Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations

Salah Eddargani, María José Ibáñez, Abdellah Lamnii, Mohamed Lamnii and Domingo Barrera
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Salah Eddargani: Department of Applied Mathematics, University of Granada, 18071 Granada, Spain
María José Ibáñez: Department of Applied Mathematics, University of Granada, 18071 Granada, Spain
Abdellah Lamnii: MISI Laboratory, Faculty of Sciences and Techniques, Hassan First University of Settat, Settat 26000, Morocco
Mohamed Lamnii: LANO Laboratory, Faculty of Sciences Oujda, Mohammed First University of Oujda, Oujda 60000, Morocco
Domingo Barrera: Department of Applied Mathematics, University of Granada, 18071 Granada, Spain

Mathematics, 2021, vol. 9, issue 18, 1-22

Abstract: In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are of class C 2 on the whole domain but fourth-order regularity is required at vertices and C 3 regularity is imposed across the edges of the refined triangulation and also at the interior point chosen to define the refinement. An algorithm is proposed to define the Powell–Sabin triangles with a small area and diameter needed to construct a normalized basis. Quasi-interpolation operators which reproduce sextic polynomials are constructed after deriving Marsden’s identity from a more explicit version of the control polynomials introduced some years ago in the literature. Finally, some tests show the good performance of these operators.

Keywords: Powell–Sabin triangulation; sextic Powell–Sabin splines; Bernstein–Bézier form; Marsden’s identity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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