Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)4473410.22363/2658-4670-2025-33-1-74-102AAAAHVModeling and SimulationМатематическое моделированиеResearch ArticleAnalytic projective geometry for computer graphicsАналитическая проективная геометрия для компьютерной графикиhttps://orcid.org/0000-0002-4834-489557190004380E-9214-2016GevorkyanMigran N.ГеворкянМ. Н.

Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Probability Theory and Cyber Security

gevorkyan-mn@rudn.ruhttps://orcid.org/0000-0001-7141-761036968057600I-3191-2013KorolkovaAnna V.КорольковаА. В.

Docent, Candidate of Sciences in Physics and Mathematics, Associate Professor of Department of Probability Theory and Cyber Security

korolkova-av@rudn.ruhttps://orcid.org/0000-0002-0877-706335194130800I-3183-2013KulyabovDmitry S.КулябовД. С.

Professor, Doctor of Sciences in Physics and Mathematics, Professor. of the Department of Probability Theory and Cyber Security of RUDN University; Senior Researcher of Laboratory of Information Technologies, Joint Institute for Nuclear Research

kulyabov-ds@rudn.ruhttps://orcid.org/0000-0002-1856-46438783969400B-8497-2016SevastianovLeonid A.СевастьяновЛ. А.

Professor, Doctor of Sciences in Physics and Mathematics, Professor of Department of Computational Mathematics and Artificial Intelligence of RUDN University

sevastianov-la@rudn.ruRUDN UniversityРоссийский университет дружбы народовJoint Institute for Nuclear ResearchОбъединённый институт ядерных исследований15062025331VOL 33, NO1 (2025)ТОМ 33, №1 (2025)7410227062025Copyright ©; 2025, Gevorkyan M.N., Korolkova A.V., Kulyabov D.S., Sevastianov L.A.Copyright ©; 2025, Геворкян М.Н., Королькова А.В., Кулябов Д.С., Севастьянов Л.А.2025Gevorkyan M.N., Korolkova A.V., Kulyabov D.S., Sevastianov L.A.Геворкян М.Н., Королькова А.В., Кулябов Д.С., Севастьянов Л.А.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/44734

The motivation of this paper was the development of computer geometry course for students of mathematical specialties. The term “computer geometry” hereafter refers to the mathematical foundations of machine graphics. It is important to emphasize separately that this course should be designed for second-year students and, therefore, they can only be required to have prior knowledge of a standard course in algebra and mathematical analysis. This imposes certain restrictions on the material presented. When studying the thematic literature, it was found out that the de facto standard in modern computer graphics is the use of projective space and homogeneous coordinates. However, the authors faced a methodological problem-the almost complete lack of suitable educational literature in both Russian and English. This paper was written to present the information collected by the authors on this issue.

Мотивом к написанию данной работы послужила разработка авторами курса по компьютерной геометрии для студентов физико-математических специальностей. Под термином «компьютерная геометрия» здесь и далее понимаются математические основы машинной графики. Важно отдельно подчеркнуть, что разрабатываемый курс должен быть рассчитан на студентов второго года обучения и, следовательно, от них можно требовать лишь предварительное знание стандартного курса алгебры и математического анализа. Это накладывает определённые ограничения на излагаемый материал. При изучении тематической литературы было выяснено, что стандартом де факто в современной компьютерной графике стало использование проективного пространства и однородных координат. Однако авторы столкнулись с проблемой методологического характера - практически полным отсутствием подходящей учебной литераторы как на русском, так и на английском языках. Для представления собранной авторами информации по данному вопросу и была написана данная работа.

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