v

QuaternionArray.v

Vector part of all Quaternions.

Having the quaternion elements \(\mathbf{q}_i=\begin{pmatrix}w_i & \mathbf{v}_i\end{pmatrix}=\begin{pmatrix}w_i & x_i & y_i & z_i\end{pmatrix}\in\mathbb{R}^4\) stacked vertically in an \(N\times 4\) matrix \(\mathbf{Q}\):

\[\begin{split}\mathbf{Q} = \begin{bmatrix} \mathbf{q}_0 \\ \mathbf{q}_1 \\ \vdots \\ \mathbf{q}_{N-1} \end{bmatrix} = \begin{bmatrix} w_0 & x_0 & y_0 & z_0 \\ w_1 & x_1 & y_1 & z_1 \\ \vdots & \vdots & \vdots & \vdots \\ w_{N-1} & x_{N-1} & y_{N-1} & z_{N-1} \end{bmatrix}\end{split}\]

The vector parts of all quaternions are:

\[\begin{split}\mathbf{V} = \begin{bmatrix} x_0 & y_0 & z_0 \\ x_1 & y_1 & z_1 \\ \vdots & \vdots & \vdots \\ x_{N-1} & y_{N-1} & z_{N-1} \end{bmatrix}\end{split}\]

Returns:

V – N-by-3 array with vector parts of all quaternions.

Return type:

numpy.ndarray

Examples

>>> Q = QuaternionArray(np.random.random((3, 4))-0.5)
>>> Q.view()
QuaternionArray([[ 0.39338362, -0.29206111, -0.07445273,  0.86856573],
                 [ 0.65459935,  0.14192058, -0.69722158,  0.25542183],
                 [-0.42837174,  0.85451579, -0.02786928,  0.29244439]])
>>> Q.v
array([[-0.29206111, -0.07445273,  0.86856573],
       [ 0.14192058, -0.69722158,  0.25542183],
       [ 0.85451579, -0.02786928,  0.29244439]])

They can also be accessed directly, slicing the Quaternion like an array, but returned as a Quaternion object.

>>> Q[:, 1:]
QuaternionArray([[-0.29206111, -0.07445273,  0.86856573],
                 [ 0.14192058, -0.69722158,  0.25542183],
                 [ 0.85451579, -0.02786928,  0.29244439]])