C-1-Cubic Quasi-Interpolation Splines over a CT Refinement of a Type-1 Triangulation
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MDPI
Materia
Bernstein–Bézier coefficients Quasi-interpolation Type-1 triangulation Clough–Tocher split
Date
2022-12-23Referencia bibliográfica
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]
Abstract
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.