An engine for multiple dimensions?

I'm obsessed with soft-coding everything under the sun, so my obsession has led me to a question that I dare not ponder myself.

What if an engine could be 3D, 2D, 1D, (theoretically also 4D, 5D, etc), all under the same code?
I'm just thinking here that it could be possible, with some kind of really crazy maths.
(At least unifying 1D - 3D under the same concept is theoretically possible).

I guess the underlying idea would be having Dimensions or Axes as engine components with which everything else works, rather than just arbitrary values from a programmer...

Anyhow, is there such a thing? It could be quite interesting to gaze wonderingly at.

Dont know. But it doesnt even sound difficult does it?
I have one (Unfinished), that just stores the scalars in an Tlist, and goes up to Memory restrictions. All the maths to 34D is exactly the same as 3D, just loads more donkey work for the computer.

What is 4-5-etc dimensional? :O

And dimention At right angles to the original three. Jeez dont you know anything. hahahahahah

Basicly if you cannot make the thing in a combination of the others it a new dimention. So we have up. Now down can be made of bits of up, so its not a new dimention. Left on the other hand cannot be made from Up (or Down), so is a new dimention. Forward is the same so now we have 3 dimentions. Now... time, cannot be made of any amount of up or down, so is a new dimention. Same with colour (RG and B) and Mass (Well... Mass per Volume space anyway) (To name but a few) So thats 8D already

So, A dimention is any scalar that cannot be created by any compination of the scalars that you already have. Of course the "Length" of X,y,z,R,g,b really makes no sence, but it exists as a number. The problem there is that the "Scale" of up and down has no real relation the Red or Blue scale, so the number is of dubious value. If though I wanted to compare the brightness of stars (say), then I would need this number, and from it, and the distance it is (from X,y,z), I could find the truer value of its brightness (ie length of r,g,b)

There is only one dimension with holographic properties. 2d is just a flat way of looking at a 3d world, and a 3d world is just a holographic reality seen from a limited vantage point. What else is there?

Well as the universe is a 4d shape unbounded in 3d, theres that one as well.
Come on it make no sence this "Finite yet without Limit" shape that the Universe is now descibed as (Since Einstien), without a folding in a forth dimention.

But anyway, I get the feeling that everyone else thinks that "Dimention" = Spacial Dimention. Which it doesnt. So Im going to shutup.

Because as the number of dimensions grow linearly, the complexity of the underlying math grows exponentially. Unfortunately computers are currently only good at solving polynomial problems. Prove otherwise, and get the Nobel prize.

Well I have problem with 1D and you ask code for more than 3D???!?! Arhrh!?

This is completely pointless, as are the arguments.
When you are writing a game, you have a specific amount of dimensions in mind, how can you even contemplate a game that will work in n dimensions?! :O

Well, I've given up on 3D and 2D, of course; clearly those paradigms lack MakePretty functions :b

This is just something I thought up but I'm near certain it is correct.

Area and volume
1 Dimension = 10cm
2 Dimensions = 10cm * 10cm=100cm squared (assuming each side of the rectangle has the the same amount)
3 Dimensions = 10cm * 10cm * 10cm=1000cm cubed (assuming each side of the cube has the the same amount)
4 Dimensions???? = 10cm * 10cm * 10cm * 10cm=10000cm to the fourth (assuming each side of the 4-dimesional cube has the the same amount)
I think you could do this an unlimited amout of times.

This is some stuff on the subject(in relation to string theory which is still theory): If I'm not mistaken the equation looks just like mine at the end of the second link (which shows a cube in 4 dimensions)
http://www.pbs.org/wgbh/nova/elegant/dimensions.html
http://www.pbs.org/wgbh/nova/elegant/math-flash.html

Hope this helps.

Note: This is for spatial dimensions the calcuation for temporal(time) dimensions are different if I remember correctly.

Hehe, I own that book (Elegant Universe)
But my point was, whats the point(pun intended :D)?

