Local axes of beams needed for gridshell structure

Hi everyone!

I'm trying to convert a Karamba model of a gridshell to SCIA (a software package for finite element analysis). In karamba I use the orientate beam component to change the Z-orientation of my beams. For this I use a reference surface on which I find the closest point to the midpoint of a beam in my gridshell. This point is then used to find the normal vector on the reference surface which I can then use to orientate said beam.

The problem arises when I want to recreate the same structure in SCIA. In this program I need to define the rotation of the local coordinate system (similar to the Alpha input of the orientate beam component). I've tried to recreate the local coordinate system as defined by karamba using the definition below. From this I thought I could compute the angle between my original LCS vector and my rotated LCS vector, thus giving me the input I need for SCIA.

As you can see in the small definition below, I was able to mimick the LCS of Karamba using some vectors, but this method is not consistent. For some beams it works, for some the coordinate system is flipped.

My question is, is there an easier way to extract the local axes from the Karamba model, or easily convert the new Z-axis to a rotation angle?

Unfortunately I cannot share the file for the gridshell itself as it is an ongoing project. Hopefully someone can still help me with this issue.

Thanks in advance,

Steven