On C2 cubic quasi-interpolating splines and their computation by subdivision via blossoming

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. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

The construction of C2 cubic spline quasi-interpolation schemes on a refined partition is discussed in this paper. These schemes are reduced in terms of degrees of freedom compared to those existing in the literature. Super-smoothing conditions are imposed to reduce them while preserving full smoothness and cubic precision. In addition, subdivision rules are provided using blossoming.