Dual quaternion representation of points, lines and planes


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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. Method. It uses the algebra of dual numbers, quaternions and dual quaternions, as well as elements of the theory of screws and sliding vectors. Results. Formulas have been obtained and systematized that use exclusively dual quaternionic operations and notation to solve standard problems of three-dimensional geometry. Conclusions. Dual quaternions can serve as a full-fledged formalism for the algebraic representation of a three-dimensional projective space.

Sobre autores

Migran Gevorkyan

RUDN University

Email: gevorkyan-mn@rudn.ru
ORCID ID: 0000-0002-4834-4895
Scopus Author ID: 57190004380
Researcher ID: E-9214-2016

Docent, Ph.D. in Physics and Mathematics, Associate Professor of Department of Probability Theory and
Cyber Security

Rússia, 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Nikita Vishnevskiy

RUDN University

Email: 1142240277@rudn.ru
ORCID ID: 0009-0004-4410-8635

PhD student of Department of Probability Theory and Cyber Security

Rússia, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Kirill Didus

RUDN University

Email: 1142240434@rudn.ru
ORCID ID: 0000-0002-5622-8480

PhD student of Department of Probability Theory and Cyber Security

Rússia, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Anna Korolkova

RUDN University

Email: korolkova-av@rudn.ru
ORCID ID: 0000-0001-7141-7610
Scopus Author ID: 36968057600
Researcher ID: I-3191-2013

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

Rússia, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Dmitry Kulyabov

RUDN University; Joint Institute for Nuclear Research

Autor responsável pela correspondência
Email: kulyabov_ds@pfur.ru
ORCID ID: 0000-0002-0877-7063
Scopus Author ID: 35194130800
Researcher ID: I-3183-2013

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

Rússia, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 6 Joliot-Curie St, Dubna, 141980, Russian Federation

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