How to convert from world coordinates to camera coordinates

Question

In the world coordinate system, there are objects with rotation values rx1,ry1,rz1 and position values px1,py1,pz1 .

Similarly, there is an camera in the world coordinate system with rotation values rx2,ry2,rz2 and position values px2,py2,pz2 .

What formula can be used to convert rx1,ry1,rz1,px1,py1,pz1 to the camera coordinate system?

The up vector of the camera is the Y-axis, always oriented toward the object near the world origin.

The camera and the model are supposed to move within the range as shown in the following gif image.

I would like to use Python to do the calculations, but I am open to any other answers, including other Unity C# or mathematical statements.

You are welcome to have commentary in quaternions or in matrices instead of euler angles.

Answer 1

Within Unity c# for the position you can simply use the built-in

var localPosition = camera.transform.InverseTransformPoint(theObject.transform.position);

for the rotation you can use

var localRotation = Quaternion.Inverse(camera.transform.rotation) * theObject.transform.rotation;

This should give you the localPosition and localRotation in the coordinate space of the camera .