Best fit plane and rotation (or using a computed plane as a reference plane?)

[nialsiG]

Hello !
So I started to use pymeshlab to automatize a pipeline of mesh modifications that I used to perform in Meshlab. At some point in the pipeline, I have to:

1. import the surface
2. select its border
3. isolate the best fit plane of the border
4. rotate the mesh so that this plane is projected onto the XY plane.

See attached figure for a simplified view:

I managed to do steps 1 to 3 but I struggle with step 4. Is there a way to do it with pymeshlab that I am missing? Or maybe other librairies that I am not aware of?

One precision: in the figure, the rotation occurs around the x-axis, but it would be even better if I could "project" the plane and the mesh onto the xy plane... I guess that to do so, I need to rotate arount the intersection between the best fit plane and the yx plane. Any idea on how to isolate the coordinates of two points on that intersection?

Thank you for your time, hoping it helps someone in the future!