$\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH

Year 2025, Volume: 15 Issue: 12, 2718 - 2731, 06.12.2025

Abdellah Lamnii Mohamed Lamnii Chaimae Mouhoub Fatima Oumellal

https://izlik.org/JA44SH46GZ

Abstract

In this work, we are interested in constructing quasi-interpolants in the space of splines $\mathcal{S}_4^3\left(\Delta_6\right)$, where $\Delta_6$ designates a triangulation of a rectangular domain generated by a uniform mesh with six directions. Firstly, we will show that we can have a subspace of $\mathcal{S}_4^3\left(\Delta_6\right)$ containing $\mathbb{P}_4$ generated by the integer translates of a box spline $\phi$ for which we specify the B-coefficients. We also give some main properties of this box spline. Naturally, the B-coefficients of the box spline $\phi$ can be obtained by convolution. However, for reasons of simplicity, we propose a method based on the subdivision schemes to determine them quickly. Finally, given the importance of this triangulation, we develop some discrete and differential quasi-interpolants, and we give numerical examples.

Keywords

Spline Approximation , Box Spline , Subdivision Scheme , Spline Quasi-Interpolation

Thanks

The authors would like to express their sincere gratitude to Mohammed First University – Oujda, Morocco, Hassan I University – Settat, Morocco, and Abdelmalek Essaadi University – T´etouan for their generous support.

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