unfortunately we can't help developing algorithms. So, what has been said here and in the Quaternion Rotation thread, is probably all we can contribute from MAXON's side.

Maybe somebody from our community is willing to step into this and help out?

Cheers,
Andreas

Best, Riccardo

The issue you notice takes place when the temporary up-vector is aligned with the forward-vector: under this scenario the rVec is ambiguous and the whole system results unstable. The solution to the issue is represented by Quaternions or, alternatively you can try to mitigate the effect by putting in place some "work-around" like:

    ...
    uVec = fVec.Cross(rVec).GetNormalized()

    # try to mitigate Gimbal-lock
    if (fVec + tmpVec).z < 0:
        uVec.x = -uVec.x

    if abs(rVec.x - 1.0) < 0.001:
        rVec.x = -rVec.x

    # fill-up the transformation matrix
    ...

Best, Riccardo

edit: @ferdinand

The approach shown here can be problematic. You instead should choose an up-vector which is not parallel or anti-parallel to the input vector. See Gimbal Lock Safe Target Expression for an example.

looking at your code I think there's a wrong assumption about the up-vector and how consequently it is used in the definition of the transformation matrix.

The correct approach should look like:

import c4d

cam = op.GetObject()    
target = cam[c4d.ID_USERDATA, 1]

def main():    
    # get "from" and "to vectors
    fromVec = cam.GetMg().off
    toVec = target.GetMg().off
    
    # use a temporary Up-vector
    tmpVec = c4d.Vector(0, 1, 0)
    # calculate the forward-vector
    fVec = (toVec - fromVec).GetNormalized()
    # calculate the right-vector
    rVec = tmpVec.Cross(fVec)
    # recalculate the proper up-vector
    uVec = fVec.Cross(rVec)
    
    # fill-up the transformation matrix
    m = c4d.Matrix()
    m.off = fromVec
    m.v1 = rVec
    m.v2 = uVec
    m.v3 = fVec
    
    # set the camera transformation
    cam.SetMg(m)

Last but not least, please set tags accordingly to your topic and use the Q&A functionality.

Best, Riccardo