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Received: 2007-01-22

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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.10 P.1657~1662

http://doi.org/10.1631/jzus.2007.A1657


A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity


Author(s):  LU Li-zheng, WANG Guo-zhao

Affiliation(s):  Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   lulz99@yahoo.com.cn

Key Words:  Degree reduction, Bé, zier curves, Optimal approximation, G1-continuity, Quadratic programming


LU Li-zheng, WANG Guo-zhao. A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1657~1662.

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author="LU Li-zheng, WANG Guo-zhao",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1657"
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%I Zhejiang University Press & Springer
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T1 - A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity
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A1 - WANG Guo-zhao
J0 - Journal of Zhejiang University Science A
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Y1 - 2007
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1657


Abstract: 
This paper presents a quadratic programming method for optimal multi-degree reduction of ;zier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of ;zier curves with their parameterizations close to arc-length parameterizations are also discussed.

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

Reference

[1] Ahn, Y.J., 2003. Using Jacobi polynomials for degree reduction of Bézier curves with Ck-constraints. Computer Aided Geometric Design, 20(7):423-434.

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[9] Lee, B.G., Park, Y., Yoo, J., 2002. Application of Legendre-Bernstein basis transformations to degree elevation and degree reduction. Computer Aided Geometric Design, 19(9):709-718.

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

[11] Lu, L., Wang, G., 2006b. Optimal multi-degree reduction of Bézier curves with G2-continuity. Computer Aided Geometric Design, 23(9):673-683.

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[13] Rababah, A., Lee, B.G., Yoo, J., 2006. A simple matrix form for degree reduction of Bézier curves using Chebyshev-Bernstein basis transformations. Appl. Math. Comput., 181(1):310-318.

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[15] Zheng, J., Wang, G., 2003. Perturbing Bézier coefficients for best constrained degree reduction in the L2-norm. Graph. Models, 65(6):351-368.

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