How to set transform.up without locking the y-axis?

Question

I'm trying to make an object's transform.up to a normal of the raycastHit point. I tried using this line of code:

transform.up = Vector3.Lerp(transform.up, normal, 1 * Time.deltaTime);

This works well but locks the y-axis rotation as a result the object can't rotate and just keeps going forward. I tried using Quaternion.LookRotation. But I couldn't make it affect the object's rotation. Here is what I tried:

bodyRotation = Quaternion.LookRotation(transform.forward, normal);
transform.rotation = Quaternion.Slerp(transform.rotation, bodyRotation, 100 * Time.deltaTime);

How can I set the transform.up without locking the y-axis?

Answer 1

When you assign a value to transform.right/up/forward, you're implicitly telling Unity "I care only about the direction of this one axis - do whatever is cheap and easy with the other two". If you care about both the up and forward direction, then you need to take responsibility for constructing a quaternion with your desired orientation.

Fortunately, this is easy, as I've covered in several past answers:

Quaternion TurretLookRotation(Vector3 approximateForward, Vector3 exactUp) {
    Quaternion zToUp = Quaternion.LookRotation(exactUp, -approximateForward);
    Quaternion yToz = Quaternion.Euler(90, 0, 0);
    return zToUp * yToz;
}

You can incorporate this like so:

var targetRotation = TurretLookRotation(transform.forward, normal);

transform.rotation = Quaternion.RotateTowards(transform.rotation, targetRotation, speed * Time.deltaTime);

I've used RotateTowards in place of Lerp/Slerp here, because your lerping expressions were not not correctly adjusting for deltaTime.