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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Communicated by: Raymond H. Chan.
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Floater, M., Beccari, C., Cashman, T. et al. A smoothness criterion for monotonicity-preserving subdivision. Adv Comput Math 39, 193–204 (2013). https://doi.org/10.1007/s10444-012-9275-y
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DOI: https://doi.org/10.1007/s10444-012-9275-y