New answers tagged angles
The sign of the dot-product of C with AB will be positive when the vector component of CD parallel to vector AB is in the direction AB, and negative when it is in the direction BA. The sign of the (z-component of the) cross-product of vector CD with vector AB will indicate which side of AB the agent is approaching from. Depending on your sign conventions, ...
If I understand what you're asking, the vector CD is just a vector, not a ray, so only the direction matters, not location. However, AB is a line segment, not just a vector, so its location matters. Your tests have one 'if' test to make two cases, but I think you actually have four cases. Let's look at the diagram in AB's reference frame: If you can ...
I think you could switch your cos with sin and vise versa if you're really against adding 90 in your function, but I think adding 90 is a perfectly viable solution. Once a function works, you shouldn't have to care what's inside of it.
atan2(y1-y2, x1-x2) or maybe atan2(-(y1-y2), x1-x2), depending on the coordinate system.
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