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c#unity-game-engineangle

Angle of camera to intersect with object vector

I am trying to determine the angle where the camera forward vector intersect with an object vector.

Sorry, not straight forward to explain with my knowledge, please find attached a diagram: The camera may not be looking directly at the object (OBJ) and I'd like to know the angle ( ? in the diagram) where the camera's forward vector (V1 in red) intersects with the vector of the object (V2 in red) (if it does), e.g. point A, or B, or C, etc depending on the x-rotation of the camera.

diagram

I tried calculating a normalized vector for the red lines, v1 and v2. Then calculate the angle between two vectors https://onlinemschool.com/math/library/vector/angl/ But the results don't match the expected values when testing.

//v1
Vector3 hypoth = Camera.main.transform.forward.normalized;
//v2
Vector3 adjacent = (new Vector3(obj.transform.position.x, obj.transform.position.y, Camera.main.transform.position.z) 
                        -obj.transform.position).normalized;

float dotProd = Vector3.Dot(adjacent, hypoth);
float cosOfAngle = dotProd / (Vector3.Magnitude(adjacent) * Vector3.Magnitude(hypoth));
double radAngle = Math.Acos(cosOfAngle);
float angle = (float)((180 / Math.PI) * radAngle);
Solution

  • Finding the angle between v1 and v2 gives you this angle, which doesn't match what you mark in your diagram:

    what your code is calculating

    Instead, solve for the angle between v1 and the plane normal to v2:

    diagram explaining why this works

    We can do this in unity by projecting v1 to the plane normal to v2 using Vector3.ProjectOnPlane, and then finding the angle between that projection and v1 using Vector3.Angle:

    Vector3 projection = Vector3.ProjectOnPlane(hypoth, adjacent); 
float angle = Vector3.Angle(projection, hypoth);