An algorithm for quaternion-based 3D rotation - Cariow, Aleksandr; Cariowa, Galina; Majorkowska-Mech, Dorota (Zielona Góra: Uniwersytet Zielonogórski)
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