Enviar artigo por via de e-mail Implementation of analytic projective geometry for computer graphics
- Autores: Gevorkyan M.1, Korol’kova A.2, Kulyabov D.1,2, Sevast’yanov L.1,2
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Afiliações:
- RUDN University
- Joint Institute for Nuclear Research
- Edição: Nº 2 (2024)
- Páginas: 51-65
- Seção: КОМПЬЮТЕРНАЯ АЛГЕБРА
- URL: https://journals.rcsi.science/0132-3474/article/view/262643
- DOI: https://doi.org/10.31857/S0132347424020089
- EDN: https://elibrary.ru/ROPXHV
- ID: 262643
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Somente assinantes
Resumo
In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed.
Sobre autores
M. Gevorkyan
RUDN University
Autor responsável pela correspondência
Email: gevorkyan-mn@rudn.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198
A. Korol’kova
Joint Institute for Nuclear Research
Email: korolkova-av@rudn.ru
Rússia, 6 ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980
D. Kulyabov
RUDN University; Joint Institute for Nuclear Research
Email: kulyabov-ds@rudn.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198; 6 ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980
L. Sevast’yanov
RUDN University; Joint Institute for Nuclear Research
Email: sevastianov-la@rudn.ru
Rússia, 6 Miklukho-Maklaya St, Moscow, 117198; 6 ul. Zholio-Kyuri 6, Dubna, Moscow oblast, 141980
Bibliografia
- Korolkova A.V., Gevorkyan M.N., Kulyabov D.S. Implementation of hyperboliccomplex numbers in Julia language, Discrete Contin. Models Appl. Comput. Sci., 2022, vol. 30, no. 4, pp. 318–329.
- Kulyabov D.S., Korolkova A.V., Sevastianov L.A. Complex numbers for relativistic operations, 2021.
- Kulyabov D.S., Korolkova A.V., Gevorkyan M.N. Hyperbolic numbers as Einstein numbers, J Phys.: Conf. Ser., 2020, vol. 1557, p. 012027.
- Gevorkyan M.N., Korolkova A.V., Kulyabov D.S. Approaches to the implementation of generalized complex numbers in the Julia language, Workshop on Information Technology and Scientific Computing in the framework of the X Int. Conf. Information and Telecommunication Technologies and Mathematical Modeling of High-Tech Systems (ITTMM), Kulyabov, D.S., Samouylov, K.E., and Sevastianov, L.A., Eds., 2020, vol. 2639, pp. 141–157.
- Gevorkyan M.N., Korol’kova A.V., Kulyabov D.S. Implementation of geometric algebra in symbolic computation systems, Programmirovanie, 2023, no. 1, pp. 48–55.
- Korol’kova A.V., Gevorkyan M.N., Kulyabov D.S., Sevast’yanov L.A. Computer algebra tools for geometrization of Maxwell’s equations, Program. Comput. Software, 2023, vol. 49, pp. 336–371.
- Velieva T.R., Gevorkyan M.N., Demidova A.V., Korol’kova A.V., Kulyabov D.S. Geometric algebra and quaternion techniques in computer algebra systems for describing rotations in Eucledean space, Comput. Math. Math. Phys., 2023, vol. 63, pp. 29–39.
- Bowman J.C. Hammerlindl A. Asymptote: A vector graphics language, 2008, vol. 29, no. 2, pp. 288–294.
- Bowman J.C. Asymptote: Interactive TEX-aware 3D vector graphics, 2010, vol. 31, no. 2, pp. 203–205.
- Shardt O., Bowman J.C. Surface parameterization of nonsimply connected planar Bzier regions, Comput.-Aided Des., 2012, vol. 44, no. 5, pp. 484.e1–484.e10.
- Bowman, J.C. Asymptote: The vector graphics language, 2023. https://asymptote.sourceforge.io.
- Gevorkyan M.N., Korolkova A.V., Kulyabov D.S. Asymptote-based scientific animation, Discrete Contin. Models Appl. Comput. Sci., 2023, vol. 31, no. 2, pp. 139–149.
- Stroustrup B. Programming: Principles and Practice Using C++, Addison-Wesley Professional, 2014, 2nd ed.
- Hobby J., Knuth D. MetaPost on the web. https://www.tug.org/metapost.html.
- Staats C. An Asymptote tutorial, 2022. https://asymptote.sourceforge.io/asymptote_tutorial.pdf.
- Kryachkov Yu.G. Asymptote for beginners. http://mif.vspu.ru/books/ASYfb.pdf.
- Volchenko Yu.M. Scientific graphics in the Asymptote language. http://www.math.volchenko.com/AsyMan.pdf.
- Ivaldi, Ph., Euclidean Geometry with ASYMPTOTE, 2011.
- Lengyel E. Foundations of game engine development, Terathon Software LLC, vol. 1. http://foundationsofgameenginedev.com.
- Marschner S., Shirley P. Fundamentals of Computer Graphics, CRC Press, 5 ed.
