One idea can average the right vector to get your control point p3 for a curved line.
Another idea is to use a circular arc like beam bending and look to other similar curvature problems like curved roads
Wait, are you any good with bones in blender? If so then would my little idea of adjusting the bones positions like the way im going to for the attachments the best idea?
For circular arc, is this using a completely different method for the gangway or is this another way for positioning the attachments?
You asked me on another topic whether or not using Vector3Curves was a good idea to be used here. Don’t want to veer off topic there so I’ll add a reply here, but I wouldn’t use Vector3Curves for this personally.
It might be more worth it to just use a quadratic bezier, and use an average point as your control point as @dthecoolest said, or you could use a line intersection algorithm to find where the two points would intersect and use said intersection point as your control point.
Creating a whole spline is going to overcomplicate things, and you will not get the result you expect because Vector3Curves pass through each control point while bezier curves do not.
Your conveyor would end up more or less looking pretty, uh, wiggly I guess for lack of a better word, because the spline has to pass through each control point.
It would look even worse the more acute the angle is