Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

被引：12

作者：

Hussain, Sardar Muhammad ^{[1
]}

Rehman, Aziz Ur ^{[1
]}

Baleanu, Dumitru ^{[2
,3
,4
]}

Nisar, Kottakkaran Sooppy ^{[5
]}

Ghaffar, Abdul ^{[6
,7
]}

Abdul Karim, Samsul Ariffin ^{[8
,9
]}

机构：

[1] BUITEMS, Dept Math Sci, Quetta 87300, Pakistan

[2] Cankaya Univ, Dept Math, Ankara 06790, Turkey

[3] Inst Space Sci, Magurele 077125, Romania

[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40447, Taiwan

[5] Prince Sattam bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser 11991, Saudi Arabia

[6] Ton Duc Thang Univ, Informetr Res Grp, Ho Chi Minh City 700000, Vietnam

[7] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City 700000, Vietnam

[8] Univ Teknol PETRONAS, Inst Autonomous Syst, Fundamental & Appl Sci Dept, Perak 32610, Malaysia

[9] Univ Teknol PETRONAS, Inst Autonomous Syst, Ctr Smart Grid Energy Res CSMER, Perak 32610, Malaysia

来源：

MATHEMATICS | 2020年 / 8卷 / 04期

关键词：

approximating; varying arity; continuity; Holder regularity; limit stencils; error bound; shape of limit curves; subdivision schemes; INTERPOLATION; SURFACES; FAMILY;

D O I：

10.3390/math8040474

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Subdivision Schemes (SSs) have been the heart of Computer Aided Geometric Design (CAGD) almost from its origin, and various analyses of SSs have been conducted. SSs are commonly used in CAGD and several methods have been invented to design curves/surfaces produced by SSs to applied geometry. In this article, we consider an algorithm that generates the 5-point approximating subdivision scheme with varying arity. By applying the algorithm, we further discuss several properties: continuity, Holder regularity, limit stencils, error bound, and shape of limit curves. The efficiency of the scheme is also depicted with assuming different values of shape parameter along with its application.

引用

页数：25