QUATERNIONS AS MATHEMATICAL TOOLS IN COMPUTER GRAPHICS: METHODOLOGICAL ASPECTS

Author:

Ilienko Maryna, National Technical University of Ukraine “Kiev Polytechnical Institute”, Kiev, Ukraine

Runovska Liudmyla, Chernihiv National University of Technology (95 Shevchenka Str., 14027 Chernihiv, Ukraine)

Language: ukrainian

Annotation:

In the paper, we propose the topic “Quaternions” to be taught at the lesson on the optional course of higher mathematics to university students who study programming. Briefly following historical facts about invention of quaternions we mention some applications of them in modern science. In particular, we explain how the rotation in three-dimensional space can be described by means of quaternions. This is widely used in computer graphics. The appropriate mathematical background is given to the extent which, on authors’ opinion, is sufficient to make interest for future specialists. In the main part of the paper we give formal mathematical definition of quaternion, consider its various interpretations, and introduce operations with quaternions. The article has a methodological nature.

Key words:

quaternions, rotation in three-dimensional space, methods of teaching higher math, games programming

References:

  1. Ватульян А. О. Кватернионы / А. О. Ватульян // Соросовский образовательный журнал. – 1999. – № 5. – С. 117–120.

  2. Виттенбург Й. Динамика систем твёрдых тел / Й. Виттенбург. – М. : Мир, 1980. – 292 с.

  3. Побегайло А. П. Применение кватернионов в компьютерной геометрии и графике / А. П. Побегайло. – Минск : Изд-во БГУ, 2010. – 216 с.

  4. Погорелов Д. Ю. Введение в моделирование динамики систем тел / Д. Ю. Погорелов. – Брянск : Изд-во БГТУ, 1997.  156 с.

  5. Чуб В. Ф. Уравнения инерциальной навигации и кватернионная теория пространства-времени / В. Ф. Чуб // Гиперкомплексные числа в геометри и физике. – 2007. – Т. 4, № 1(7). – С. 133–140.

  6. Hamilton W. R. Elements of Quaternions / W. R. Hamilton // Chelsea Publishing Company, third edition. – Vol. I. – 1969.

  7. John H. Conway On quaternions and octonions: Their geometry, arithmetic, and symmetry / Conway John H., Smith Derek A.  Natick : A K Peters, Ltd. – 2003. – 159 p.

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