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Generalized 5-Point Approximating Subdivision Scheme of Varying Arity

Author

Listed:
  • 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
    Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan)

  • 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
    Faculty of Mathematics & Statistics, 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)

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.

Suggested Citation

  • Sardar Muhammad Hussain & Aziz Ur Rehman & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Abdul Ghaffar & Samsul Ariffin Abdul Karim, 2020. "Generalized 5-Point Approximating Subdivision Scheme of Varying Arity," Mathematics, MDPI, vol. 8(4), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:474-:d:339247
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    References listed on IDEAS

    as
    1. Ghulam Mustafa & Faheem Khan, 2009. "A New 4-Point Quaternary Approximating Subdivision Scheme," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-14, June.
    2. Rehan, Kashif & Siddiqi, Shahid S., 2015. "A family of ternary subdivision schemes for curves," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 114-123.
    3. Rehan, Kashif & Sabri, Muhammad Athar, 2016. "A combined ternary 4-point subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 278-283.
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    Cited by:

    1. Pakeeza Ashraf & Abdul Ghaffar & Dumitru Baleanu & Irem Sehar & Kottakkaran Sooppy Nisar & Faheem Khan, 2020. "Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme," Mathematics, MDPI, vol. 8(5), pages 1-14, May.

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