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RESEARCH PRODUCT

Calculation of Splines Values by Subdivision

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Assume, the samples of a spline \(S(t)\in {}^{p}\fancyscript{S}\) on the grid \(\mathbf{g} =\{k\}_{k\in \mathbb {Z}}\) are available: \(S(k)=y[k]\). Subdivision schemes are proposed to calculate the spline’s values at dyadic and triadic rational points \(S(k/2^m)\) and \(S(k/3^m)\). The SHA technique provides fast and explicit implementation of the subdivision for one- and two-dimensional periodic splines.