Euler Angle Convention

[ahannam]

Hi Daniel:
Thanks for the work you're doing with CloudCompare…it’s very impressive.
We're using the Fine Registration tool to register one object to another. First we move and rotate the object to be aligned so its bounding box is centred on CCs World origin and oriented to CCs World XYZ axes.
After registration to the Reference object we need to interpret the transformation matrix CC provides, (using the Transformation Panel). We know the problems with Euler Angles, but we have to use them to explain the biological outcomes we're studying.
From previous Forum Discussions it seems CC uses the Tait-Bryan ZYX convention for its Euler angles. After lots of tests, we think “phi” in the Euler Angle tab represents rotation around CC’s World Z axis, “theta” around the World Y axis and “psi” around the World X axis. Could you confirm this?
It’s important to know which convention is used by CC since there are various object-centred and World-centred XYZ coordinate systems, different Greek-symbol conventions, and f course the different rotation sequences in use.

[daniel]

Hi,

So I confirm that we use the Tait-Brian ZYX convention. Which means that it's the composition of 3 rotations around the "fixed frame" axes. And phi is the rotation angle about Z, theta about Y and psi about X (I doubled checked by playing with the Apply Transformation tool and it seems to work).

[ahannam]

Thanks Daniel...that's what we worked out too!