IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i11p1736-d1407724.html
   My bibliography  Save this article

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

Author

Listed:
  • Abdelouahed Kouibia

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Miguel Pasadas

    (Department of Applied Mathematics, University of Granada, 18071 Granada, Spain)

  • Loubna Omri

    (FSJES of Tetuan, University Abdelmalek Essaidi, Tetuan 93030, Morocco)

Abstract

In the study of some real cases, it is possible to encounter well-defined geometric conditions, of an industrial or design type—for example, the case of a specific volume within each of several holes. In most of these cases, it is recommended to fulfil a function defined in a domain in which information is missing in one or more sub-domains (holes) of the global set, where the function data are not known. The problem of filling holes or completing a surface in three dimensions appears in many fields of computing, such as computer-aided geometric design (CAGD). A method to solve the shape-preserving variational spline approximation problem for hole filling in generalized offset surfaces is presented. The existence and uniqueness of the solution of the studied method are established, as well as the computation, and certain convergence results are analyzed. A graphic and numerical example complete this study to demonstrate the effectiveness of the presented method. This manuscript presents the resolution of a complicated problem due to the study of some criteria that can be traduced via an approximation problem related to generalized offset surfaces with holes and also the preservation of the shape of such surfaces.

Suggested Citation

  • Abdelouahed Kouibia & Miguel Pasadas & Loubna Omri, 2024. "A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces," Mathematics, MDPI, vol. 12(11), pages 1-11, June.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1736-:d:1407724
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/11/1736/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/11/1736/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yousif, Majeed A. & Hamasalh, Faraidun K., 2024. "The fractional non-polynomial spline method: Precision and modeling improvements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 512-525.
    2. Kouibia, A. & Pasadas, M., 2008. "Bivariate variational splines with monotonicity constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 228-236.
    3. Fortes, M.A. & Medina, E., 2022. "Fitting missing data by means of adaptive meshes of Bézier curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 33-48.
    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. Cemil Tunç & Fahir Talay Akyildiz, 2024. "Unique Solutions for Caputo Fractional Differential Equations with Several Delays Using Progressive Contractions," Mathematics, MDPI, vol. 12(18), pages 1-15, September.
    2. Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.
    3. Ying-Ying Yu & Xin Li & Ye Ji, 2024. "On Intersections of B-Spline Curves," Mathematics, MDPI, vol. 12(9), pages 1-17, April.

    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:12:y:2024:i:11:p:1736-:d:1407724. 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.