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Software systems and computational methods

Cyclographic modeling of solutions of geometric optics problems on the plane
Panchuk Konstantin Leonidovich

Doctor of Technical Science

Professor, Department of Engineering Geometry and CAD, Omsk State Technical University

644050, Russia, Omskaya oblast', g. Omsk, ul. Pr. Mira, 11, aud. 8-513

Lyubchinov Evgenii Vladimirovich

Lecturer, Department of Engineering Geometry and CAD, Omsk State Technical University

644050, Russia, Omskaya oblast', g. Omsk, ul. Pr. Mira, 11, aud. 8-518




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The subject of research is the optical transformations of pairs of basic geometric objects on a plane that simulate various sources of radiation. In the general case, when solving problems of geometric optics on a plane, the task of transforming one beam of rays into another, for example, converting rays of a point source into a system of parallel rays, is distinguished. Such tasks require the creation of a relatively simple method based on the laws of geometrical optics and allowing one to obtain reflective lines of a certain geometry corresponding to the given initial data. Obtaining a reflective line for different combinations of central, parallel and scattered direct beam transformations in this work is based on the cyclographic display method. The method is based on the optical properties of a cyclographic model of a spatial curve of a line and makes it possible to obtain reflective curves of various shapes during optical transformations of straight beams. The use of this method in building a source-receiver system makes it possible to select a receiver (or source) from a variety of receivers (sources) with the same reflector line. The study showed that the cyclographic mapping method makes it relatively easy to obtain reflective lines during optical transformations of various beam beams, while the analytical algorithm makes it possible to obtain parametric equations of this line. The results of the work can be used in the design of various optical systems in the antenna, laser and lighting engineering industries.

Keywords: evolvent, reflective lines, cyclographic mapping, pencil of rays, geometrical optics, Optical transformations, evolute, ruled surface, intersection line, spatial visualization
This article written in Russian. You can find full text of article in Russian here .

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