3D movies

Before “Avatar,” I’d seen a couple of movies in 3D and had not really been impressed with what the extra five bucks got me. Up until that point there was really only a single scene in a single movie in which I thought the 3D effect actually added anything to my experience. (It’s the shot in Pixar’s “Up” in which the house floats in front of the sunset…all the colors of the sunset shine through all the colors of the balloons, each balloon is a nice round object, and the whole collection of balloons looks three-dimensional. Beautiful.) For the most part, though, I tend not even to notice that a movie is 3D unless I’m specifically looking for the three-dimensionality – if it’s a good movie, the story and characters ought to hold my attention more than that – or if the filmmakers try some cheesy, gimmicky, amusement-park-style 3D “popping” effects, a la “Beowulf.”

“Avatar” changed my mind a little, in that many more of the scenes looked so damn cool in 3D. But the more I thought about it, the more I became convinced that while the 3D experience was pretty neat, if I go see “Avatar” any more it will be in 2D, because it really didn’t add that much to the movie. The forest creatures and sweeping panoramas will look just as good projected in 2D. The only aspects of that movie that would miss out are the holographic computer displays, and those aren’t really that important.

In fact, I think that Hollywood ought to just abandon this 3D movie kick. It’s not that I get a headache or think that cool things can’t possibly be done in 3D. It’s that even when filmmakers do the cool things, it adds so little to a movie that I’m definitely not inclined to shell out for a 50% surcharge on a ticket. Here’s why…

Here’s a terrible schematic cartoon of a person looking at an object located a distance x from their nose:

Geometry of a horrible disembodied cartoon face

When this person looks straight at the object, their eyes angle inwards from a direct line forward by ?. (I only drew one eye, because the situation is the same for the other.) Suppose that the object moves away from the person, on a direct line drawn from their nose, by a distance ?x. This reduces the angle ? by ??, as you can see in the picture. That angle, from each eye, is what your brain figures out distances from using your binocular vision. From this situation, I can write down the following two equations.

Then, with a little rearrangement of Eq (2) and plugging in Eq (1), I get this funky expression:

Here’s what this equation says: given the half-width of a person’s face r, the distance to the object x, and the minimum angular deflection of the eyeball the person can distinguish ??, the object must move a certain minimum distance away from their nose before they can distinguish that it moved. I expressed that distance as a fraction of the original distance x. For example, let’s say that r is 3 cm and ?? is 1° – meaning that this person’s brain cannot really tell if their eye moves by an angle of less than 1°. Then, if the object is x = 1 m away from their nose, ?x/x is about 1.4. This means that the person cannot tell if the object moves away from them, as long as it doesn’t move any more than 1.4 times away from them than its original distance. Alternatively, this means that the person can’t really tell the difference between an object 1 m away from them and one 1.4 m away.

Let’s keep r = 3 cm, and plot ?x/x for a couple sample values of ??.

Apparently, the better angular resolution your eye and brain have, the less a distant object has to move in order for you to tell that it’s moving. (For two eyes, you’re really figuring out the difference between the angle of each eye to gauge distance, but this is probably an okay approximation.) I have to admit that I don’t actually know what the average value of ?? is for a human, but I imagine that a fraction of a degree isn’t too far off.

Here’s the punchline of my plot. Even if you can distinguish a tenth of a degree of angular difference between the directions your eyes point, if an object is 15 meters away from you, with stereo vision along you won’t really be able to tell that a second object is farther away unless it’s seven times farther away. And the ?x/x curves asymptote at a finite value of x. (You might have been able to tell that as soon as you saw the presence of tangent in Eq. (3), but I like gleaning information from plots. What can I say, I’m an experimentalist! Ooh, I should do an experiment to figure out my ??!) This means that no matter how good your eyes are, there is some distance beyond which you can’t tell how far away things are. This really shouldn’t be that surprising – ever been to the Grand Canyon, scouted from the top of a mountain, or looked out of an airplane? What’s even more important is that this distance is not that far away from you. Even if you have really good binocular vision, this distance is probably less than about ten meters!

The truth is that our binocular vision is really not that effective at long range. It’s for close-in tasks that require manual dexterity. Try this experiment: close one eye – or, if you feel piratey, put on an eyepatch. Now try and see specifically what tasks you find difficult, choosing tasks at a range of distances from you. Can you tie your shoe? Make a sandwich? Thread a needle? How about lobbing a ball of paper into a wastebasket? Tossing a dart? Making a free throw? You will probably find that you fumble over your fingers when doing things close to your face, but when you’re looking farther away, your performance isn’t impacted that much.

For those tasks that require far-field attention, our brains don’t use binocular vision to figure out how far away objects are. Instead, we use a combination of other techniques: our brains interpret which objects in our field of view are in or out of focus, compare how much objects appear to move in perspective as we shift our point of view, or compare distant objects to the scale of objects that we know the size of.

What does all this boil down to for 3D movies? Well, unless all the action takes place within a few feet of your nose, a movie can look 3D just by using camera motion and focus. That will correlate completely with our everyday experience.

Small depth of field when everything is far away

The other problem with using stereo vision to make a 3D movie is that most movie action does not take place in scenes with large enough depth of field for the effect to really be apparent to us. “Depth of field” means, roughly, what’s the range of distances away from the viewer that the objects in the scene cover? That is, what’s the difference between the distance to the farthest object and the distance to the nearest object? In a panoramic landscape shot, all objects are far away. In an interior shot, all objects are close in. For a stereo vision 3D effect to be really noticeable to humans, you need distant objects and close objects – hence all the “ohmigosh that thing just popped out of the screen at me!” gimmicks that 3D movies try to pull – which is not usually a situation movie scenes present unless they were specifically arranged that way. Or, you have to hunt around in the scene specifically to find objects that are really close and really far away.

Small depth of field with all near objects

What made “Avatar” different was that they did manage to arrange many scenes with a large depth of field, without obvious gimmickry, in the process of showing off Pandora.

A wide range of depths for full depth of field

Even in “Avatar,” the 3D wasn’t always used to great effect. It looked best on the holographic consoles – because the hologram is in the near field and the human characters are clustered around it in the far field – and the flying-over-landscapes shots – because the flying vehicle or animal is in the near field and the landscape sweeps around us. But in the first shot of the movie, we see an extreme close-up of Jake Sully’s eye, viewed over the bridge of his nose, in 3D. The focus is on his eye. So we have a giant out-of-focus nose popping out of the screen. The focus alone is enough for our brains to determine the three-dimensional structure of the face! And if you try to focus on the fuzzy nose, you get conflicting inputs. (That’s why some people get motion-sick in 3D movies. Motion sickness comes when your senses disagree with each other or with your brain.)

The panoramic scenes in “Avatar” were spectacular, but many scenes were interior shots of the human base or deep within the forest. In these situations, the low depth of field issue arises. When I saw the movie, I so impressed with the vibrant colors and exobiology in the forest that I barely noticed any 3D effects. (Okay, the close-up of the da-Vinci-flying-machine-chameleon was awesome.) Many human-base-interior shots were from the perspective of Sully’s video blog, so again, pretty small depth of field with Sully’s face in the foreground and the back wall of a trailer in the not-too-distant background, with the middle ground cluttered up by all kinds of scientific equipment. But those shots had computer graphics popping right out of the screen, looking very cool and futuristic and 3D in front of the image they were recording. (I even noticed that the images on computer screens angled away from the viewer looked 3D.) In several of Jake’s monologue scenes, I found myself paying much more attention to the little 3D objects than to what he was saying. Maybe this would have mattered more if his monologues had been better written, I guess.

And then, of course, there’s the pretty weird effect you get when an obviously three-dimensional foreground object is not all the way on screen. Like, say we get a torso shot of Sigourney Weaver as a Cat in a Stanford Shirt Playing Basketball. Her upper body and head are three-dimensional, show up nicely in front of the distant base buildings and trees, and then suddenly she disappears into flatness below her stomach. Or say we get a swooping, attacking Scorpion helicopter coming in from stage right – all of a sudden, half a chopper pops into view.

“Avatar” definitely scored points from me for most effective use of 3D scenes to date. But I’m worried that the standard it sets will be for big blockbusters that lean on artificial three-dimensionality more than anything else. As I said above, getting three-dimensional perception from stereoscopic vision alone is really too much to expect of our eyes. And when I do get it, it’s likely that my attention will be on the 3D effects rather than the story. I think that’s one of the major reasons why I barely noticed that “Up” was in 3D, except for a few scenes – I wasn’t looking for it, and because of my depth-of-field arguments above, I tend not to notice the 3D in 3D movies unless I am specifically looking for it. So, I think I will stretch my money a bit more in the future.

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