ON ONE METHOD OF INVESTIGATING FAMILIES OF POINTS IN THE PROBLEM OF CALCULATING THE DEGREE OF NON-DEGENERACY OF A SIMPLEX

Igumnov Alexander Yurievich

The degree of non-degeneracy of a simplex (tetrahedron) in is understood as a quantitative quantity that characterizes its difference from a degenerate one (if the simplex in question is degenerate, then this difference is zero). One of the ways to calculate the degree of non-degeneracy it consists in considering the vertices of the simplex as a numbered set of points . By introducing a metric on the set of such sets defined by all possible simplices (with the same number of vertices), the degree of non-degeneracy can be considered as the distance from to the set of sets defined by degenerate simplices. The task is reduced to the study of the set in order to identify in it the families closest to . The previously proposed research scheme boils down to splitting the set into parts and examining each of them based on the empirical classification of elements of families of the set . The use of this classification leads to a significant amount of calculations already in the simplest case. In this paper, a different, uniform classification of the elements of the families of the set is proposed. As an example, a new study of families in the case is carried out and a finite class of families sufficient to calculate the desired characteristic is presented. The results of the article can be used both for theoretical and practical application in the tasks of determining the quality of the grid, preserving the properties of the grid with a certain type of mapping, grid generation tasks.

Keywords:non-degeneracy of the simplex, triangular grids, grid quality