Interesting...
Although I do wonder what would make Time different. I always read that string theory stuff (note: I know nothing of string theory) as meaning that Time and Space are the same concept; that if a 3-dimensional object exists for 10 units of time (following the same scale as that object), then that object's volume when taking into account the Time dimension consumes 10 times more mmf.
The only difference, then, is the idea (very well conveyed by that article!) that the next dimension up is wrapped into every fraction of our dimension, thus making the sort of thing very difficult to comprehend.
Anyway, I know nothing of string theory.


I think such an engine would be interesting because it's sort of the holy grail of soft-coded software.
Program creates an interface for X dimensions, displayed in a way dictated via a simple config file. Yummy :)

Noel Cower has probably already made just such an engine. It sounds like the kind of thing he'd do in his spare time.

You won't.

http://www.superliminal.com/cube/cube.htm

^4-dimensional rubic's cube application. And some other examples near the bottom of that page. Of course, it's probably an 'artistic' interpretation of what 4-D looks like. But the math behind it seems plausible, but haven't read too much into it.

http://technabob.com/blog/2007/01/27/crush-psp-2d3d-platformer-looks-promising/

this game alters between 2D and 3D as a gameplay mechanic. real cool.

@zenith

I actually see a lot of use for a multiple dimension engine(beyond 3). Think about how awesome it would be for a spooky video game to have a haunted house that exists in 4-dimensional space. Or in a sci-fi space ship game you can have some sort of ray gun that temporairily makes part of the arena more than 3 spacial dimensions(totally disorientating players in online games!)

@Picklesworth
You could very well be correct about time and space being EXACTLY the same concept but I'm not really sure. Also, including time as an actual dimension in a video game(the way we think it is in real life) might be useful in a simulator but totally pointless and hinderous in a sci-fi shooter. Also I remember the equations for time dilation and Lorentez contraction be very similar if not the same. About the dimensions being wrapped, I remember reading(I think in Brian Greene's book The Elegant Universe) that the theorys state wrapped up dimensions can actually expand. I personally think it would be awesome to see something along the lines of this in a sci-fi shooter video game)

Note: Time Dilation is the difference of time experience by a stationary observer watching an object in relative motion. Lorentez contraction is the shrinking of objects to an observer as they go faster. You might want to google these for a more exact and probably more correct explanation.

I can't see how anything more than 3 dimensions could be of any use beyond maybe a novelty. If you consider time to be a dimension, then that might be useful in a game, but a 4th/5th/etc. spatial dimension would be useless.

Maybe it would work if the camera was restricted to the XYZ region (as with normal 3D games) and you were allowed to "sidestep" into the 4th dimension to go "around" walls. But then what would be in the parallel 3D space? A separate world? A slightly different world? A blank world? Really, more than 3 dimensions really don't work well unless you're referring to time.


This kind of this is best done as a "fictional" addition, where you artistically create disorienting effects. Have you ever tried to imagine a full 4D world? It's not easy. A 4D game would look like nothing more than weirdly warping lines which resemble nothing at all, since mapping a 4D world onto a 2D screen would be like mapping a 3D world onto a 1D screen.

A haunted house in 3D wouldn't make sense since a house is a human 3D object. You would have to "invent" the rest of the 4-dimensional shape, where the 3D house is only a single "slice" out of a 4D world.

A 4D space warp in a 3D space game would make a little more sense, where possibly your weapons could warp 3D space to open up wormholes or teleport objects.

If you are flying around in your 3d Elite Clone, and you fly ahead without turning (With a "when you get to the edge of the map" it moves you to the other edge, like CIV, implementation), then you will eventualy get back to the spacestation
Then the game space is a 3d model of a 4d space. (Just like real space is)

It's called polymorphism ... using virtual functions on a class you could have a class (or a BMax Type with methods) 'simulation' or 'universe' and then have a 1D, 2D, 3D, 4D, etc... derived from 'simulation' or 'universe' or whatever you want to call it and using that typical object oriented thought process you could have it all under the same codebase calling the same functions to act upon it as well. Of course at this point 2D and 3D are the only seemingly applicable choices but if you want extendability in programming it's there for the taking.

