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Open AccessArticle

Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

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Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
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Department of Mathematics, Cankaya University, 06790 Ankara, Turkey
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan
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Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
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Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
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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
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(4), 474; https://doi.org/10.3390/math8040474
Received: 22 February 2020 / Revised: 25 March 2020 / Accepted: 27 March 2020 / Published: 31 March 2020
(This article belongs to the Special Issue Discrete and Computational Geometry)
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. View Full-Text
Keywords: approximating; varying arity; continuity; Hölder regularity; limit stencils; error bound; shape of limit curves; subdivision schemes approximating; varying arity; continuity; Hölder regularity; limit stencils; error bound; shape of limit curves; subdivision schemes
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Hussain, S.M.; Rehman, A.U.; Baleanu, D.; Nisar, K.S.; Ghaffar, A.; Abdul Karim, S.A. Generalized 5-Point Approximating Subdivision Scheme of Varying Arity. Mathematics 2020, 8, 474.

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