Modeling and visualization of the intersection of a polyhedral surface by a plane

Abstract

The questions of constructing a line of intersection of a polyhedral surface with a plane in general position are considered on the example of a triangular straight prism. Equations are analyzed that make it possible to calculate the coordinates of the obtained points of intersection of surface elements (side edges) with a plane in general position. With the help of a mathematical model, the coordinates of the vertices of the resulting triangle were found, i.e. sections of a right triangular prism by a plane in general position. Then the perimeter of the section of the surface by the plane was determined. As a method for solving the problem, the method of replacing projection planes is used. In this case, the plane of general position is transformed into a front-projecting plane. The problem is simplified, reduced to a simpler problem that can be solved formally. The equations of three lateral faces of a straight prism are composed. The system of equations of two intersecting side faces is analyzed. The system of equations for finding the point of intersection of the side edge and the transformed plane of particular position is solved. The perimeter of the resulting section is determined as the sum of the lengths of the sides of the section triangle. A 3D model of the intersection of a triangular prism and a plane in general position is made. The visualization tools of the AutoCAD computer-aided design system were used.