Compiler for physical and geometric construction of sets

Abstract

This article is devoted to the geometric representation of sets. The paper presents an implementation that allows using operations on sets to build any images. For this algorithm, the equations of first-and second-order lines on the plane and first-and second-order surfaces in space are used. Restrictions are introduced by setting segments on the coordinate axes, indicating whether lines or surfaces belong to these segments. Inequalities are used to create the shaded area of the drawings. In the course of research on this topic, a software tool was developed that allows you to model drawings using the entered formulas, build images based on a set of operations on given sets of points, which allows you to have an analytical description of the drawings. This software tool can be used both in the educational process to test the correctness of the assimilation of the material, and to create flat geometric shapes and three-dimensional bodies for the purpose of engineering the optimal forms of structures and various parts. This application allows the user, performing operations with mathematical expressions and inequalities, to get a graphical display of the result with a mathematical description of any part of the figure.