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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
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    References listed on IDEAS

    as
    1. Kouibia, A. & Pasadas, M., 2008. "Bivariate variational splines with monotonicity constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 228-236.
    2. 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.
    3. 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.
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