АЛГОРИТМИ ПОБУДОВИ МНОЖИННОЗНАЧНОГО ВІДОБРАЖЕННЯ В R³

In many applied problems, there is a need to construct convex sets, but if these sets are obtained as a solution to a mathematical model, then the concept of a support function is most often used. Although this function is defined only for convex sets, it can also be constructed for convex hulls of compact sets. With the help of this function, it is possible to introduce the concepts of differentiation and integration in the space of convex compact sets. The problem arises of constructing a convex hull of a set if the values of its support function in some directions are known. Three algorithms can be used for this. The first uses the property of the support function and constructs the set through the intersections of hyperplanes defined by the support function. The second algorithm uses the values of the Minkowski functional, which is related to the support function. The third constructs the set according to the meaning of the deformation function, which is also related to the values of the support function. In this article, the task is to compare the construction speed for these three algorithms. The Intel Core i5-13450HX processor was used for calculations. Also in this article, a numerical method for constructing a solution for equations with a set-valued right-hand side, similar to the Euler method, is implemented.