Abstract
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
Highlights
One of the most common ways of representing three-dimensional bodies in the problems of their synthesis and analysis using computer graphics is discrete models composed of voxels – volume elements in the form of parallele pipeds or, much less commonly, balls [1]
A complete discrete matrix model (DMM) of a three-dimensional body is constructed on the basis of its Voxel models (VM) and is case the face Fi closest to Gi remains in consideration
A matrix model is proposed that describes the surface of a spatial object in the form of six relief matrices and possesses the advantages of existing voxel models
Summary
One of the most common ways of representing three-dimensional bodies in the problems of their synthesis and analysis using computer graphics is discrete models composed of voxels – volume elements in the form of parallele pipeds (most often cubes) or, much less commonly, balls [1]. Voxel models (VM) are the basis of volumetric graphics and are used, as a rule, for the synthesis of virtual or approximations of real three-dimensional objects in the tasks of their visualization They are widely used in medical diagnostic systems (computer, magnetic resonance, positron emission tomography), for creating virtual reality of various kinds of simulators, in 3D printers, in systems of modeling of spatial forms. For example, it should be noted that they are independent of the complexity of the modeled objects and their surroundings, the regula rity of the structure, the simplicity of processing, which is especially important for solving the problems of shape reconstruction [3, 4] The relevance of this issue is determined by the fact that VMs contain a significant amount of redundant information that is not directly related to the description of the shape of a three-dimensional object, which is the main obstacle to Information technology. The initial data in them, as a rule, are discrete data from different types of scanners
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Eastern-European Journal of Enterprise Technologies
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
