Особенности твердотельного моделирования в точечном исчислении

Abstract

The basic operations of constructing solid-state geometric objects in the form of an organized threeparameter set of points in three-dimensional space are described based on algorithms implemented in point calculus. These include shaping operations of extrusion and rotation and a kinematic operation with the possibility of axial rotation of the section plane. For the kinematic operation and the extrusion operation, algorithms are given in a general form without reference to specific examples. Moreover, due to the use of point calculus, the proposed algorithms can be generalized to a multidimensional space and allow for an analytical description of multidimensional solid models. Particular attention was paid to the construction of a surface of revolution with a generatrix of a semicycloid in various parametrizations, examples of constructed curves and surfaces were given, and an algorithm for constructing a body of revolution was obtained. Solid models are currently widely used in simulation modeling and differ from geometric modeling and computer graphics by the maximum approximation of the model to its physical prototype. The use of solid modeling methods makes it possible to carry out complex engineering calculations performed during the design process in a semi-automatic mode. The paper gives examples of the use of the obtained geometric algorithms, justifies the use of point calculus as the main tool for the implementation of three-dimensional solid models.