Numerical and analytical building surface crossing lines in some transport tasks

Abstract

The work is devoted to the creation of three-dimensional models. They explain the sequence and features of constructing lines of intersection of surfaces. This article presents algorithms for constructing lines of intersection of surfaces. This is relevant in the field of computer graphics. Methods for constructing intersection lines of surfaces are developed using the Dragilev’s method. Construction methods are considered by reducing the solution of the problem to the Cauchy problem. And a solution without reduction to the Cauchy problem. The geometric model is also used to solve some transport problems: visualization, construction of calculation grids, etc. The solution is presented for planes specified in parametric form and for planes specified in parametric form. The article has examples of creating virtual models that explain the construction of intersection lines of various planes. The texts of the programs are presented. For example, they illustrate the capabilities of the method of constructing intersection lines of planes, which is performed in the MathCAD 11 system. Computer models help visually convert information in a two-dimensionspace into a three-dimension space and, conversely, a three-dimension space into a two-dimension space. The method described is relevant for use in computer-aided design systems. This approach can be used to solve problems in the field of descriptive geometry.