In a few cases one is allowed a second entry into a continent (e.g. Asia from SWP if one is a transit). Does this come out of the four segments allowed in SWP or is it essentially "free"?

In case that wasn't a clear question, does YVR->HKG->(transit)->AKL->CCH->SYD->MEL->PER->DPS->SIN->BKK->HKG->LHR->etc get me through SWP, Asia with 4 segments, 3 segments, or does the PER->DPS re-entry into Asia count against one or the other total?