C-1-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation Benharzallah, Haithem Barrera Rosillo, Domingo Bernstein–Bézier coefficients Quasi-interpolation Type-1 triangulation Clough–Tocher split C1 continuous quasi-interpolating splines are constructed over Clough–Tocher refinement of a type-1 triangulation. Their Bernstein–Bézier coefficients are directly defined from the known values of the function to be approximated, so that a set of appropriate basis functions is not required. The resulting quasi-interpolation operators reproduce cubic polynomials. Some numerical tests are given in order to show the performance of the approximation scheme. 2023-02-09T09:57:01Z 2023-02-09T09:57:01Z 2022-12-23 journal article Benharzallah, H.; Mennouni, A.; Barrera, D. C1-Cubic Quasi-Interpolating Splines in the Bernstein Basis over a Clough–Tocher Refinement of a Type-1 Triangulation. Mathematics 2023, 11, 59. [https://doi.org/10.3390/math11010059] https://hdl.handle.net/10481/79783 10.3390/math11010059 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI