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Sometimes in movies a character is shown in an interesting way. It's usually shot from a side and he or she is facing the frame with little to none of a space between their nose and the edge of the screen.

I was watching the latest Narcos movie and noticed it in a scene when Kiki and Jaime are chatting in a restaurant. Both are shown without much of a leadroom.

Curious when this type of shot is chosen? What meaning does it try to convey?

It's called 'negative space' and is often used to convey a sense of isolation - Watch: What's Negative Space

Mr Robot does a similar thing, called quadrant framing - The Socially Anxious Framing of 'Mr. Robot'

I don't know enough about it to provide a full answer, as I'm not certain precisely what is gained by having the negative space behind the subject, with them looking out of frame.

The general 'rule' is to leave more space in front of the subject than behind - known as 'Looking Space' or 'Nose Room'.

It's a technique I've used occasionally in stills photography and animation, but I'm not a cinematographer.

I thought it worth adding a large quote from the second link, which explains some of the emotional power of this type of framing...

There are many different established theories about composition that
look to explain how a subject's positioning within a frame affects the
audience's interpretation of that scene. The popular concept of the
"Rule of Thirds" states that the frame is divided by imaginary
horizontal and vertical guide lines that create a multi-quadrant grid,
the intersections of which serve as focal points for important
features of the image (faces, objects, etc.)

There are a lot of ways to play around with this concept, like, yes,
placing important stuff at an intersection, but you can also
communicate different things by placing your subject within a certain
quadrant. For example, placing Elliot in the bottom left quadrant
gives the impression that he is isolated, even untrusting of the world
around him. The reason for this stems from the relationship between
"negative space" and "positive space." (Negative space is the space
that surrounds a subject, while positive space is the subject itself.)
If a subject, which is traditionally the focal point of a composition,
only takes up a small fraction of the frame, the negative space
becomes much more noticeable and even overpowering, which can result
in eliciting emotions like loneliness, isolation, distrust, suspicion,
and powerlessness.

This specific image from Narcos is a mix of the Eyeline Match technique, Negative Space and the 180-Degree Rule, I found a great explanation of it in this book "Film: A Critical Introduction".

This article gives a great summary and examples for Negative Space technique.

I'm sure there are more videos on youtube with visual examples, but in short:

Eyeline Match: The use of a character's line of sight to direct the cut, in a way that emphasizes that the character is looking at something offscreen that is important to the scene, be it an object or a character, followed by a shot of what he is looking at. It is done to create a spatial awareness and clearness to the viewer.

The 180-Degree Rule: To film one side (A) of an action that will have an axis (the end of the screen), and to cross that axis the director will cut to the other side of the axis (B). This is also used to create a better spatial understanding for the viewer, the director can also break the rule to create more effects.

Negative Space: Use of Contrast between the focus of a shot and a low impact field or object.

Maybe there are even more techniques being used in this shot that I didn't catch, but these are the main ones.

I haven't see that particular scene, but I know that shots are framed and lit a particular way to give the viewer a particular emotional impression. Personally, I get two things from the images you provided.

1. If you lay the two shots over each other, the characters appear back to back. This means they are looking away from each other. This is emphasized by the visual divider in the horizontal middle of each shot: the wall shadows + booth back in the top shot, and the black chair in the bottom shot. The way these shots are framed would give me, as an audience member, the sense that the two characters are willfully not communicating. Were the two characters in the scene refusing to see each others' point of view? Was there some intentional miscommunication between them, or some secret / lie they were obviously not talking about?
   




2. As other answers have stated, the two characters look isolated, even in a claustrophobic sense. That is, their surroundings appear oppressive to them, boxing them into a tiny space in the frame.

The other answers are great about explaining this type of use of negative space generally.

Having seen this scene, I'd say that this particular framing is meant to show starkly that the characters are up against a wall, metaphorically.

They have constantly been hamstrung by their own higher-ups, repeatedly blocked from doing the very job they are there to do, and in this scene the character on the right (your second image, framed so he is on left side, facing left), who is the team leader, is delivering the bad news to the other character (left side physically, facing right), that their latest attempt at making progress, when they thought they really had a win, has failed yet again.

While they're both on the same team, working together, and facing the same obstacles, perhaps the framing further reinforces that they have to deal with different walls (barriers), or at least different parts of the same one, in that the superior is trying to fight for his team and the mission to higher ups, and must do that alone, while the other officer has only his own superior to convince, and having already done that, has no other avenue to succeed. Both are isolated in their own way, even as their interests and intentions are aligned.