Analysis of Geometric Properties of Ternary Four-Point Rational Interpolating Subdivision Scheme

Pakeeza Ashraf, Bushra Nawaz, Dumitru Baleanu, Kottakkaran Sooppy Nisar, Abdul Ghaffar, Muhammad Aqeel Ahmed Khan and Saima Akram
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Pakeeza Ashraf: Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan
Bushra Nawaz: Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, 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
Muhammad Aqeel Ahmed Khan: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Saima Akram: Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University Multan, Multan 66000, Pakistan

Mathematics, 2020, vol. 8, issue 3, 1-19

Abstract: Shape preservation has been the heart of subdivision schemes (SSs) almost from its origin, and several analyses of SSs have been established. Shape preservation properties are commonly used in SSs and various ways have been discovered to connect smooth curves/surfaces generated by SSs to applied geometry. With an eye on connecting the link between SSs and applied geometry, this paper analyzes the geometric properties of a ternary four-point rational interpolating subdivision scheme. These geometric properties include monotonicity-preservation, convexity-preservation, and curvature of the limit curve. Necessary conditions are derived on parameter and initial control points to ensure monotonicity and convexity preservation of the limit curve of the scheme. Furthermore, we analyze the curvature of the limit curve of the scheme for various choices of the parameter. To support our findings, we also present some examples and their graphical representation.

Keywords: Monotonicity-preservation; convexity-preservation; curvature; rational interpolating; subdivision schemes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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