Calculate quaternion from rotation angles
The Rotation Angles to Quaternions block converts the rotation described by the three rotation angles (R1, R2, R3) into the four-element quaternion vector (q0, q1, q2, q3). A quaternion vector represents a rotation about a unit vector through an angle θ. A unit quaternion itself has unit magnitude, and can be written in the following vector format.
An alternative representation of a quaternion is as a complex number,
where, for the purposes of multiplication,
The benefit of representing the quaternion in this way is the ease with which the quaternion product can represent the resulting transformation after two or more rotations.
|3-by-1 vector||Contains the rotation angles, in radians.|
|4-by-1 matrix||Contains the quaternion vector.|
The limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' implementations generate an R2 angle that is between ±90 degrees, and R1 and R3 angles that are between ±180 degrees.
The limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' implementations generate an R2 angle that is between 0 and 180 degrees, and R1 and R3 angles that are between ±180 degrees.