Resumen
A matrix model of the representation of spatial objects for the synthesis, reconstruction, and analysis of their shape is proposed. The model is built on the basis of discrete data about the object, such as, for example, raster images or readings of spatial scanners. Unlike similar voxel models, matrix models describe not the volume but the surfaces of objects and, while preserving the advantages of voxel models, such as simplicity and regularity of structure, eliminate their inherent redundancy. It is shown in the work that, while retaining information on the form sufficient for visualizing the object, the matrix model can occupy 1.5?3 times less memory (the comparison was carried out for models in the VOX format of the MagicaVoxel package). The conditions are established under which the matrix model remains more economical than the voxel model, and it is shown that these conditions are satisfied for practically significant cases.An algorithm for constructing a discrete matrix model based on a voxel is described.A general approach to solving the problem of the resampling of models of three-dimensional graphics objects is proposed, which does not depend on the dimension of the source data array. In the framework of this approach, the matrix model is resampled. The necessary transformations of the model matrices are described, including both resampling and requantization, which ensures their controlled accuracy of the representation of spatial objects.Procedures for monitoring and restoring integrity have also been developed for the proposed matrix model. The obtained conditions for monitoring the integrity of the model in practically significant cases (when the number of model elements is more than 153) can reduce the number of elements viewed, compared with the voxel model.The limitations of matrix models are established associated with the possible loss of information about a part of the surface hidden from an external observer