On one approach to the assessment of a triangular element degeneration in a triangulation

A quantitative estimate of a triangular element quality is proposed – the triangle degeneration index. To apply this estimate, the simplest model triangulation is constructed, in which the coordinates of the nodes are formed as the sum of the corresponding coordinates of the nodes of some given regular grid and random increments to them. For different values of the parameters, the empirical distribution function of the triangle degeneration index is calculated, which is considered as a quantitative characteristic of the quality of triangular elements in the constructed triangulation.