带约束条件的C-Bézier曲面最优降多阶逼近

周联; 林新辉; 赵宏艳; 陈军

doi:10.1631/FITEE.1700458

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带约束条件的C-Bézier曲面最优降多阶逼近

常规文章 | Updated：2022-06-06

- 带约束条件的C-Bézier曲面最优降多阶逼近
- Optimal multi-degree reduction of C-Bézier surfaces with constraints
- 信息与电子工程前沿（英文） 2017年18卷第12期页码：2009-2016
- Affiliations：
  
  Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China
  Zhejiang Institute of Economics and Trade, Hangzhou 310018, China
  College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China
  Faculty of Science, Ningbo University of Technology, Ningbo 315211, China
- Author bio：
  
  Lian ZHOU, E-mail: lianzhou@shmtu.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 11401373, 61402281, and 11601322) and the Zhejiang Provincial Natural Science Foundation, China (No. LY16F020020)
- DOI：10.1631/FITEE.1700458
  中图分类号： TP391.72
- 收稿：2017-07-09，
  
  修回：2017-12-20，
  
  纸质出版：2017-12
- Accepted：
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周联, 林新辉, 赵宏艳, 等. 带约束条件的C-Bézier曲面最优降多阶逼近[J]. 信息与电子工程前沿（英文）, 2017,18(12):2009-2016.

ZHOU Lian, LIN Xin-hui, ZHAO Hong-yan, et al. Optimal multi-degree reduction of C-Bézier surfaces with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 2009-2016.
周联, 林新辉, 赵宏艳, 等. 带约束条件的C-Bézier曲面最优降多阶逼近[J]. 信息与电子工程前沿（英文）, 2017,18(12):2009-2016. DOI： 10.1631/FITEE.1700458.

ZHOU Lian, LIN Xin-hui, ZHAO Hong-yan, et al. Optimal multi-degree reduction of C-Bézier surfaces with constraints[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(12): 2009-2016. DOI： 10.1631/FITEE.1700458.

摘要

本文提出了一种在

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G

连续。数值实验表明该方法的优质高效。

Abstract

We propose an optimal approach to solve the problem of multi-degree reduction of C-Bézier surfaces in the norm

with prescribed constraints. The control points of the degree-reduced C-Bézier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Bézier 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 G

continuous. Finally

numerical examples are presented to show the effectiveness of the method.

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references

R. Ait-Haddou , M. Bartoň . Constrained multi-degree reduction with respect to Jacobi norms . Comput. Aided Geom. Des. , 2016 . 42 23 - 30 . DOI: 10.1016/j.cagd.2015.12.003 http://doi.org/10.1016/j.cagd.2015.12.003 .

Q.Y. Chen , G.Z. Wang . A class of Bézier-like curves . Comput. Aided Geom. Des. , 2003 . 20 ( 1 ): 29 - 39 . DOI: 10.1016/S0167-8396(03)00003-7 http://doi.org/10.1016/S0167-8396(03)00003-7 .

J.H. Fan , Y.J. Wu , X. Lin . Subdivision algorithm and G 1 condition for C-Bézier curves . J. Comput. Aided Des. Comput. Graph. , 2002 . 14 ( 5 ): 421 - 424 . DOI: 10.3321/j.issn:1003-9775.2002.05.009 http://doi.org/10.3321/j.issn:1003-9775.2002.05.009 .

P. Gospodarczyk . Degree reduction of Bézier curves with restricted control points area . Comput. Aided Des. , 2015 . 62 143 - 151 . DOI: 10.1016/j.cad.2014.11.009 http://doi.org/10.1016/j.cad.2014.11.009 .

J.Z. Huang , N. Nguyen-Thanh , K. Zhou . Extended isogeometric analysis based on Bézier extraction for the buckling analysis of Mindlin-Reissner plates . Acta Mech. , 2017 . 228 ( 9 ): 3077 - 3093 . DOI: 10.1007/s00707-017-1861-0 http://doi.org/10.1007/s00707-017-1861-0 .

L.G. Liu , L. Zhang , B.B. Lin , 等 . Fast approach for computing roots of polynomials using cubic clipping . Comput. Aided Geom. Des. , 2009 . 26 ( 5 ): 547 - 559 . DOI: 10.1016/j.cagd.2009.02.003 http://doi.org/10.1016/j.cagd.2009.02.003 .

E. Mainar , J.M. Peña . A basis of C-Bézier splines with optimal properties . Comput. Aided Geom. Des. , 2002 . 19 ( 4 ): 291 - 295 . DOI: 10.1016/S0167-8396(02)00089-4 http://doi.org/10.1016/S0167-8396(02)00089-4 .

