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Frontiers of Information Technology & Electronic Engineering

ISSN 2095-9184 (print), ISSN 2095-9230 (online)

2017 Vol.18 No.12 P.2009-2016

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

Lian Zhou, Xin-hui Lin, Hong-yan Zhao, Jun Chen

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

lianzhou@shmtu.edu.cn

Abstract: We propose an optimal approach to solve the problem of multi-degree reduction of C-Bézier surfaces in the norm L2 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 G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

Key words: C-Bézier surfaces; Degree reduction; Boundary constraints

Chinese Summary  <18> 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。

关键词组：C-Bézier曲面；降阶；边界约束


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DOI:

10.1631/FITEE.1700458

CLC number:

TP391.72

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On-line Access:

2018-02-06

Received:

2017-07-09

Revision Accepted:

2017-09-13

Crosschecked:

2017-12-20

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