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