N. Nguyen-Thanh , K. Zhou . Extended isogeometric analysis based on PHT-splines for crack propagation near inclusions . Int. J. Numer. Methods Eng. , 2017 . 112 ( 12 ): 1777 - 1800 . DOI: 10.1002/nme.5581 http://doi.org/10.1002/nme.5581 .

N. Nguyen-Thanh , K. Zhou , X. Zhuang , 等 . Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling . Comput. Methods Appl. Mech. Eng. , 2017 . 316 1157 - 1178 . DOI: 10.1016/j.cma.2016.12.002 http://doi.org/10.1016/j.cma.2016.12.002 .

X.Q. Qin , W.W. Wang , G. Hu . Degree reduction of C-Bézier curve based on genetic algorithm . Comput. Eng. Appl. , 2013 . 49 ( 5 ): 174 - 178 . DOI: 10.3778/j.issn.1002-8331.1107-0346 http://doi.org/10.3778/j.issn.1002-8331.1107-0346 .

A. Rababah , S. Mann . Linear methods for G 1 , G 2 , and G 3 -multi-degree reduction of Bézier curves . Comput. Aided Des. , 2013 . 45 ( 2 ): 405 - 414 . DOI: 10.1016/j.cad.2012.10.023 http://doi.org/10.1016/j.cad.2012.10.023 .

W.Q. Shen , G.Z. Wang . Geometric shapes of C-Bézier curves . Comput. Aided Des. , 2015 . 58 242 - 247 . DOI: 10.1016/j.cad.2014.08.007 http://doi.org/10.1016/j.cad.2014.08.007 .

W.Q. Shen , G.Z. Wang . Degree elevation from Bézier curve to C-Bézier curve with corner cutting form . Appl. Math. A J. Chin. Univ. , 2016 . 31 ( 2 ): 165 - 176 . DOI: 10.1007/s11766-016-3369-0 http://doi.org/10.1007/s11766-016-3369-0 .

P.F. Tan , N. Nguyen-Thanh , K. Zhou . Extended isogeometric analysis based on Bézier extraction for an FGM plate by using the two-variable refined plate theory . Theor. Appl. Fract. Mech. , 2017 . 89 127 - 138 . DOI: 10.1016/j.tafmec.2017.02.002 http://doi.org/10.1016/j.tafmec.2017.02.002 .

Q.M. Yang , G.Z. Wang . Inflection points and singularities on C-curves . Comput. Aided Geom. Des. , 2004 . 21 ( 2 ): 207 - 213 . DOI: 10.1016/j.cagd.2003.11.002 http://doi.org/10.1016/j.cagd.2003.11.002 .

J.W. Zhang . C-Curves: an extension of cubic curves . Comput. Aided Geom. Des. , 1996 . 13 ( 3 ): 199 - 217 . DOI: 10.1016/0167-8396(95)00022-4 http://doi.org/10.1016/0167-8396(95)00022-4 .

J.M. Zheng , G.Z. Wang . Perturbing Bézier coefficients for best constrained degree reduction in the L 2 -norm . Graph Models , 2003 . 65 ( 6 ): 351 - 368 . DOI: 10.1016/j.gmod.2003.07.001 http://doi.org/10.1016/j.gmod.2003.07.001 .

L. Zhou . Algorithm for explicit multi-degree reduction of C-Bézier curves . J. Shanghai Marit. Univ. , 2012 . 33 ( 4 ): 86 - 90 . DOI: 10.3969/j.issn.1672-9498.2012.04.017 http://doi.org/10.3969/j.issn.1672-9498.2012.04.017 .

L. Zhou , G.J. Wang . Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer . J. Zhejiang Univ.-Sci. A , 2009a . 10 ( 4 ): 577 - 582 . DOI: 10.1631/jzus.A0820290 http://doi.org/10.1631/jzus.A0820290 .

L. Zhou , G.J. Wang . Constrained multi-degree reduction of Bézier surfaces using Jacobi polynomials . Comput. Aided Geom. Des. , 2009b . 26 ( 3 ): 259 - 270 . DOI: 10.1016/j.cagd.2008.10.003 http://doi.org/10.1016/j.cagd.2008.10.003 .

L. Zhou , Y.W. Wei , Y.F. Yao . Optimal multi-degree reduction of Bézier curves with geometric constraints . Comput. Aided Des. , 2014 . 49 18 - 27 . DOI: 10.1016/j.cad.2013.12.004 http://doi.org/10.1016/j.cad.2013.12.004 .

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