In this paper we study subdivision schemes that both interpolate and preserve the monotonicity of the input data, and we derive a simple ratio condition that guarantees the continuous differentiability of the limit function. We then show that the condition holds for both a scheme of Kuijt and van Damme, based on rational functions, and a scheme of Sabin and Dodgson, based on square roots.
M. Floater, C. Beccari, T. Cashman, L. Romani (2013). A smoothness criterion for monotonicity-preserving subdivision. ADVANCES IN COMPUTATIONAL MATHEMATICS, 39, 193-204 [10.1007/s10444-012-9275-y].
A smoothness criterion for monotonicity-preserving subdivision
BECCARI, CAROLINA VITTORIA;L. Romani
2013
Abstract
In this paper we study subdivision schemes that both interpolate and preserve the monotonicity of the input data, and we derive a simple ratio condition that guarantees the continuous differentiability of the limit function. We then show that the condition holds for both a scheme of Kuijt and van Damme, based on rational functions, and a scheme of Sabin and Dodgson, based on square roots.File in questo prodotto:
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