COMPUTER SYNTHESIS OF VECTOR IMAGES BASED ON THE MATHEMATICAL DESCRIPTION OF CONTOURS IN A POLAR COORDINATE SYSTEM

UDC 655.26;004.92

  • Sipaila Siarhei Uladzimiravich – PhD (Engineering), Associate Professor, Assistant Professor, the Department of Printing Production. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: svsip@yandex.by

DOI: https://doi.org/10.52065/2520-6729-2021-249-2-56-61

Key words: contour traceries, symmetry, vector graphics, image synthesis.

For citation: Sipaila S. U. Computer synthesis of vector images based on the mathematical description of contours in a polar coordinate system. Proceedings of BSTU, issue 4, Print- and Mediatechnologies, 2021, no. 2 (249), pp. 56–61 (In Russian). DOI: https://doi.org/10.52065/2520-6729-2021-249-2-56-61.

Abstract

The article describes the process of creating vector images formed by curvilinear contours, the shape of which is described by a mathematical function using a polar coordinate system. The relevance of the problem being solved is revealed, the basic tools of vector graphics programs are assessed, and the possibility of automating the synthesis of vector images using script programs is noted.

Using a function specified in a polar coordinate system makes it possible to mathematically describe curvilinear objects of various shapes and expand the set of generated traceries. To synthesize curvilinear paths in the form of vector objects, it is necessary to transform the original functional description of the path into a set of Bezier curve segments. The article proposes formulas for performing this transformation by calculating the coefficients of the Bezier function. The software implementation of the synthesis of curvilinear objects in the VBA language in the vector graphics program CorelDRAW is described.

The results of computer synthesis of vector images indicate the adequacy of the proposed mathematical apparatus for modeling the shape of curvilinear objects. Based on the generated contours, it is possible to form more complex decorative traceries according to the principles of symmetry. Also, the synthesis of curvilinear objects allows you to solve technical graphics problems.

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06.09.2021