I have a 12-point isometry matrix made of four three-dimensional points. They are some point o and the tips of orthogonal unit vectors from that point, x, y, and z.
Here's a drawing for clarity:
\begin{bmatrix} x_{x} & x_{y} & x_{z} \\ y_{x} & y_{y} & y_{z} \\ z_{x} & z_{y} & z_{z} \\ o_{x} & o_{y} & o_{z} \\ \end{bmatrix}
I need to convert this pose to a translation from the origin and quaternion, and vice versa: \begin{bmatrix} x \\ y \\ z \\ \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ w \\ \end{bmatrix}
I'm dealing with 3D CAD software which stores all of its poses in 12-point isometry matrices, but to manipulate them with more standard software libraries I need the data in standard pose format x, y, z, qx, qy, qz, qw which is simply the translation vector and quaternion.
How can I convert between the two pose representations?