Hermitian-type interpolation at point of the system of disjoint lines on a surface

Abstract

A method of construction of the Hermitian-type operators of interlineation of a function of two variables in the cylindrical coordinate system Orφz in the case where the experimental data (traces of a function and its partial derivatives up to the given order in the variable z) are set on the system of known closed disjoint lines. These operators conserve automatically a class of smoothness of the approximated function. On their basis, a method of construction of the Hermitian-type operators of interlineation of a function of two variables on a system of M unknown closed disjoint lines with conservation of a class of smoothness, to which the approximated function belongs. In the cases where the derivatives of some orders or all derivatives are unknown, they can be considered as parameters that allow one to control the ensuring of isogeometric properties of a surface under construction.