How to get the angular displacement of a point on the robot from a point an arbitrary distance away

I want to be able to calculate angular displacement around a point factoring in translation and rotation and radius from a point. How can I achieve this?

What I am trying to achieve is below.

Angular displacement doesn’t care about distance (unless you’ve somehow misused the term and I’m misunderstanding what you’re getting at). Angular displacement is simply the target’s angle relative to your own heading.

To accurately identify the vector (on a 2d plane) to an object relative to yourself, you need heading(angle relative to a known reference) and magnitude(distance). If you don’t have the angle, but know one of the component vectors, you can use sine/cosine (or specifically their inverses) to solve for the angle. Likewise, if you have the angle and a component distance, but are lacking the magnitude (straight-line distance), you can solve for that as well.

Displacement is simply the difference of your current heading (relative to that same reference) and the angle to that point.

To give an example, let’s assume your known reference is the X axis. If your heading is -25° (25° counter-clockwise from reference, and the object is at 20° (20° clockwise from reference), then your angular displacement is currently 45° (20-(-25)).

I suspect this is related to a shooter angle based on camera/limelight feedback. Ultimately the math is the same, though