Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

Sardar Muhammad Hussain, Aziz Ur Rehman, Dumitru Baleanu, Kottakkaran Sooppy Nisar, Abdul Ghaffar and Samsul Ariffin Abdul Karim
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Sardar Muhammad Hussain: Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
Aziz Ur Rehman: Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
Dumitru Baleanu: Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Abdul Ghaffar: Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
Samsul Ariffin Abdul Karim: Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Seri Iskandar 32610, Perak DR, Malaysia

Mathematics, 2020, vol. 8, issue 4, 1-25

Abstract: 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, Hölder 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.

Keywords: approximating; varying arity; continuity; Hölder regularity; limit stencils; error bound; shape of limit curves; subdivision schemes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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