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I wasn't sure how to formulate the title for this question, but in general terms my idea, what I think it's an axiom, there are movements in a 3D space that are more expensive to perceive and process for our brain, I'm assuming that the cognitive workload is different between different kind of movements no matter what is the shape of your object, probably less expensive for round-ish 3D objects, but I still don't think that translations, rotations, mirroring, and so on have are taxing the brain in equal parts.

There is some research done in this field and so is possible to grade the less expensive movements up to the more taxing ones ?

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Our brains have evolved specifically to process movement in 3D space - being able to spot the sabre toothed tiger leaping at you would be the difference between being around to pass on your genes rather than becoming lunch.

This book by Gibson is worth a read:

The Ecological Approach To Visual Perception

This is a book about how we see: the environment around us (its surfaces, their layout, and their colors and textures); where we are in the environment; whether or not we are moving and, if we are, where we are going; what things are good for; how to do things (to thread a needle or drive an automobile); or why things look as they do.

For a more information processing analyisis the work of David Marr is worth looking at: en.wikipedia.org/wiki/David_Marr_%28neuroscientist%29

The key point is that the brain is an active system: it doesn't just passively process information which is coming into it, but uses stored information to build images from the incoming data. Its not a computer.

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Forgive me if I've missed the point of your question, it is a little confusing.

Your brain is not doing matrix math to draw the world. The things you mention are components, remnants or artifacts of 3D computer graphics and the way computers use numbers to operate. I think our brains work differently in that we don't need to maintain a list of vertices that represent 3D space because we do not need to draw and composite 3D objects like a computer does; the objects are already there and we are viewing them akin to a 2D/3D image. Each eye generally sees in 2D (no depth) but with two eyes (binocular) your brain creates the sense of depth, or 3D.

I do however think that we find harmony in certain patterns and tend to prefer certain patterns or shapes over others, likely due in part to the subconscious mind.

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  • nope, you are stuck at a level of information that even predates the perception. It's like talking about photons and which wavelengths contribute to the red color when in fact you are interested in why our brain perceives the red as a hue with some strong properties . there are also problems with your approach, imagine to be at a cinema, it's your 3D world, but the surface where the film is being projected is basically a simple 2D surface, but again the film, in 2D, contains objects that your brain perceives as 3D. Do you think that your brain perceives everything around you ? Probably not. – user2485710 Oct 22 '14 at 23:09
  • there are also other kinds of problems to solve, like why a director picks a certain lens to shoot a movie or why animated movie use certain patterns, and so on, there is an entire science on visual perception, on a lot of animations there are frames that are even skipped because the authors know that your brain will interpolate the 2 frames for you, or they trick your brain into this with some clever tricks . – user2485710 Oct 22 '14 at 23:12

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