Abstract. The authors present a method to construct operators of inerlineation of Hermitian type for functions of two and three variables in the Cartesian and cylindrical systems of coordinates for the case where experimental data (traces of the function and its partial derivatives to a prescribed order) are set on a system of nonintersecting lines. These operators save the class of differentiability of the approximated function. On their basis, a method is proposed to construct interpolation operators for functions of two variables of Hermitian type in cylindrical system of coordinates with automatic preservation of the class of differentiability to which the approximated function belongs. For the case where the values of derivatives of some or all orders are unknown, they can be considered control parameters of the isogeometrical properties of the surface under construction.

Keywords: Hermite interpolation, Hermite inerlineation, interlineation with keeping differentiability class, isogeometric properties of surface being constructed.