Sufficient conditions for the comonotone interpolation of cubic $C^2$

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.