IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v188y2024ics0960077924010245.html
   My bibliography  Save this article

C1-Positivity preserving Bi-quintic blended rational quartic zipper fractal interpolation surfaces

Author

Listed:
  • Vijay,
  • Chand, A.K.B.

Abstract

In this article, we introduce a new class of bi-quintic partially blended rational quartic zipper fractal interpolation surfaces (RQZFISs) tailored for surface data over a rectangular grid. The construction of these surfaces begins with the generation of a network of curves using univariable rational quartic spline zipper fractal interpolation functions (RQS ZFIFs) with variable scalings. These fractal curves are then blended with quintic blended functions. The proposed RQZFISs encompass traditional rational surfaces and a class of fractal surfaces as particular cases. We demonstrate that the bivariable interpolant uniformly converges to the data-generating function. Additionally, the theory of positivity preservation for these interpolants is explored, with practical examples provided to illustrate positivity-preserving bivariable interpolants.

Suggested Citation

  • Vijay, & Chand, A.K.B., 2024. "C1-Positivity preserving Bi-quintic blended rational quartic zipper fractal interpolation surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924010245
    DOI: 10.1016/j.chaos.2024.115472
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924010245
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115472?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Katiyar, S.K. & Chand, A. K. B & Saravana Kumar, G., 2019. "A new class of rational cubic spline fractal interpolation function and its constrained aspects," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 319-335.
    2. Zhu, Yuanpeng, 2018. "C2 positivity-preserving rational interpolation splines in one and two dimensions," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 186-204.
    Full references (including those not matched with items on IDEAS)

    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. Yu, Binyan & Liang, Yongshun, 2024. "On two special classes of fractal surfaces with certain Hausdorff and Box dimensions," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    2. Ri, Mi-Gyong & Yun, Chol-Hui & Kim, Myong-Hun, 2021. "Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Tyada, K.R. & Chand, A.K.B. & Sajid, M., 2021. "Shape preserving rational cubic trigonometric fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 866-891.

    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:eee:chsofr:v:188:y:2024:i:c:s0960077924010245. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.