1 
Name of the discipline

Mathematical foundations of computer graphics. 
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Course of Study

3, specialty “Computer mathematics” 
3 
Semester of training

5 
4 
Amount of credits

3 
5 
Full name of lecturer

Candidate of Physical and Mathematical Sciences, Denis Vylegzhanin 
6 
Objectives of the study of discipline 
Form knowledge of the basic algorithms, methods and mathematical constructions. As a result of the study, the student should be able to: construct lines and surfaces using the theory of splines, curves and Bezier surfaces; freely master the basic algorithms for solving problems in computational geometry, solve problems using algorithms and methods of computational geometry; apply geometric transformations to solve practical problems including computer graphics problems. 
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Prerequisites

Computer mathematics. 
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Content of discipline 
The subject of the study of computational geometry. Methods for specifying lines and planes. Mutual arrangement of the simplest geometric objects. Tasks of localization of a point. Convex shells. Mutual arrangement of polygons. The algorithm for finding the pair of nearest points. Determination of the existence of intersecting segments. Methods of constructing projections onto a plane. Using quaternions to describe geometric transformations. Raster algorithms. Bezier curves. Bsplines. Triangulation. 
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Recommendedliterature 
1. Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L. (1990). Introduction to Algorithms (2nd ed.). MIT Press and McGrawHill. 2. F.Preparata, M.Shamos, Computational Geometry. 3. Е.А. Никулин, Компьютерная геометрия и алгоритмы машинной графики, СанктПетербург: “БХВПетербург”, 2003, 560с. 4. Н.Н. Голованов Геометрическое моделирование, Москва: “Физматлит”, 2002, 472с. 5. Е.В.Шикин, А.И. Плис Кривые и поверхности на экране компьютера, Москва: “ДиалогМИФИ”, 1996, 240 с. 6. М.М. Постников, Аналитическая геометрия, Москва: «Наука», 1973, 760 с. 7. В.Н. Пореев, Компьютерная графика, СПб.:БХВПетербург, 2004. – 432 с. 
10 
Teaching Methods 
Motivationalcompetent, problematic, dialogueheuristic, visual. 
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Language of teaching 
Russian 
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Conditions (requirements),routine control  – Individual tasks; – test papers.The final evaluation is made taking into account:30% – assessment of current academic performance,70% – oral answer in the exam

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Form of current assessment 
Exam 