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Статья

Gevorkyan, M.N.
Dual Quaternion Representation of Points, Lines and Planes / M.N.Gevorkyan, N.A.Vishnevskiy, D.S.Kulyabov, [a.o.]. – Text : electronic // Discrete and Continuous Models and Applied Computational Science. – 2025. – Vol. 33, No. 4. – P. 411-439. – URL: https://doi.org/10.22363/2658-4670-2025-33-4-411-439. – Bibliogr.: 30.

Background. The bulk of the work on dual quaternions is devoted to their application to describe helical motion. Little attention is paid to the representation of points, lines, and planes (primitives) using them. Purpose. It is necessary to consistently present the dual quaternion theory of the representation of primitives and refine the mathematical formalism.MethodIt uses the algebra of dual numbers, quaternions and dualquaternions, as well as elements of the theory of screws and sliding vectors. Results. Formulas have been obtainedand systematized that use exclusively dual quaternionic operations and notation to solve standard problemsof three-dimensional geometry. Conclusions. Dual quaternions can serve as a full-fledged formalism for the algebraic representation of a three-dimensional projective space.



Спец.(статьи,препринты) = С 131 - Высшая алгебра. Линейная алгебра. Теория матриц
Спец.(статьи,препринты) = С 17 - Вычислительная математика. Таблицы
ОИЯИ = ОИЯИ (JINR)2025