Typically when using an axis of symmetry, it proposes a theoretically perfect axis. What measurement could be used as a +/- margin of error when looking at such an axis in an applied situation?
For instance, assume a 100m east-west tunnel that is engineered to be as perfectly straight as possible, with the left and right openings both perfectly parallel. A line down the center of the tunnel would be 100m. The axis of symmetry would be a perpendicular line at the 50m mark with a 0° curve or bend. Is there a unit of measurement by which this could be written?
In a real world engineering problem, let's say that the right end of the tunnel was 13mm south of being perfectly east of the left tunnel, and the opening, while having perfect geometry was also shifted -0.17° as compared to the left tunnel. Is there a unit of measurement by which this could be written?
I'm trying to understand how this could be written both directly as well as how it could be written as a margin of error.
Edit (20230326):
Hopefully this will help clarify what I'm asking.
A is the ideal; a 100m tunnel with a 100m path. The midpoint/axis is at 50m, the line of symmetry is at 0° (90° or precisely perpendicular to a path drawn down the center of the tunnel), and the center point at the entrance and exit is ±0.000m.
B is more realistic; a 100m tunnel with a path that will, mathematically, be slightly more than 100m due to the curve I would imagine. However, due to the slight curve (the exit/red is at 2 meters south of the entrance/blue, so has a measurement of -2m) the angle from a "perfect" line of symmetry to the path is 91°, or the line of symmetry would have a 0.5° angle from perfectly parallel to the entrance.
I apologize if this is still confusing - my trig and geometry days happened decades ago. Perhaps this would be better (and maybe some of what I'm measuring isn't really relevant):
The measurements should always presume one side is an entrance and one side is an exit, regardless of whether the tunnel is bidirectional or not (the measurement would just be the inverse if the entrance and exit were swapped). I guess what's important with angle is the angle at which an object facing the entrance when entering would be facing on exit.
So in C, it's a 100+m tunnel (due to curvature), the exit is -25m from the entrance on a north/south plane, and exits at 180° to the entrance. The more I think about it, the more it seems like the measurement would possibly be more like a normalized vector? Not exactly, but maybe something that gives a difference in X/Y/Z position of the exit from the entrance, length of the tunnel, and the difference in facing direction on exit?
I was initially thinking margin of error as compared to a "perfect" tunnel, but perhaps that isn't as important. What happens inside the tunnel is less important than the difference between vector on entry and vector on exit.