Quasi-Interpolation in a Space of C 2 Sextic Splines over Powell–Sabin Triangulations Eddargani, Salah Ibáñez Pérez, María José Lamnii, Abdellah Lamnii, Mohamed Barrera Rosillo, Domingo Powell–Sabin triangulation Sextic Powell–Sabin splines Bernstein–Bézier form Marsden’s identity 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. 2021-10-18T09:43:55Z 2021-10-18T09:43:55Z 2021 journal article 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 http://hdl.handle.net/10481/70927 10.3390/math9182276 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI