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Two methods based on spline quasi-interpolants to estimate volumes enclosed by parametric surfaces

Author

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  • Saidi, S.
  • Abbadi, A.
  • Tahrichi, M.

Abstract

In this study, we explore two methods based on spline quasi−interpolants (abbr. QI) that rely exclusively on point evaluations to estimate the volume of a closed parametric surface. The first method involves a division of this surface evenly into parallel slices in order to approximate the contours of each slice using quadratic QI. Subsequently, we calculate numerically the areas of the interior surfaces, which will be used in a quadrature formula to obtain the approximate volume. The second method uses a bivariate QI to calculate the entire area, and an integration formula is applied to estimate the desired volume. In both methods, we study the associated error estimates. Numerical examples are provided to illustrate our methods, as well as a real-world application, as well as a study of the effect of noise on the robustness of both volume estimation methods.

Suggested Citation

  • Saidi, S. & Abbadi, A. & Tahrichi, M., 2025. "Two methods based on spline quasi-interpolants to estimate volumes enclosed by parametric surfaces," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 470-483.
    • Handle: RePEc:eee:matcom:v:230:y:2025:i:c:p:470-483
    DOI: 10.1016/j.matcom.2024.10.032
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    References listed on IDEAS

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    1. Andrea Raffo & Silvia Biasotti, 2021. "Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images," Mathematics, MDPI, vol. 9(23), pages 1-16, November.
    2. Abbadi, A. & Ibáñez, M.J. & Sbibih, D., 2011. "Computing quasi-interpolants from the B-form of B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1936-1948.
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