ГЕОМЕТРИЧНЕ МОДЕЛЮВАННЯ СКЛАДНИХ ОБ’ЄКТІВ НА ОСНОВІ ПОЛІТОЧКОВИХ ВІДОБРАЖЕНЬ ВІДРІЗКІВ ПРЯМИХ

Abstract

In this paper, we propose a method of polypointed mappings of line segments in geometric modeling of complex objects, which differs from ordinary polypointed mappings in that you can set straight lines as an inverse image, not in an implicit form, but as a set of points and obtain a transformed object as a set of points. In addition, it is proposed to use weights for each base point, which allows you to control the shape of the transformed curve in such a way that the curve is somehow attracted to a point with a higher weight compared to other base points. Polypoint transformations are used in the design of complex geometric shapes in mechanical engineering. Enhancing the capabilities of polypoint transformations is an important issue at the present time. The aim of the article is the use of line segments in the method of polypoint mappings for geometric modeling of complex objects. The proposed process of weighted political dot mapping can be applied in the implementation of geometric modeling of complex shape objects with the ability to control the shape of a simulated object by changing the weights of the points. As shown in test examples, the shape of the transformed figure changes in such a way that it seems to be attracted to points with increased weight and, conversely, is repelled from points with reduced weight. As the disadvantages of the proposed method, one can indicate an insufficient level of predictability of the result. Further research is proposed in identifying the properties of using weighted polypoint mappings in the direction of increasing the level of predictability of the results for effective use in geometric modeling of complex objects. Key words: discrete-given curve, line segment, polypoint mapping of lines, geometric modeling.