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Paper details
Number 1 - March 2020
Volume 30 - 2020
An algorithm for quaternion-based 3D rotation
Aleksandr Cariow, Galina Cariowa, Dorota Majorkowska-Mech
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).
Keywords
quaternions, space rotation, design of algorithms