Critical point analysis of an irregular surface model

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The article discusses approaches to modeling a surface by its discrete values. Possible passage positions are shown when modeling the surface according to the amount of information. Existing classification schemes for models according to the structure of input data are considered. The difference in the concepts of mathematical modeling in a narrow and broad sense is shown. The concept of an irregular critical point of a surface is considered, which is associated with the concept of the rank of a map. there are two types of metric points metrizing a given space. The definition of the curvature of the vertex and the degree of curvature is given. Types of points on the surface are defined. a method is proposed for determining irregular (critical) points of a surface by differentiating a matrix of initial data. Here the second partial and mixed derivatives are calculated. Possible cases of analysis of each vertex of the surface are considered. For each vertex, its degree of curvature and the type of vertex are determined. The original matrix with the source data is converted to a new matrix, where the elements show the type of vertex for each point. The task of identifying the desired model is reduced to constructing it in each cell.