Discrete-voxel representation of object models for the identification and calculation of their fractal parameters

The paper proposes an approach to the discrete-voxel representation of models of various types of objects and investigates a set of geometric parameters that influence the technical and technological characteristics of their effective functioning.
On the basis of the basic element, which is a voxel, the relationship between the neighborhood characteristics of individual component models, which are decisive during the discrete presentation of images of different dimensions, is considered. The work provides a methodology for calculating the main geometric parameters of objects represented by voxels, and the analysis of the neighborhood parameters of their elementary components made it possible
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to effectively distinguish the boundary and internal points on the images and combine them into integral geometric images on the spatial image.
Algorithms for calculating characteristic parameters of voxel models of different dimensions are presented. It is proposed to calculate the areas of the compartment and the outer surface of two- and three-dimensional models through the geometric characteristics of families of discrete-voxel models of the border lines of the frame in one of the directions.
Emphasis is placed on the fact that one of the basic geometric characteristics in relation to this issue is the fractal dimension of discrete-voxel models of the studied objects. Fractal theory methods are quite well developed, but their implementation is time-consuming and, as a rule, it is not related to complex generalization and identification of basic geometric characteristics of modeled objects, especially in voxel representation. Therefore, in a number of published works known to us, only the synthesis of simple, as a rule, two-dimensional structures was brought to the stage of practical implementation of the process of modeling fractal structures.
The paper describes an approach to calculating the fractal dimension of discrete-voxel models and identifies ways to improve the functional qualities of objects due to effective management of a set of their geometric parameters. An algorithm is proposed that allows you to significantly simplify the procedure for calculating the fractal dimension by reducing the dimension of the space for each layer along one of the axes of the coordinate system.
Prospects for further scientific research both in the direction of improving the proposed software algorithms and in expanding the scope of their application are determined.