Unity calculate quaternion relative to main camera

Question

I have world coordinates for the GameObject object and for Camera.main, and I would like to calculate the position and rotation relative to Camera.main.

Position is easy:

object.transform.position - Camera.main.transform.position 

How to calculate Quaternion for given object relative to camera?

I can set object.transform.parent = Camera.main.transform and read localRotation, but is there more elegant solution.

Answer 1

By definition:

obj.transform.parent.rotation * obj.transform.localrotation = obj.transform.rotation

So, another way of phrasing your question is that you want to find the quaternion q such that Camera.main.transform.rotation * q == object.transform.rotation. So, you can solve this algebraically:

                        cam_rotation * q = obj_rotation  
inverse(cam_rotation) * cam_rotation * q = inverse(cam_rotation) * obj_rotation  
                                       q = inverse(cam_rotation) * obj_rotation

And to calculate that in unity:

Quaternion q = Quaternion.Inverse(Camera.main.transform.rotation) 
               * object.transform.rotation;