![\[ \overrightarrow{v}= \left\{ q_x, q_y, q_z \right\} \]](form_0.png)
vec im(const quat & q)
Pull out the imaginary part of q, and put it into v.
v =im(q);
quat vr2q(const vec & v, const double & r)
Put v into im(q), and put r into q.r .
q =vr2q(v,r);
![\[ \mathbf{q}= \left[ v_x, v_y, v_z; r \right] \]](form_1.png)
quat vt2q(const vec & u, const double & phi) The rotation quaternion, which axis direction is v and angular is theta.
q =vt2q(u,phi);
![\[ \mathbf{q} = \left[ \frac{{u_x}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right), \frac{{u_y}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right), \frac{{u_z}}{|\vec{u}|}\sin \left( \frac{\phi}{2} \right); \cos \left( \frac{\phi}{2} \right) \right] \]](form_2.png)
1.4.1