# quat_bound¶

Given a quaternion, $$\vec{\chi}$$, associated to a rotation of angle $$\psi$$ about an axis $$\mathbf{\hat{n}}$$, the function “bounds” the quaternion, i.e. sets the rotation axis $$\mathbf{\hat{n}}$$ such that $$\psi$$ in $$[-\pi,\pi]$$.

Notes

As quaternions are defined as:

$\vec{\chi}= \left[\cos\left(\frac{\psi}{2}\right),\, \sin\left(\frac{\psi}{2}\right)\mathbf{\hat{n}}\right]$

this is equivalent to enforcing $$\chi_0\ge0$$.

param quat

quaternion to bound

type quat

np.array

returns

bounded quaternion

rtype

np.array