AUTOMATION OF THE SELECTION OF CONTROL PARAMETER VALUES FROM THE SOLUTION POLYGON IN THE METHOD OF VARIABLE FORMATION OF DIFFERENT SCHEMES OF ANGULAR PARAMETERS

Abstract

Using geometric modeling, it is possible to solve a certain number of scientific and industrial tasks, for example, designing functional surfaces of the car body, turbine blades, channel surfaces of internal combustion engines, etc. Among the known methods of discrete interpolation, a separate direction should be singled out - variable discrete geometric modeling (VDM) [3], the defining feature of which is that as a result of the simulation, not one value of the parameter is calculated, but the interval of its permissible values, from which the desired, optimal in the sense of the problem, the value of the parameter. Among the well-known VDGM methods, the interpolation method based on the variable formation of difference schemes of angular parameters should be noted [4]. When using this method, the condition of no oscillation was used in the thickening process. When applying this condition, we get a polygon of solutions. And the task of automating the search for the center of a given polygon becomes

 

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urgent.

The paper considered how the process of finding the geometric center of a convex polygon can be automated, which will allow to implement the algorithm for finding the values of the control parameters in the method of variable formation of the difference schemes of the angular parameters.

The sequence of actions is as follows. After imposing the condition of absence of oscillation, we get a system of inequalities, the solution of which gives us the solution polygon. Its vertices are the result of the intersection of paired straight lines. We arrange the vertices, while assuming (conditionally) that the vertices are traversed in the order of numbering clockwise starting from the point for which the value of x0 = min (xi). After that, we determine the geometric center (centroid) according to the formula [2] of this closed polygon, the coordinates of the vertices of which form a discrete point series.

Keywords: variable discrete geometric modeling, condensation method, convex polygon, centroid, automation.