FORMATION OF A VARIETY TAKING INTO ACCOUNT THE SPECIFIED CONDITIONS

Abstract

The paper considers the device of a multidimensional geometric object that simulates a system of dependencies of many parameters using geometric modeling. A visual representation of the dependencies of many variables in geometric modeling uses many lines as one-dimensional manifolds. The article discusses the formation of multidimensional objects according to given conditions. It is noted that in the construction of geometric objects there are problems of fulfilling the specified conditions and the need to model the relationship between all or some part of the parameters of a given system. The process of solving the problem requires the construction of a manifold that integrates certain features as its components in terms of their importance, as well as for given manifolds of lower dimension. A technique is being developed for constructing multidimensional geometric figures formed by other manifolds of different dimensions and weights in accordance with specified conditions by gradually changing the dimension and the number of parameters in its analytical expression. The dependence of the coefficients of the equations of the generating geometric objects of lower dimension of variables is used in the geometric model of a multidimensional function. The publication shows the features of the structure of a geometric multidimensional object using many other figures of lower dimension. A different number of parameters in an analytical expression describing a multidimensional geometric object corresponds to a set of other figures of a lower dimension in parallel spaces of the corresponding coordinate system. The definition of sets of lines incident to multidimensional figures at different levels is presented. The structural multidimensional object can be used in solving complex optimization problems with many criteria in the environments of computer-aided design systems..

Keywords: geometric modeling, the variety, dependencies of many variables.