4 semester

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Computational geometry and computer graphics.

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Candidate of Physical and Mathematical Sciences,

Denis Vylegzhanin

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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

Computational geometry.

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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. B-splines. Triangulation.

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1.  Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L. (1990). Introduction to Algorithms (2nd ed.). MIT Press and McGraw-Hill.

2. F.Preparata, M.Shamos, Computational Geometry.

3. Е.А. Никулин, Компьютерная геометрия и алгоритмы машинной графики, Санкт-Петербург: “БХВ-Петербург”, 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: “Диалог-МИФИ”, 1996, 240 с.

6. М.М. Постников, Аналитическая геометрия, Москва: «Наука», 1973, 760 с.

7. В.Н. Пореев, Компьютерная графика, СПб.:БХВ-Петербург, 2004. – 432 с.

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Motivational-competent, problematic, dialogue-heuristic, visual.

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Russian

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Exam