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

ZHOU Lian; LIN Xin-hui; ZHAO Hong-yan; CHEN Jun

doi:10.1631/FITEE.1700458

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

Regular Papers | Updated：2022-06-06

- Optimal multi-degree reduction of C-Bézier surfaces with constraints
- 带约束条件的C-Bézier曲面最优降多阶逼近
- Frontiers of Information Technology & Electronic Engineering Vol. 18, Issue 12, Pages: 2009-2016(2017)
- 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：
- DOI：10.1631/FITEE.1700458
  CLC： TP391.72
- Received：09 July 2017，
  
  Revised：2017-12-20，
  
  Published：2017-12
- Accepted：
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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：

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

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