I have an affine transform from $R^3$ to $R^3.$ It is described as Rotation about Z axis, rotation about X axis, a translation, rotation about Z axis, and lastly a scaling (same in all 3 dimensions).
It is therefore a similarity. Now, I would like to represent this affine transform as the following composition instead: Translation, rotation about X, rotation about Y, rotation about Z, and lastly scale.
Thus, given a similarity, how do I find the 3 angles, the translation, and the scale? I know this representation is not unique, but any one should do.
If it helps, I have access to all parameters in the first representation.