The type for quaternions.

v x y z w is the quaternion xi+ yj + zk + w.

zero is the zero quaternion.

id is the identity quaternion 1.

mul q r is the quaternion multiplication q * r.

conj q is the quaternion conjugate q*.

unit q is the unit vector q/|q| (same as V4.unit).

inv q is the quaternion inverse q^-1.

slerp q r t is the spherical linear interpolation between q and r at t. Non commutative, torque minimal and constant velocity.

squad q cq cr r t is the spherical cubic interpolation between q and r at t. cq and cr indicate the tangent orientations at q and r.

nlerp q r t is the normalized linear interpolation between q and r at t. Commutative, torque minimal and inconstant velocity.

of_m3 m is the unit quaternion for the rotation in m.

of_m4 m is the unit quaternion for the rotation in the 3x3 top left matrix in m.

Unit quaternion for the rotation, see M3.rot3_map.

Unit quaternion for the rotation, see M3.rot3_axis.

Unit quaternion for the rotation, see M3.rot3_zyx.

to_rot3_axis q is the rotation axis and angle in radians of the unit quaternion q.

to_rot_zyx q is the x, y, z axis angles in radians of the unit quaternion q.

apply3 q v applies the 3D rotation of the unit quaternion q to the vector (or point) v.

apply4 q v apply the 3D rotation of the unit quaternion q to the homogenous vector (or point) v.