<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes 15 ordinary multiplications, 6 trivial multiplications by 2 (left-shifts), 21 additions, and 4 squarings of real numbers, while the proposed algorithm can compute the same result in only 14 real multiplications (or multipliers—in a hardware implementation case), 43 additions, 4 right-shifts (multiplications by 1/4), and 3 left-shifts (multiplications by 2).</p></abstract>

In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes 15 ordinary multiplications, 6 trivial multiplications by 2 (left-shifts), 21 additions, and 4 squarings of real numbers, while the proposed algorithm can compute the same result in only 14 real multiplications (or multipliers—in a hardware implementation case), 43 additions, 4 right-shifts (multiplications by 1/4), and 3 left-shifts (multiplications by 2).

An Algorithm for Quaternion–Based 3D Rotation

Faculty of Computer Science and Information Technology

West Pomeranian University of Technology in Szczecin

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"An Algorithm for Quaternion\u2013Based 3D Rotation"}

In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of...

An Algorithm for Quaternion–Based 3D Rotation

Publié en ligne: 03 avr. 2020

Pages: 149 - 160

Reçu: 21 mars 2019

Accepté: 18 oct. 2019

DOI: https://doi.org/10.34768/amcs-2020-0012

Mots clés
quaternions, space rotation, design of algorithms

© 2020 Aleksandr Cariow et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

An Algorithm for Quaternion–Based 3D Rotation

Publié en ligne: 03 avr. 2020

Pages: 149 - 160

Reçu: 21 mars 2019

Accepté: 18 oct. 2019

DOI: https://doi.org/10.34768/amcs-2020-0012

Mots clésquaternions, space rotation, design of algorithms

© 2020 Aleksandr Cariow et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
quaternions, space rotation, design of algorithms