TheChitterneFlyer has nicely reinforced the truth in different words to mine, but we stand together
Chitterne has stated correctly that in inserting en-route waypoints for a continuous Great Circle Track, the integrity of the Entire GC Track is maintained, but now broken into smaller components, each of which will, by dint of Longitudinal convergence and changeing Magnetic Variation, have differing Initial Magnetic Tracks. This, then, is a series of Great Circles, all of which exactly make up the 'complete' Great Circle. This is akin to what we did in olden days pre-FMC/INS, the Great Circle over a long distance would be broken into smaller 'flyable' Rhumb Lines. Such a case is
NOT a continuous GC, but a composite routing, simply because aircraft of earlier eras did not have Great Circle navigational capability.
I will make one very minor concession in the continuous GC discussion, and that is that SOME units calculate the new en-route positions, and round off the results to DMT (Degrees, Minutes, and tenths of Minutes) or DMH (Degrees, Minutes, and hundredths of Minutes). It's then up to the programmer to decide if the intermediate Tracks are from the 'rounded off' positions, or the much more accurate position of up to 10 decimal places which is retained 'internally, with DMT or DMH used for display. This might produce very minor track kinking, but probably not so much that you'd notice.
Yours truly is guilty of writing programmes for the LNAV portion of some FMC units, and I have always opted for the exact position used for navigation, and the 'rounded off' position (DMT or DMH) used for display. (Do you REALLY want to know that your latitude is 61.3752398231 degrees North? I think not.)
Bear in mind also that FMC/FMS units have internal prioritisation. The highest of all priorities is the acquisition of the aircraft position. The
LAST of the unit's priorities is map display, which, with several seconds between display refresh, may occasionally produce a slightly kinked track display, which LOOKS like map shift as screen refreshes occur, but is not.
Regards,
Old Smokey