SOME ASPECTS OF COMPUTER GEOMETRIC MODELING USING BESIER CURVES

Abstract

In our time, computer information technologies play a very important role in various areas of modern society. This applies to such branches as industry, agriculture, science, education, medicine, culture and others. Today, the outlined directions cannot be imagined without the intensive use of computer graphics, the basic component of which is geometric modeling. Therefore, its further development is an urgent scientific and applied problem. The wide popularity of graphic computer devices and related software is due to their simplicity, convenience and visibility of use. The basis of many modern means of vector geometric modeling is the corresponding parametric lines, in particular, Bezier curves of various degrees, among which the most common are cubic lines. This is due to their sufficient flexibility, the predicted nature of the formation and the effectiveness of computer implementation. However, in some cases it is necessary to use Bezier curves and other degrees, both lower and higher. This fact requires elaboration and improvement of the corresponding mathematical apparatus and computer software. The article is devoted to the further improvement of computer calculation of the areas of curvilinear trapezoids bounded by Bezier curves, the amelioration of appropriate mathematical apparatus and computer software. Such problems constantly spring up, in particular, in case of variant iterative optimization engineering calculations of various technical structures for strength in connection with parametric calculations of the crosssectional areas of power elements, etc. The study examines in detail the proposed mathematical apparatus and the corresponding computer algorithms, emphasizes their advantages over existing methods and provides relevant examples. The presented materials can be successfully implemented in practice in order to improve many means of geometric modeling of modern computer graphics. Some perspectives for the further development of the presented scientific research are determined.