ABSTRACT
Finally, the authors introduce “quaternion representation,” specifying 3D rotation by four parameters q0, q1, q2, and q3 whose square sum is unity. This is an extension of complex numbers for describing 2D rotations in plane to 3D rotations in space. Rotations around the coordinate axes are traditionally called roll, pitch, and yaw. These terms are used for describing the posture of vehicles, ships, and airplanes. The reason that 3D rotation is often represented as a composition of rotations around three coordinate axes is that in practical applications object postures are usually controlled by rotation around three orthogonal axes fixed to the object. The Euler angles were introduced by the Swiss mathematician-astronomer Leonhard Euler for rigid body motion analysis.
