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

Abdellah Lamnii; Mohamed Lamnii; Chaimae Mouhoub; Fatima Oumellal

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

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

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.

References

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Chui, C.K., and Jiang, Q., (2003), Surface subdivision schemes generated by refinable bivariate spline function vectors, Appl. Comput. Harm. Anal., 15, pp. 147-162.
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Davydov, O., and Sablonnière, P., (2010), $C^2$ piecewise cubic quasi-interpolants on a 6-direction mesh, Journal of Approximation Theory, 162, pp. 528-544.
de Boor, C., Höllig, K., and Riemenschneider, S., (1998), Box Splines, in Applied Mathematical Sciences, Springer-Verlag.
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Details

Primary Language

English

Subjects

Numerical Analysis, Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Abdellah Lamnii ^* This is me
0000-0002-0538-8812
Morocco

Mohamed Lamnii This is me
0000-0002-2532-3418
Morocco

Chaimae Mouhoub This is me
0009-0007-6209-5307
Morocco

Fatima Oumellal This is me
0009-0006-4429-4196
Morocco

Publication Date

December 6, 2025

Submission Date

December 20, 2024

Acceptance Date

March 25, 2025

Published in Issue

Year 2025 Volume: 15 Number: 12

IZ

https://izlik.org/JA44SH46GZ

Cite

RIS / Bibtex

APA

Lamnii, A., Lamnii, M., Mouhoub, C., & Oumellal, F. (2025). $\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH. TWMS Journal of Applied and Engineering Mathematics, 15(12), 2718-2731. https://izlik.org/JA44SH46GZ

AMA

1.Lamnii A, Lamnii M, Mouhoub C, Oumellal F. $\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH. JAEM. 2025;15(12):2718-2731. https://izlik.org/JA44SH46GZ

Chicago

Lamnii, Abdellah, Mohamed Lamnii, Chaimae Mouhoub, and Fatima Oumellal. 2025. “$\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH”. TWMS Journal of Applied and Engineering Mathematics 15 (12): 2718-31. https://izlik.org/JA44SH46GZ.

EndNote

Lamnii A, Lamnii M, Mouhoub C, Oumellal F (December 1, 2025) $\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH. TWMS Journal of Applied and Engineering Mathematics 15 12 2718–2731.

IEEE

[1]A. Lamnii, M. Lamnii, C. Mouhoub, and F. Oumellal, “$\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH”, JAEM, vol. 15, no. 12, pp. 2718–2731, Dec. 2025, [Online]. Available: https://izlik.org/JA44SH46GZ

ISNAD

Lamnii, Abdellah - Lamnii, Mohamed - Mouhoub, Chaimae - Oumellal, Fatima. “$\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH”. TWMS Journal of Applied and Engineering Mathematics 15/12 (December 1, 2025): 2718-2731. https://izlik.org/JA44SH46GZ.

JAMA

1.Lamnii A, Lamnii M, Mouhoub C, Oumellal F. $\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH. JAEM. 2025;15:2718–2731.

MLA

Lamnii, Abdellah, et al. “$\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 12, Dec. 2025, pp. 2718-31, https://izlik.org/JA44SH46GZ.

Vancouver

1.Abdellah Lamnii, Mohamed Lamnii, Chaimae Mouhoub, Fatima Oumellal. $\mathcal{C}^3$ QUARTIC QUASI-INTERPOLANTS OVER A 6-DIRECTION MESH. JAEM [Internet]. 2025 Dec. 1;15(12):2718-31. Available from: https://izlik.org/JA44SH46GZ