The development of computer-aided design systems involves a combination of fundamental and applied research. The conceptual foundation of the mathematical framework for such systems lies in the notion of a complete geometric body—a geometric set of points where the number of active parameters matches the dimensionality of the space, with the geometric body represented as a distinct part of that space. The analytical representation of these point sets is achieved through the mathematical apparatus of point calculus, which can be generalized to multidimensional spaces. The article compares this proposed approach to solid modeling of geometric objects with existing methods. Examples demonstrating the modeling of geometric bodies using the new approach are provided. The advantages of this ap-proach are emphasized, including the compactness of the analytical description, the elimination of transformation ma-trices, the facilitation of parallel computations within the mathematical framework, and more. Additionally, the article explores the capabilities of modeling geometric bodies in point calculus, such as the representation of isotropic and ani-sotropic bodies as solid geometric objects with a functionally controlled linear or nonlinear spatial structure.
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