Comments on 2D vs. 3D

Some great comments on my previous post.

A popular theory is that our affinity for 2D could be an artifact of the displays we are using. JeBus says: "If we had holographic technology, where the game objects actually appeared around the player in a 3-dimensional space, we'd be much better at it in-game."

But people were creating artwork and visualizing mathematics in 2D long before the invention of the computer screen! Archeologists believe cave paintings and sculptures appeared at roughly the same time. Since then, our species has devoted far more effort to creating 2D images than to carving in 3D.

I find it interesting that early paintings were not 2D projections of a 3D world, but a true 2D geometry where the third axis is simply non-existent. The idea of projecting 3D space with a vanishing point was not discovered until much later.

Beringela suggests what I'm going to call the Ender's Game theory: "We have evolved on what is essentially a 2D plane. When our ancestors hunted, they really only needed to think in 2D - how far away is that deer and what direction is it going. Its height above the ground didn't really matter."

This makes a lot of sense to me. Sure, reality is 3D, but for a species living on the surface of a planet with gravity, one axis is fundamentally different from the other two.

If this was the entire story, I would expect us to be happy to discard the vertical axis when playing a top-down game, but less comfortable with 2D sidescrollers where we keep the not-important-for-hunting-deer vertical axis while collapsing our usual north/south/east/west coordinate system into just a single left/right dimension. Yet most people seem equally at home with top-down or side-on 2D views.

DMG suggests our brains may simplify geometric problems by choosing between a variety of different projections: "We've evolved to naturally project 3D problems into 2D models. Need to find your way home to the cave? Refer to your mental 2D map. Need to hit a mammoth with a spear? Consider the vertical plane joining you and the mammoth."

That certainly matches my experience of using simplified coordinate systems for game AI.

Comments (12)

  1. John Sedlak says:

    I can certainly see the logic behind the deer hunting example. To put it another way, if we were a species that existed solely in (outer) space, I believe our perception of the world would be in 3D.

  2. Steve says:

    I think 2D vs 3D has to do with the fact that we are actualy very poor are precieving the 3D axis. Our eyes are set too close together to figure out distance or even movement that is more than 50 yards or so away. For example it is very hard to tell if something that is 100 yards away is moving directly tward you or away from you, but it is easy to tell of something far away is moving left/right/up/down. We usally use other clues to figure out if far away things are moving tward or away from us. such as if the animal is facing us it must be moving twards us.

  3. ShawnHargreaves says:

    > Our eyes are set too close together to figure out distance or even movement that is more than 50 yards or so away.

    But does our lack of visual accuracy wrt. the depth axis necessarily mean we must also have poor mental models in that area?

    It seems to me this might even be the opposite! If we can see something accurately, there is less need to model this inside our minds. The great value of abstract mental models is to help us fill in details that our physical sensors were unable to percieve…

  4. John O'Kane says:

    Are we perhaps missing one of the more obvious ideas: the canvas is 2d. One of the big breakthroughs in renaissance art was how to implement perspective – people had been struggling for a long time before then to create a sense of depth.

    It’s not necessarily that we can’t think in 3d but that we have a strong refusal to accept what’s on the monitor as natural or intuitive. As for visualisations, they’re often done on 2d canvases as well, your hand motions and ability to rotate, project, tangent is fairly much one to one. Give people a 3d canvas (holographic) and the ability to really interact and I think there would similar intuitions.

  5. I once learned (not sure if academia has changed its mind in the ensuing years tho!) that art in a culture always starts in 3d and later also uses 2d, unless the idea is introduced. 2D is a bit of a leap in that sense.

    I only use one eye and live on very flat land, so I guess I don’t appreciate the diff with 3D as much : ), but it seems to me that image that is finally projected into our brain is 2D. I read once (How the Mind Works) that there was an experiment were able to ‘develop’ a monkey’s brain that was looking at a pattern, and found the pattern on the cells. I believe it was injected with a radioactive substance, and blood flow in the brain was based on stimulus. The visual cells were approximately in a 2D grid.

    Interesting to think about this wrt games, thanks for the posts!

  6. Duncan Colvin says:

    Interesting stuff!  As someone who spans the areas of both academic psychology and game programming I thought I would venture my own understanding of why do 2D worlds make such intuitive sense, in case it might be helpful.

