Implementation of analytic projective geometry for computer graphics

M. N. Gevorkyan; Геворкян М. Н.; A. V. Korol’kova; Королькова А. В.; D. S. Kulyabov; Кулябов Д. С.; L. A. Sevast’yanov; Севастьянов Л. А.

doi:10.31857/S0132347424020089

Implementation of analytic projective geometry for computer graphics

Authors: Gevorkyan M.N.¹, Korol’kova A.V.², Kulyabov D.S.¹^,2, Sevast’yanov L.A.¹^,2
Affiliations:
1. RUDN University
2. Joint Institute for Nuclear Research
Issue: No 2 (2024)
Pages: 51-65
Section: COMPUTER ALGEBRA
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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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

projective geometry, Asymptote system, Plücker coordinates, proper and improper points, lines and planes

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References

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