Crossing the line is an interesting concept that the script supervisor will absolutely encounter on set. It’s a good idea to sketch an in plan view of each set you are shooting on so that you can refer to it should the director or DP be concerned when it happens. You will also find that the idea of crossing the line has been drummed into many DP’s heads as if it’s some artistically deadly situation. This is mostly first-timers right out of film school.
X and Y are your horizontal and vertical axes and Z is your depth. Crossing the line can occur along 180° lines within any of those dimensions. “Horizontal plane to horizontal plane” crossings are most uncommon unless you are filming underneath one subject and above the other.
In the early days of film, most action was directed with a fourth wall. This world outside of the frame provided the limits of what could be visible in frame. The thinking went, “We can’t cross the line because the audience needs to be in a fixed location like a theater audience. They’ll get confused if they see someone flip from one side of the screen to the other.” Now (and I mean decades, since we’ve been doing it from the beginning of film and regularly crossing the line since the 60s) audiences get it. You hear gaffers ask where they’ll be safe and DPs respond that, “we’ll see the world.” It’s a 360° world in film.
So what does this mean for scriptys on set? Our job is to make sure the film cuts. So two things help us, geography and eyelines. Items such as set pieces that can be static (geography) locate the audience’s perception. If a house and tree are the same “logical” proximity to the actors from whatever angle you shoot them, the audience isn’t confused. Just make sure that you have enough coverage shot so that if the geography disappears (like in close ups) the audience isn’t taken by surprise. And eyelines locate the items that are dynamic; actors, extras, explosions, vehicles, etc.
It’s not that difficult. However, there are times on set when discussions get confusing. Pull out your sketch with all the 180° lines you’ve shot along and you’ll have the answer right there.
See the famous example in Kubrick’s The Shining. Jack Torrence and Delbert Grady have a conversation in the men’s room. Kubrick goes back and forth with the camera. See how the actors’ body positions and the unwavering location of the urinals and walls roots the audience perception of a whole room. This is not confusing at all. It’s been a long time since an audience was afraid the train on the screen was going to crash into them.