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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

Quaternary subdivision scheme with two parameters

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双参数四重细分法

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Jun.2024, Vol.47 No.6: 823-828

DOI: 10.3969/j.issn.1003-5060.2024.06.016

Authors

LIU Zhi $ ^{1} $, LI Rui $ ^{1} $, WANG Xuhui $ ^{2} $

(1. School of Mathematics, Hefei University of Technology, Hefei 230601, China; 2. School of Mathematics, Hohai University, Nanjing 210098, China)

Abstract and Keywords

Abstract: A quaternary subdivision scheme with two parameters is proposed by using reverse construction and multiplying smoothing factor. The continuity of this quaternary subdivision scheme is analyzed by generator polynomial. The specific parameter value intervals satisfying $ C^{0}-C^{3} $ continuity are provided. Numerical examples demonstrate the influence of each parameter on the curve formation, and the dynamic parameter iteration process describes the change details of the curve generation.

Keywords: reverse construction; generator polynomial; quaternary subdivision; $ C^{k} $-continuity; parameter selection

作者信息

刘植 $ ^{1} $，李睿 $ ^{1} $，王旭辉 $ ^{2} $

(1. 合肥工业大学数学学院，安徽合肥 230601；2. 河海大学数学学院，江苏南京 210098)

摘要和关键词

摘要: 文章借助反向构造和倍乘平滑因子操作提出一种双参数四重细分法,运用生成多项式推导证明该四重细分方法的连续性,求解出满足 $ C^{0}\sim C^{3} $ 连续性的具体参数取值区间。该文通过数值实例分析各参数对形成曲线的影响,用动态的参数迭代过程描述曲线生成的变化细节。

关键词: 反向构造；生成多项式；四重细分； $ C^{k} $ 连续性；参数选取

Funding

国家自然科学基金资助项目（62172135）

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