上海交通大学学报

上海交通大学学报 >

2018 , Vol. 52 >Issue 1: 111 - 119

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2018.01.017

学报（中文）

区间q-Bézier曲线的降阶算法

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  • 1. 合肥工业大学 数学学院， 合肥 230009; 2. 拉文大学 数学系， 美国 拉文 91750

网络出版日期: 2018-01-01

基金资助

国家自然科学基金项目(11471093)，安徽省教育厅自然科学重大研究项目(KJ2014ZD30)，中央高校基本科研业务费专项经费(JZ2015HGXJ0175)

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Algorithms for Degree Reduction of Interval q-Bézier Curves

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  • 1. School of Mathematics, Hefei University of Technology, Hefei 230009, China; 2. Department of Mathematics, University of La Verne, La Verne 91750, America

Online published: 2018-01-01

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摘要

基于一类广义Bernstein基函数定义了区间q-Bézier曲线，并研究了区间q-Bézier曲线的3种降阶逼近算法，即扰动法、基于Chebyshev多项式的最佳一致逼近法和约束最佳一致逼近法，得到3种降阶逼近方法的显式误差界，并通过实例分析了3种方法的优缺点.数值实例结果表明，与扰动法相比，最佳一致逼近法所得区间q-Bézier曲线的误差最小.

关键词： 计算机辅助几何设计; 区间算法; q-Bernstein基; 区间q-Bézier曲线; 降阶

本文引用格式

刘植1，吕雁燕1，刘晓雁2，张莉1 . 区间q-Bézier曲线的降阶算法[J]. 上海交通大学学报, 2018 , 52(1) : 111 -119 . DOI: 10.16183/j.cnki.jsjtu.2018.01.017

Abstract

Interval q-Bézier curves are presented using a generalized Bernstein basis and the problem of degree reduction approximation of them is studied. We propose three different methods, namely, perturbation method, best uniform approximation method and constrained best uniform approximation method based on Chebyshev polynomials. The explicit representation of bounding error of each method is derived. The advantages and disadvantages of these methods are discussed by several numerical examples. These examples show that the best uniform approximation algorithm provides much tighter approximation interval curves than the perturbation method.

Key words： computer aided geometric design; interval arithmetic; q-Bernstein basis; interval q-Bézier curves; degree reduction

参考文献

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