
A1 - WANG Guo-jin
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 10
SP - 1650
EP - 1656
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A1650


Abstract: 
Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bézier curves to the algorithms of constrained multi-degree reduction for rational Bé;zier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bé;zier curves, which are used to make uniform the weights of the rational Bé;zier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of “cancelling the best linear common divisor” and “shifted Chebyshev polynomial”, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.

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

Reference

[1] Chen, F.L., 1994. Constrained best linear common divisor and degree reduction for rational curves. Numerical Mathematics: A Journal of Chinese University, (Suppl.):14-21.

[2] Chen, G.D., Wang, G.J., 2000. Integral computation relating to rational curves with approximate degree reduction. Prog. Nat. Sci., 10(11):851-858.

[3] Hu, S.M., Sun, J.G., Jin, T.G., Wang, G.Z., 1998. Approximate degree reduction of Bézier curves. Tsinghua Science and Technology, 3(2):997-1000.

[4] Lu, L.Z., Wang, G.Z., 2006a. Optimal multi-degree reduction of Bézier curves with G1-continuity. J Zhejiang Univ. Sci. A, 7(Suppl. II):174-180.

[5] Lu, L.Z., Wang, G.Z., 2006b. Optimal multi-degree reduction of Bézier curves with G2-continuity. Computer Aided Geometric Design, 23:673-683.

[6] Park, Y., Lee, N., 2005. Application of degree reduction of polynomial Bézier curves to rational case. J. Appl. Math. & Comput., 18(1-2):159-169.

[7] Sederberg, T.W., Chang, G.Z., 1993. Best linear common divisor for approximation degree reduction. Computer-Aided Design, 25(3):163-168.

[8] Zhang, R.J., Wang, G.J., 2005. Constrained Bézier curves’ best multi-degree reduction in the L2-norm. Prog. Nat. Sci., 15(9):843-850.

[9] Zheng, J.M., 2005. Minimizing the maximal ratio of weights of a rational Bézier curve. Computer Aided Geometric Design, 22:275-280.

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