Rotate an object with 'Quaternion.Slerp' in world space

Question

I'm currently working on a multiplayer skydiving Unity game in which i rotate the players like this:

transform.rotation = Quaternion.Slerp(transform.rotation, desiredRotation, delta);

Now this rotates the player relative to it's own rotation. I know rotation in world space is done by multiplying the quaternion of the desired positon with the quaternion of the current position like this:

localRotation = transform.rotation * desiredRotation
worldRotation = desiredRotation * transform.rotation

But how do i slerp to that position in world space?

Thank you all in advance and have a great day!

Answer 1

First you grab the total rotation quaternion.

fullRelativeRotation = Quaternion.inverse(transform.rotation)*desiredRotation;
rotationTime = 0;
//persist over frames

then every frame until you complete the rotation you slerp the identity quaternion with it.

if(rotationTime < 1){
    rotationThisFrame = Quaternion.Slerp(Quaternion.identity, fullRelativeRotation, min(delta, 1-rotationTime));
    rotationTime+=delta;
    transform.rotation = transform.rotation * rotationThisFrame;
}

Answer 2

Usually, in order to get from a local coordinate frame to world coordinates, you need to go through the rotation hierarchy, like worldToParent.rotation * parentToLocal.rotation = worldToLocal.rotation.

So, in order to rotate towards a desired orientation in world space, your computation look something like transform.rotation = Quaternion.Slerp(worldToLocal.rotation, desiredRotation, delta). Note that desiredRotation in this case is not transformed, as it is a relative rotation anyways and will thus be applied within the same coordinate frame as the base rotation (in this case worldToLocal, defined as above, which resides in the world frame).