westhawk:
The distance at which an FMS/FMC/GPS navigator sequences to the next waypoint in the flight plan must certainly vary according to the navigational mode it's in at the time. (enroute, terminal. approach, RNP 10, 5, 1, .3 etc..) I think it also might matter whether the waypoint is coded as flyover or flypast.
I did a quick search of TSO 129 in hopes of finding a quick answer but alas no success. I feel certain the answer is hidden in a technical standard order somewhere...
TSO 129, like 145/145 is a shell behind proprietary RTCA technical documents.
Later generation equipment does much better job with fly by waypoints than the earlier stuff. The point at which the turn begins is a function of ground speed and angle of course change. The RNP value or the sensitivity mode has nothing to do with it.