SHAPING OPERATIONS OF EXTRUSION AND ROTATION OF SOLID-STATE MODELING OF GEOMETRIC OBJECTS IN THE POINT CALCULUS

Abstract

The shaping operations of extrusion and rotation within the framework of point calculus are implemented. The principles of parametrization of bodies in point calculus are described. When considering the extrusion operation, the cases of performing this operation at a right angle and with a variable inclination angle of the generatrix are taken into account. When implementing the rotation operation, the method of polar parameterization of the sketch plane is considered. Due to the use of point calculus, the proposed approach makes it possible to obtain body models in the form of a three-parameter set of points in the three dimensional space, the density of which depends on the parameters of the three dimensional model set by the designer. The analysis of existing systems of solid modeling and their capabilities in the direction of creating solid models of bodies is carried out. It showed that almost all of them provide the user with models presented as surfaces of body shells and are not filled with points. None of the existing CAD makes it possible to model a body in the form of a three parameter set of points. And when trying to use the proposed modeling apparatus within existing computeraided design systems (for example, outputting a model in the form of a set of points through the API of these systems), we risk getting a body model that is simply impossible to work with due to the excessive consumption of PC resources used for modeling (for example, even a model of a simple body with a high density of points can lead to a “freeze” of the system even on a computer with high computing power). In addition, the evaluation of the effectiveness of the mathematical apparatus embedded in the modeling systems cannot be effectively carried out since the mathematical basis of these CAD systems is a trade secret. In this case comparison is necessary, since the proposed three dimensional models consist of the same type of equations along all coordinate axes, which, if used correctly in CAD, can lead to significant savings in computing power due to parallelization of the data processing across different computational threads.