The idea is that the movable point defaults to the center between the two corner points, and you'll mostly be using the movable point to determine if the entity is on the ground or not.
If the movable point is on the ground, then the entity is on the ground, regardless of the corner points.
If the movable point is off the ground, but both of the corner points are on the ground, then you're on the ground, just too wide to fall through whatever gap is there.
If the movable point is off the ground, but just one of the corner points is on, then you're either floating over a slope, or you're stepping off of a ledge. The way you tell is by checking up to x amount of pixels underneath the movable point. If there's something solid under the point, within that tolerance, then you can simply reposition the entity on the ground, relative to the movable point.
If there's nothing under the movable point within the tolerance, then you slide the movable point towards the corner that still registers a collision, until the point is over the ledge, and you basically just glue the point to that edge, until you move in a way that the corner point moves off the ledge too, because that's when you fall.
If you walk back towards the ledge, rather than away from it, then once the movable point is back in the center of the entity, you unglue it from the ledge and you go back to repositioning the entity on top of the slope.
Hope this makes sense, I kinda had to think back to my TGF and MMF days to come up with it.



