If you don't want to keep two state copies around to extrapolate (or
interpolate) then you can render iff you actually stepped, else snooze for
a few milliseconds. Although snoozing on 16-bit based versions of Windows
(98, ME) is likely to be very jittery.
If you use EXTRAPOLATE, then the graphics display will be "current" (or
as current as you can make it) but it'll always be slightly non-physical,
with small overshoots etc.
If you use INTERPOLATE, then the graphics display will be physically
based (no penetration right before a collision, etc) but there will be a
graphics lag of about one step/frametime. If you can keep the frame time
high (> 50 fps) this is not a problem, and is recommended.
The MAX_ALLOWED_FRAMETIME check is there to avoid the spiral of
death that might happen if physics suddenly runs slightly slower than real
time -- if that happens, we want to limit the amount of updating we do to
some fixed time-step, such that the real time speed of the game will slow
down, but at least it won't spiral out of control with ever-longer frame
times trying to catch up. It's worth noting, though, that if you run a
distributed simulation (networked game), falling behind for any longer
period of time will lead to de-synch of the game. This is why networked
games are often more serious about their PC minimum spec requirements than
traditional first-person games.
So what are reasonable values for these constants? Of course, it depends
on your game. For a rigid body simulation, you probably want the physics
update rate to be 100 Hz, so STEPSIZE is 0.01 seconds. In that case, you
probably want to set MAX_ALLOWED_FRAMETIME to something like 0.05 or 0.1
For an interpolator class, see the
article on this web page.