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Frontiers of Information Technology & Electronic Engineering

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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-Bézier surfaces; Degree reduction; Boundary constraints

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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,in press.https://doi.org/10.1631/FITEE.1700458

@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",
year="in press",
publisher="Zhejiang University Press & Springer",
doi="https://doi.org/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
%P 2009-2016
%@ 2095-9184
%D in press
%I Zhejiang University Press & Springer
doi="https://doi.org/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
SP - 2009
EP - 2016
%@ 2095-9184
Y1 - in press
PB - Zhejiang University Press & Springer
ER -
doi="https://doi.org/10.1631/FITEE.1700458"

Abstract
Chinese Summary
Academic Network
Reviewer Comment

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.

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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Reference

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带约束条件的C-Bézier曲面最优降多阶逼近

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