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.
Floater, M., Beccari, C., Cashman, T., Romani, L. (2013). A smoothness criterion for monotonicity-preserving subdivision. ADVANCES IN COMPUTATIONAL MATHEMATICS, 39(1), 193-204 [10.1007/s10444-012-9275-y].
A smoothness criterion for monotonicity-preserving subdivision
ROMANI, LUCIA
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.
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