    It’s certianly true that physically the outside world is projected onto a 2D surface (curved, but nevertheless 2D) at the back of the eye.  To a degree this information initially maintained in 2D form in the early parts of the visual cortex.  But, of course, the brain then goes on to do a lot more than this; inferring depth, motion, shape, and so on.

    However, the most important point I think that needs mentioning is that we do not percieve the external world directly – rather, we percieve the world as ‘things’ in various relations to each other.  By that I mean that the brain sees more than just abstract 3D or 2D shapes and objects – the brain sees tables, chairs, cars, cats, dogs.

    This is illustrated well by the difficulty that most of us have in doing 2D drawings of a scene that we are looking at.  We tend to draw what we percieve to be there and not what is actually there.  It takes a certain natural talent and/or training to draw things ‘as they are out there’ and not ‘as they are in our heads’.

    And yet, even a child of 4 can draw recognizable 2D representations of things in the world around them.  The key word there is ‘representations’.  We are remarkably good at recognizing abstracted representations of things.

    And here I believe is where we can find the answer to Shawn’s original question: "Why do 2D worlds make sense?".  In short, the brain has absolutely no problems with the 2D worlds because it has absolutely no problems with abstracted representations(1).  In fact, the success of early computer games was heavily reliant on this aspect of brain processing.

    (1) interestingly, there are examples of patients with damage to some brain areas, who are actually unable to see ‘things’ and can only see abstracted shape and colour.

  7. Rim says:

    Good point Duncan, our brains really seem to love abstractions. I’d wish things were tied together so clearly in the cognitive psychology course I attended, cheers 🙂

  8. Ted says:

    "But people were creating artwork and visualizing mathematics in 2D long before the invention of the computer screen! Archeologists believe cave paintings and sculptures appeared at roughly the same time. Since then, our species has devoted far more effort to creating 2D images than to carving in 3D."

    Are you just flinging stuff out there or do you have references to cite?  The Greeks were sculpting realistic sculptures a thousand years before we discovered perspective in 2D during the Renaissance.

  9. Duncan Colvin says:

    Rim: stick with it – it’ll come together for you in the end I’m sure – psychology is a fascinating subject 🙂

  10. ShawnHargreaves says:

    Ted: 2D perspective projections of 3D scenes were a relatively late discovery, but pure 2D painting has been around pretty much forever:

  11. Verminaard says:

    I think this simply boils down to how the human brain works. Duncan makes a good point in that we don’t actually see in three dimensions, we see a 2D representation. If you think about it, we can even judge depth that well. If someone lined up a small object and a far away object so they looked identical, you eyes, in themselves, could not tell the difference. What does allow you to is you brain filling in the blanks and making assumptions based on your memory / instincts / other senses.

    At the other end of the scale, you brain is also designed to filter out what it feels is irrelevant from your higher levels of thought. In Shawn’s example of the hunter and the deer, the reality is that even within the two planes, the hunter is only really focusing on the ~180 degree arc facing the deer. I believe that this is largely why many people (including myself) struggle with visualizing / modelling in 3D – our brains are simply not optimized for visualizing the ‘big picture’ and as a result it fights you to try to fit it into a 2D representation or some other abstraction.

  12. Duncan Colvin says:

    Verminaard: I didn’t actually say we don’t see in three dimensions.  The main point was that we see more than just ‘dimensions’; we see recognizable ‘things’.  It could be in 2D or 3D, but so long as a visual image is recognizable as an X we have no problems.  2D vs 3D is interesting, but it’s not the brain’s main concern – its main concern is survival, and recognizing distinct ‘things’ based on a few key cues is what it has evolved to excel at (because of this we are also great at seeing patterns in ‘noise’ – Jesus on a piece of toast, Samuri warriors in the patterns of turtle shells, patterns in clouds, and so on).

    The difficulty of visualization and spacial awareness is a slightly different, but related issue.  Perhaps visualization and spacial awareness aren’t usually big difficulties in 2D games because 2D tends to lay it all out right there infront of us.  Whereas in 3D games you need to form a more detailed mental map of your environment, which is a more cognitively demanding task.

    In many 3D games you are looking at a small piece of the environment that is local to your character, but all of the local environment is important so you need to mentally map it so you can act in effectively in the game world.  In a 2D game you typically get a 360 degree view of your local environment, which means there is less mental mapping work to be done – so less cognitive load.

    Compare, for example, 3D games that are more top-down/isometric, with a first person or close-in 3rd person camera.

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