Geodesic
Sufficient conditions for the comonotone interpolation of cubic $C^2$
Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 3-13.

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We consider the problem of interpolation of a function under the condition of the preservation of the nature of its piecewise monotonicity. We give sufficient conditions for the comonotone interpolation by a classical cubic $C^2$-spline in the representation based on the expansion of its first derivative in a basis consisting of $B$-splines. These conditions allow to determine whether the soobtained spline is comonotone without solving the interpolation problem. 
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V. V. Bogdanov. Sufficient conditions for the comonotone interpolation of cubic $C^2$. Matematičeskie trudy, Tome 14 (2011) no. 2, pp. 3-13. http://geodesic.mathdoc.fr/item/MT_2011_14_2_a0/

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