An air carrier aircraft departed SIN (WSSS) on the ADPAX 1X SID and entered restricted military airspace after the FMS made wide turns near BOBAG and BASIX according to the 'Fly By' design parameters.

Narrative

We were filed and cleared for the ADPAX 1X (Air Defense Exercise) SID from SIN (Singapore); departing Runway 20C. Tower cleared us for takeoff and assigned us to fly runway heading. As the Captain; I was the pilot flying this leg. Shortly after takeoff the autopilot was engaged. Still on runway heading and somewhere southwest of the field; the Tower Controller switched us to departure control. We were soon given the clearance to proceed direct to BOBAG and resume the ADPAX 1X SID. The First Officer selected direct BOBAG in the FMS and I selected NAV. Since BOBAG and BASIX (the next fix on the SID) are both 'fly-by waypoints' and not 'fly-over waypoints' the FMC produced a track that drastically cut the corner to the east of BOBAG and BASIX on the way to ADPAX. Since the Airbus FMS is certified to fly this way; I did not think anything of it. Shortly thereafter; ATC asked us if we were proceeding direct to BOBAG; and informed us that we had flown through restricted military airspace. We were then given a westerly heading to fly; and eventually cleared direct to BASIX. Again the FMC calculated a large short cut from our present position; to fly 'near' BASIX and then to ADPAX. Just to be sure; I took the airplane out of NAV mode and flew in heading select to get closer to BASIX before turning to ADPAX.