Full Text:   <418>

Summary:  <214>

CLC number: TP391.72

On-line Access: 2018-02-06

Received: 2017-07-09

Revision Accepted: 2017-09-13

Crosschecked: 2017-12-20

Cited: 0

Clicked: 1623

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Lian Zhou

http://orcid.org/0000-0001-7137-0162

-   Go to

Article info.
Open peer comments

Frontiers of Information Technology & Electronic Engineering  2017 Vol.18 No.12 P.2009-2016

http://doi.org/10.1631/FITEE.1700458


Optimal multi-degree reduction of C-Bézier surfaces with constraints


Author(s):  Lian Zhou, Xin-hui Lin, Hong-yan Zhao, Jun Chen

Affiliation(s):  Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China; more

Corresponding email(s):   lianzhou@shmtu.edu.cn

Key Words:  C-Bé, zier surfaces, Degree reduction, Boundary constraints


Lian Zhou, Xin-hui Lin, Hong-yan Zhao, Jun Chen. Optimal multi-degree reduction of C-Bézier surfaces with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 2009-2016.

@article{title="Optimal multi-degree reduction of C-Bézier surfaces with constraints",
author="Lian Zhou, Xin-hui Lin, Hong-yan Zhao, Jun Chen",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="18",
number="12",
pages="2009-2016",
year="2017",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1700458"
}

%0 Journal Article
%T Optimal multi-degree reduction of C-Bézier surfaces with constraints
%A Lian Zhou
%A Xin-hui Lin
%A Hong-yan Zhao
%A Jun Chen
%J Frontiers of Information Technology & Electronic Engineering
%V 18
%N 12
%P 2009-2016
%@ 2095-9184
%D 2017
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1700458

TY - JOUR
T1 - Optimal multi-degree reduction of C-Bézier surfaces with constraints
A1 - Lian Zhou
A1 - Xin-hui Lin
A1 - Hong-yan Zhao
A1 - Jun Chen
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 18
IS - 12
SP - 2009
EP - 2016
%@ 2095-9184
Y1 - 2017
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1700458


Abstract: 
We propose an optimal approach to solve the problem of multi-degree reduction of c-Bé;zier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced c-Bé;zier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the c-Bé;zier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

带约束条件的C-Bézier曲面最优降多阶逼近

概要:本文提出了一种在L2范数下C-Bézier曲面带约束条件的降多阶逼近最优方法。利用C-Bézier基函数的转换矩阵,得到了降阶曲面控制顶点的显式矩阵表示。结合指定的边界约束条件,该法利用于对分片连续曲面或细分子曲面同时降多阶逼近,所得到的系列降阶曲面整体上保持G1连续。数值实验表明该方法的优质高效。

关键词:C-Bézier曲面;降阶;边界约束

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

Reference

[1]Ait-Haddou, R., Bartoň, M., 2016. Constrained multi-degree reduction with respect to Jacobi norms. Comput. Aided Geom. Des., 42:23-30.

[2]Chen, Q.Y., Wang, G.Z., 2003. A class of Bézier-like curves. Comput. Aided Geom. Des., 20(1):29-39.

[3]Fan, J.H., Wu, Y.J., Lin, X., 2002. Subdivision algorithm and G1 condition for C-Bézier curves. J. Comput. Aided Des. Comput. Graph., 14(5):421-424

[4]Gospodarczyk, P., 2015. Degree reduction of Bézier curves with restricted control points area. Comput. Aided Des., 62:143-151.

[5]Huang, J.Z., Nguyen-Thanh, N., Zhou, K., 2017. Extended isogeometric analysis based on Bézier extraction for the buckling analysis of Mindlin-Reissner plates. Acta Mech., 228(9):3077-3093.

[6]Liu, L.G., Zhang, L., Lin, B.B., et al., 2009. Fast approach for computing roots of polynomials using cubic clipping. Comput. Aided Geom. Des., 26(5):547-559.

[7]Mainar, E., Peña, J.M., 2002. A basis of C-Bézier splines with optimal properties. Comput. Aided Geom. Des., 19(4): 291-295.

[8]Nguyen-Thanh, N., Zhou, K., 2017. Extended isogeometric analysis based on PHT-splines for crack propagation near inclusions. Int. J. Numer. Methods Eng., 112(12):1777-1800.

[9]Nguyen-Thanh, N., Zhou, K., Zhuang, X., et al., 2017. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Comput. Methods Appl. Mech. Eng., 316:1157-1178.

[10]Qin, X.Q., Wang, W.W., Hu, G., 2013. Degree reduction of C-Bézier curve based on genetic algorithm. Comput. Eng. Appl., 49(5):174-178.

[11]Rababah, A., Mann, S., 2013. Linear methods for G1, G2, and G3-multi-degree reduction of Bézier curves. Comput. Aided Des., 45(2):405-414.

[12]Shen, W.Q., Wang, G.Z., 2015. Geometric shapes of C-Bézier curves. Comput. Aided Des., 58:242-247.

[13]Shen, W.Q., Wang, G.Z., 2016. Degree elevation from Bézier curve to C-Bézier curve with corner cutting form. Appl. Math. A J. Chin. Univ., 31(2):165-176.

[14]Tan, P.F., Nguyen-Thanh, N., Zhou, K., 2017. Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory. Theor. Appl. Fract. Mech., 89:127-138.

[15]Yang, Q.M., Wang, G.Z., 2004. Inflection points and singularities on C-curves. Comput. Aided Geom. Des., 21(2):207-213.

[16]Zhang, J.W., 1996. C-Curves: an extension of cubic curves. Comput. Aided Geom. Des., 13(3):199-217.

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

[18]Zhou, L., 2012. Algorithm for explicit multi-degree reduction of C-Bézier curves. J. Shanghai Marit. Univ., 33(4):86-90.

[19]Zhou, L., Wang, G.J., 2009a. Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer. J. Zhejiang Univ.-Sci. A, 10(4):577-582.

[20]Zhou, L., Wang, G.J., 2009b. Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials. Comput. Aided Geom. Des., 26(3):259-270.

[21]Zhou, L., Wei, Y.W., Yao, Y.F., 2014. Optimal multi-degree reduction of Bézier curves with geometric constraints. Comput. Aided Des., 49:18-27.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE