How can I get a normalized direction vector from an objects rotation?
As @jimmyjjeeter suggested, you can use transform.forward (as well as transform.up for the up direction, transform.right for right, -transform.right for left etc.).
If you have a quaternion but not the transform, you can rotate a vector like this:
var rotatedVector = someQuaternion * Vector3.forward;
NOTE: Order matters in the quaternion world: it must always be quaternion x vector (vector x quaternion produces an error).
I always end up here when I’ve forgotten how to convert a rotation to a direction vector, so here’s a complete answer for anyone else ending up here or for me 6 months from now.
For a Quaternion rotation:
Vector3 forwardVector = yourQuaternionRotation * Vector3.forward
And for a Vector3 rotation:
Vector3 forwardVector = Quaternion.Euler(yourVector3Rotation) * Vector3.forward
Isn’t that just transform.forward?