GENERAL SCHEME OF THE METHOD OF VARIATIVE FORMATION OF DIFFERENT SCHEMES OF ANGULAR PARAMETERS

Abstract

An analysis of the known methods of continuous geometric modeling showed that they rely on a predetermined class of functions. This leads to the replacement of the differential-geometric characteristics of the DPC by the characteristics of these functions and does not exclude the influence of the properties of the modeling function on the simulation result. Discrete interpolation methods are deprived of the above drawbacks, which, in addition to guaranteeing the absence of oscillations and having wide possibilities for local solution correction, have the simplicity of computational algorithms and their software implementation.

There is a wide variety of discrete geometric modeling methods that allow you to solve the problem of thickening of the duodenum of arbitrary shape. These methods differ in complexity and versatility in solving applied problems of geometric modeling. Among the well-known methods of discrete interpolation, a separate direction should be distinguished - variable discrete geometric modeling (VDGM) [1], the defining feature of which is that as a result of modeling not one parameter value is calculated, but the interval of its admissible values, from which the desired one is selected, optimal in the sense of the problem, the value of the parameter. One of the methods of VDGM is the method of variably forming difference schemes of angular parameters, the distinguishing feature of which is that it uses angular parameters in the process of condensation, as well as that which is equally effective for convex (concave) DPC, and DPC with features in geometry. However, like most existing methods, in its practical application not only the main algorithm of the method is used, but also its modifications depending on the type of condensed sections (concave, convex, contain transitional or rectilinear sections, singular points). Therefore, for the practical use of this method, it was necessary to develop a general scheme of the method, which in the future will increase the efficiency of its application.

Keywords: geometric modeling, variable discrete geometric modeling, discrete interpolation, general interpolation scheme.