Analytical and Computergraphic Method of Surfaces’ Formation Projected by Rays of Congruence of Cylindrical Screw Lines With the Constant Step

Abstract

Abstract-Relevance of the research: The relevance of this study is due to the fact that the condition for the use of computer technologies in design requires an analytical interpretation of existing constructive ways of shaping products of complex shape. Development of the general analytical model of nonconventional systems of projection and their projecting surfaces applicable in computer technologies makes a current problem. Since screw motion is one of the most "technological" movements after the translational and rotational motion, the problem of computer-aided design of screw surfaces is relevant. Relevance of the problem The central and parallel projection due to the fact that at their application the straight line is mapped onto any plane of projections of a straight line, they have the most widespread use. We will call them traditional. The purpose of traditional systems is the graphic modelling of three-dimensional objects by their projections, at least on two planes making the system of projections.Recently in application-oriented geometry many non-traditional systems of projection are introduced. Emergence of non-traditional systems is caused by need for graphical representation and research of specific objects, in particular, the surfaces formed by the family of rays of the corresponding system, projecting the presented line. Such systems can be classified by type of the ray and by determinant of the system itself, which would provide the passage of one ray through an arbitrary point of the area of space defined for it. In this case, the concept of a projecting ray extends to a planar or three-dimensional curve. In case of systems with rectilinear