On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming
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Bernstein-Bézier representationCubic splinesQuasi-interpolation schemesSubdivision rules
D. Barrera, S. Eddargani, A. Lamnii, On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming, Journal of Computational and Applied Mathematics, Volume 420, 2023, 114834, ISSN 0377-0427, [https://doi.org/10.1016/j.cam.2022.114834]
Sponsorship"Maria de Maeztu" Excellence Unit IMAG (University of Granada, Spain) CEX2020-001105-MICIN/AEI/10.13039/501100011033; University of Granada University of Granada/CBUA
We discuss the construction of C2 cubic spline quasi-interpolation schemes defined on a refined partition. These schemes are reduced in terms of degrees of freedom compared to those existing in the literature. Namely, we provide a rule for reducing them by imposing super-smoothing conditions while preserving full smoothness and cubic precision. In addition, we provide subdivision rules by means of blossoming. The derived rules are designed to express the B-spline coefficients associated with a finer partition from those associated with the former one.