Drawing intersection lines between two surfaces is a crucial problem to solve in technical drawing. In machining the surfaces of mechanical casings, complex intersections are often encountered. Common surfaces can be divided into polyhedra and curved surfaces. Finding the intersections of these surfaces is a practical problem in machining mechanical surfaces and a fundamental issue in graphic-drawing techniques. In principle, it is essential to determine the projections of specific points and then connect the lines of intersection in a defined order. Connecting the intersection lines in the correct sequence poses significant challenges. The author has proposed a set of rules for connecting the intersections of two polyhedra and incorporated computer assistance to develop surface applications for production practices.