Visualization of Regular Polyhedrons during Their Formation

Abstract

In this work the automated formation of surfaces correct to convex polyhedrons of Platon and two regular not convex star-shaped polyhedrons of Kepler-Poinsot by the kinematic method. Researches on realization of a goal were carried out in the environment of AutoCAD with use of the programs developed in the functional Autolisp programming language which is built in AutoCAD. The AutoLisp language and the AutoCAD environment are chosen for achievement of a goal as they allow showing bodies in the movement. The technique of formation of electronic models of the polyhedrons necessary for performance of visualization of polyhedrons is stated. The model is a set of compartments of a surface, issued in the form of the block. The user function in the AutoLisp language which identifier is team in the environment of AutoCAD is developed for each model. Each compartment was placed in the drawing layer which is taken away for it. When developing the user functions were taken into account to a possibility of the AutoCAD environment – the available teams for formation of surfaces. The user functions in the AutoLisp language for formation of the studied surfaces in the environment of AutoCAD are made by the defrosting method of the block containing surface compartments. In the course of "defrosting" of layers with compartments on the screen of the monitor process of formation of a surface is shown – drawings of compartments of a surface appear one by one. The last drawing is an image of a surface. The user functions in the AutoLisp language for formation of the studied surfaces in the environment of AutoCAD are made. The fragment of the program by training of one side of a tetrahedron is given Drawings of elements of surfaces of all regular polyhedrons of Platon and star-shaped polyhedrons of Kepler-Poinsot are provided in initial situation and in the course of stage-by-stage formation of these surfaces, the programs received in the environment of AutoCAD with use in the AutoLisp language. Drawings of elements of surfaces of all regular polyhedrons of Platon and star-shaped polyhedrons of Kepler-Poinsot are provided in initial situation and in the course of stage-by-stage formation of these surfaces, the programs received in the environment of AutoCAD with use in the AutoLisp language. The possibility of formation of surfaces of regular polyhedrons is shown by a kinematic method: the movement rectilinear forming on the directing lines as which edges of polyhedrons are used.