Methods for geometric modelling of curves with a given set of properties interpolating point series of complex configuration form the foundation for developing computer-aided design systems for products bounded by functional surfaces. The key characteristics of the interpolating curve, which ensure the necessary surface properties, include a regular change in curvature values and a minimum number of singular points. The article aims to develop a method for generating a sequence consisting of an arbitrarily large number of specified reference points and assigned intermediate points, which can be interpolated by a monotone curve. The positions of intermediate points are determined based on the pre-assigned properties of the interpolating curve, including the positions of normals and curvature values. The correctness of the solutions proposed in the article is validated through the resolution of a test example. The method developed in the paper is a crucial step towards solving the problem of forming a contour that represents, with given accuracy, a curve with specified properties, interpolating a point series of arbitrary configuration.