The application of discrete (voxel) geometric models in computer-aided design problems is shown. In this case, the most difficult formalized task of computer-aided design is considered—computer-aided layout. The solution to this problem is most relevant when designing products with a high density of layout (primarily transport equipment). From a mathematical point of view, these are placement problems; therefore, their solution is based on the use of a geometric modeling apparatus. The basic provisions and features of discrete modeling of geometric objects, their place in the system of geometric modeling, the advantages and disadvantages of discrete geometric models, and their primary use are described. Their practical use in solving some of the practical problems of automated layout is shown. This is the definition of the embeddability of the placed objects and the task of tracing and evaluating the shading. Algorithms and features of their practical implementation are described. A numerical assessment of the accuracy and performance of the developed geometric modeling algorithms shows the possibility of their implementation even on modern computers of medium power. This allows us to hope for the integration of the developed layout algorithms into modern systems of solid-state geometric modeling in the form of plug-ins.
Part of the book: Recent Trends in Computational Intelligence