RAS MathematicsПрограммирование Programming and Computer Software

  • ISSN (Print) 0132-3474
  • ISSN (Online) 3034-5847

Implementation of analytic projective geometry for computer graphics

PII
10.31857/S0132347424020089-1
DOI
10.31857/S0132347424020089
Publication type
Article
Status
Published
Authors
Volume/ Edition
Volume / Issue number 2
Pages
51-65
Abstract
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.
Keywords
проективная геометрия система Asymptote координаты Плюккера собственные и несобственные точки прямые и плоскости
Date of publication
17.09.2025
Year of publication
2025
Number of purchasers
0
Views
16

References

  1. 1. 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.
  2. 2. Kulyabov D.S., Korolkova A.V., Sevastianov L.A. Complex numbers for relativistic operations, 2021.
  3. 3. Kulyabov D.S., Korolkova A.V., Gevorkyan M.N. Hyperbolic numbers as Einstein numbers, J Phys.: Conf. Ser., 2020, vol. 1557, p. 012027.
  4. 4. 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.
  5. 5. Геворкян М.Н., Королькова А.В., Кулябов Д.С. Реализация геометрической алгебры в системах символьных вычислений // Программирование. 2023. № 1. С. 48–55.
  6. 6. Королькова А.В., Геворкян М.Н., Кулябов Д.С., Севастьянов Л.А. Средства компьютерной алгебры для геометризации уравнений Максвелла // Программирование. 2023. Т. 49, № 4. С. 33–38.
  7. 7. Велиева Т.Р., Геворкян М.Н., Демидова А.В. и др. Аппарат геометрической алгебры и кватернионов в системах символьных вычислений для описания вращений в евклидовом пространстве // Журнал вычислительной математики и математической физики. 2023. Т. 63. № 1. С. 31–42.
  8. 8. Bowman J.C. Hammerlindl A. Asymptote: A vector graphics language, 2008, vol. 29, no. 2, pp. 288–294.
  9. 9. Bowman J.C. Asymptote: Interactive TEX-aware 3D vector graphics, 2010, vol. 31, no. 2, pp. 203–205.
  10. 10. 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.
  11. 11. Bowman, J.C. Asymptote: The vector graphics language, 2023. https://asymptote.sourceforge.io.
  12. 12. 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.
  13. 13. Страуструп Б. Программирование. Принципы и практика с использованием C++. 2 изд. Вильямс, 2018. 1328 с.
  14. 14. Hobby J., Knuth D. MetaPost on the Web. https://www.tug.org/metapost.html.
  15. 15. Staats C. An Asymptote tutorial, 2022. https://asymptote.sourceforge.io/asymptote_tutorial.pdf.
  16. 16. Крячков Ю.Г. Asymptote для начинающих. http://mif.vspu.ru/books/ASYfb.pdf.
  17. 17. Волченко Ю.М. Научная графика на языке Asymptote. http://www.math.volchenko.com/AsyMan.pdf.
  18. 18. Ивальди Ф. Евклидова геометрия на языке векторной графики Asymptote.2015. http://mif.vspu.ru/books/geometry_new_ru.pdf.
  19. 19. Lengyel E. Foundations of game engine development, Terathon Software LLC, vol. 1. http://foundationsofgameenginedev.com.
  20. 20. Marschner S., Shirley P. Fundamentals of Computer Graphics, CRC Press, 5 ed.
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