IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p474-d339247.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/474/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/4/474/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Aamir Shahzad & Faheem Khan & Abdul Ghaffar & Shao-Wen Yao & Mustafa Inc & Shafqat Ali, 2021. "A Novel Numerical Method for Computing Subdivision Depth of Quaternary Schemes," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    3. Amat, S. & Choutri, A. & Ruiz, J. & Zouaoui, S., 2018. "On a nonlinear 4-point ternary and non-interpolatory subdivision scheme eliminating the Gibbs phenomenon," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 16-26.
    4. Sofiane Zouaoui & Sergio Amat & Sonia Busquier & Mª José Legaz, 2022. "Some New n -Point Ternary Subdivision Schemes without the Gibbs Phenomenon," Mathematics, MDPI, vol. 10(15), pages 1-22, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:474-:d:339247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.