Let’s say, I have a game object in the space. And I know the positions and rotations in two different coordinate systems.

For example, the position and rotation of this game object in local space (let’s say relative to another game object) is **P_l** and **R_l**, which is a vector and a quaternion respectively.

Similarly, the position and rotation of this game object in the world space is **P_w** and **R_w**.

How should we find out the transformation from local space to world space? (algorithmically or leveraging Unity API). By leveraging the computed transformation, my goal is the transform the position and rotation of any game objects in the local space to the world space.

This is somewhat similar to the Unity transform API:

```
Y = transform.transformPoint(X);
```

However in our case, we know the details of X and Y, and want to find out transform?

Thank you so much! Any suggestions would be helpful!