{"id":7295,"date":"2021-04-19T09:53:16","date_gmt":"2021-04-19T06:53:16","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=7295"},"modified":"2021-08-05T13:32:57","modified_gmt":"2021-08-05T10:32:57","slug":"%d0%b0%d0%bd%d1%96%d0%bc%d1%83%d0%b2%d0%b0%d0%bd%d0%bd%d1%8f-%d0%be%d0%b1%d1%94%d0%ba%d1%82%d1%96%d0%b2-%d0%b7%d0%b0-%d0%b4%d0%be%d0%bf%d0%be%d0%bc%d0%be%d0%b3%d0%be%d1%8e-%d0%b0%d1%84%d1%96","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=7295","title":{"rendered":"\u0410\u043d\u0456\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u043e\u0431\u2019\u0454\u043a\u0442\u0456\u0432 \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0430\u0444\u0456\u043d\u043d\u0438\u0445 \u043f\u0435\u0440\u0435\u0442\u0432\u043e\u0440\u0435\u043d\u044c"},"content":{"rendered":"

<\/p>\n

\u0410\u041d\u0406\u041c\u0423\u0412\u0410\u041d\u041d\u042f \u041e\u0411\u2019\u0404\u041a\u0422\u0406\u0412 \u0417\u0410 \u0414\u041e\u041f\u041e\u041c\u041e\u0413\u041e\u042e \u0410\u0424\u0406\u041d\u041d\u0418\u0425 \u041f\u0415\u0420\u0415\u0422\u0412\u041e\u0420\u0415\u041d\u042c<\/p>\n

ANIMATION OF OBJECTS BY MEANS OF AFFINE TRANSFORMATIONS<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 73-77. \u041d\u043e\u043c\u0435\u0440: \u21161, 2021 (293)<\/strong> \"\"<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u041e. \u042e. \u0428\u0410\u041c\u0423\u0420\u0410\u0422\u041e\u0412, \u041d. \u0411. \u0428\u0410\u0425\u041e\u0412\u0421\u042c\u041a\u0410
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u00ab\u041b\u044c\u0432\u0456\u0432\u0441\u044c\u043a\u0430 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u043a\u0430\u00bb
\nO. Y. SHAMURATOV, N. B. SHAKHOVSKA
\nNational University Lviv Polytechnic
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2021-293-1-73-77<\/a>
\n\u0420\u0435\u0446\u0435\u043d\u0437\u0456\u044f\/Peer review :<\/strong> 20.02.2021 \u0440.
\n\u041d\u0430\u0434\u0440\u0443\u043a\u043e\u0432\u0430\u043d\u0430\/Printed :<\/strong> 10.03.2021 \u0440.<\/p>\n

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\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0430\u0444\u0456\u043d\u043d\u0456 \u043f\u0435\u0440\u0435\u0442\u0432\u043e\u0440\u0435\u043d\u043d\u044f, \u0430\u043d\u0456\u043c\u0443\u0432\u0430\u043d\u043d\u044f \u043e\u0431\u2019\u0454\u043a\u0442\u0456\u0432, \u0447\u0430\u0441\u043e\u0432\u0430 \u0441\u043a\u043b\u0430\u0434\u043d\u0456\u0441\u0442\u044c.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The algorithm of creation of effect of animation of objects on static images by means of affine transformations in the conditions of limited capacitive and time complexity is developed in the work. Today, image animation is increasingly used in the entertainment industry and is performed with limited resources – on mobile devices, in real time and more. Animation objects can be of various natures, from human faces, non-physical objects (avatars) to anything user-defined in an image. By image animation we mean changing the parameters of selected objects in the image over time. This will be based on the fact that the human visual system perceives a set of individual images that are presented at a fairly high speed, as a continuous movement. By variable parameters of an object we mean moving an object while preserving its shape. The need to develop such an algorithm arises for image processing on mobile devices. For this purpose, such affine transformations as rotation and transfer were chosen. By repeating the combination of these transformations for a given period of time and at a constant speed, the effect of animating the object will be achieved. Affine transformations are chosen because of their ability to preserve the proportions of parallel objects, namely the length of segments on parallel lines and areas on parallel planes. This property allows you to build parallel prototypes of an object polygon on a plane along a finite set of points that express the object polygon. The number of parallel planes depends on the number of objects in the image that will be exposed to the animation effect. The problem of computational complexity in performing methods was also outlined, namely the calculation of trigonometric functions. To solve this problem, a calculation using the Taylor series with a certain error and the use of trigonometric identities were proposed.
\nKeywords:<\/strong> affine transformations, object animation, time complexity.<\/p>\n

References<\/strong><\/p>\n

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