FD, was VNAV a typo? I assume you mean LNAV.
The FMC route is constructed based on the maximum allowable bank angle (for the conditions, eg altitude) when in LNAV. The FMC software has been updated many times with various tweaks to the algorithms to prevent overbanks; the last was U10.6 where the nominal bank angle was set at half the track change but min 8deg & max 23deg. It had previously been max 25deg.
Note that this is only applicable when the aircraft is already on the magenta line, so when you engage LNAV or the A/P after T/O the aircraft may exceed this bank angle to get onto the track.
The actual logic of flying the track, or regaining it on a SID, comes from the FCC. Like the FMC this software is also updated, usually annually, and each version is improved slightly. You would think that after 40 years they would have got it right by now but new aircraft series/engines, winglets, features (Cat IIIb) and even autopilots (Collins) all require new software and some bedding in.
In short, you need to know what FMC and FCC software is installed and be on the magenta line to be able to accurately predict the bank angle.
S&L