Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations
Metadatos
Mostrar el registro completo del ítemAutor
Eddargani, Salah; Ibáñez Pérez, María José; Lamnii, Abdellah; Lamnii, Mohamed; Barrera Rosillo, DomingoEditorial
MDPI
Materia
Powell–Sabin triangulation Sextic Powell–Sabin splines Bernstein–Bézier form Marsden’s identity
Fecha
2021Referencia bibliográfica
Eddargani, S.; Ibáñez, M.J.; Lamnii, A.; Lamnii, M.; Barrera, D. Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations. Mathematics 2021, 9, 2276. https://doi.org/10.3390/ math9182276
Patrocinador
Erasmus+ International Dimension programme, European Commission; PAIDI programme, Junta de Andalucía, SpainResumen
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.