Dual Hermite subdivision schemes of de Rham-type
The vector subdivision scheme belongs to the iterative algorithms when the resulting refined vector data (containing function values and associated derivatives in the case of Hermite-type data) are obtained from the initial set of vector data by recurrent application of refinement rules. In this paper, a novel method for construction of non-interpolatory Hermite subdivision schemes based on a generalization of the de Rham corner cutting algorithm is presented. The de Rham construction at each subdivision step consists in the double application of an interpolatory Hermite subdivision operator followed by a decimation step selecting only the odd elements of the resulting sequence. Therefore, the de Rham strategy provides Hermite subdivision schemes which are dual by construction, hence approximating the initial data rather than interpolating them. The suggested method is demonstrated on examples, convergence and smoothness investigation including.
scientific article; zbMATH DE number 6387216
scientific article