STRUCTURAL-PARAMETRIC MODEL OF SECOND-ORDER SURFACES

Abstract

One of the modern directions for the further development of the applied geometry scientific school of the Igor Sikorsky Kyiv Polytechnic Institute is the structural-parametric shaping of various technical objects. Currently, the general theoretical foundations of this methodology and specialized means of its practical implementation are being developed. The results obtained in the design, manufacture and operation of specific industrial products largely depend on their efficiency.
 The created mathematical models serve as the basis for software modules, which become components of the applied computer information systems. In these conditions, the issues of developing the necessary methodological support are also important. From the side of the theory of structural-parametric shaping, requirements are imposed on new geometric means in accordance with the principles of universality and unification, variability, openness and development, a system approach, etc.
 As can be seen from the title of the publication, in our case we are talking about second-order surfaces, which, due to their useful properties, are quite common in many technical objects. Note that the plane is considered a simplified version of these figures. The indicated universality and unification consist in solving a wide range of problems using the same type of methods, techniques, algorithms, etc. Variability is the need to implement for the geometric model of its flexible and productive use, the openness and the development – of easy updating, expansion and improvement its components. The systems approach requires considering the created mean not only as interconnected elements, but also as a part of systems of a higher hierarchical level. The submitted second-order surface model satisfies the rules described above. Its main peculiarity lies in the combination of the vector definition of these items with the structural-parametric methodology. The developed techniques of shaping are suitable for wide practical use during the automated design of various technical objects, the processes of their production and operation.