ModeShiftPeriod makes it easier to tune the camera transitions.  The "rate" used to be a multiplicative factor on "deltaTime" and the combination of the two represented a fraction toward a full transition (where 180 degrees was a full transition on a cosine shaped curve).  The "period" specifies the time it takes for the camera to transition -- the identical argument here (1.0) is not a coincidence: in both cases it represents a "full transition in on second".