True, but your ship and view is still restricted to your local 3D world. There is no way to travel "sideways" into the 4th dimension.

For example, imagine a 2D space game running on a sheet of paper. Imagine the ships that reach the end of your sheet of paper would "fall" off the end of the universe, so you roll the sheet into a tube, then roll that tube into a torus. Now all your ships loop around the the other side of the universe - there are no "edges" any more.

However, from your 2D ship's viewpoint, nothing has changed visually. You still are living in a 2 dimensional world, even though some strange "magical" effects can occur due to the "real" 3D world outside. And you can't exit that 2D world by rotating off the 2D world plane and heading an a totally different 3D direction.

If you did "break" out of 3D and into 4D space in a 3D game, there's no way you can visualize more than a 3D scene with only 3D eyes. Since what you would see would be a 3D cross-section of a 4D world, any 4D rotations would make that 3D image warp and morph strangely, almost like taking 100 2D slices of a 3D object and animating them as though they were a movie.


That would work, but that's theoretically no different from implementing a different engine for each dimension space - you still have to write different code for 2D/3D/4D/5D/6D/7D/etc., even though it's all provided through the same interface.

The original question was: can this be done all under the same code? It's probably possible, I just don't understand why you would waste time on dimensions which cannot be seen.

Incorrect, you ARE traveling in the Forth dimention, simply because of the nature of the spaceshape. If you defined your elite game without this wraparround, then you are not traveling in this specific forth Dimention. But if you defined is as stated you are. Its not a question of noticing.

A snake on the surface of the planet cannot know if the world is a 3d space, until it repeats a full circuit.

Mass.
Again, the original question didnt specify that it was spacial dimentions that was in question. If it is, (Which I now belive), then yes your right, (apart form as I said the shape of the 3dspace may be 4d), if on the other hand we just mean, any other scalar undefinable in the dimentions that we have, then no you are not right.

This is a very interesting topic. I don't see how one can implement more than 3 dimensions into a game without completely confusing the player. Everything beyond the 3rd dimension is vague in my opinion. 1D, 2D, and 3D are directly related but time is different. Time is a very mind-boggling subject where the first 3 dimesions are comprehendable.

I love thinking about these things :)

Notice I said "but your ship and view is still restricted to your local 3D world." What this means is, in 4D space our 3D world may be crumpled up, like a piece of 2D paper in your 3D trash bin. But in our 3D world nothing has changed.

Imagine a 2D universe living on a sheet of paper. If you crumpled that paper up, it wouldn't make any difference in the 2D world - since your changes only affect it in 3D. True, the 2D creatures would be constantly moving around in 3D space now, but from their local perspective nothing has changed.

When I say you "rotate" into the 4th dimension, I'm referring to one of those 2D creatures actually leaving the 2D paper and floating out into 3D space, into your world.



That analogy almost works, except the snake is a 3D animal moving on a 3D planet. It's different when a 3D entity observes 4D space, or a 2D entity observes 3D space.

Unlike being on a planet, no matter where you go in 3D space, you don't notice the curvature of the universe, because the curvature is in the 4D space - you can't see it, being only a 3D entity.


That's true. Although time can be considered a dimension, it's different. Time keeps the universe dynamic, rather than simply a static existence.


Yeah, these are very interesting things to think about. What if there was no time, no space, nothing? Can you imagine not a universe with nothing, but pure nothingness? A nothingness where everything that is or everything that could have been, can never be or will never be.

In that case, the answer is yes. The engine is life.

Yes, it is a highly interesting topic. It has got be one of my favorites.

Time is directly related to the 3 spacial dimensions but harder to think about. (Movement in spacial dimensions slows down your preception of time.)

I think with some complex math however you shoud be able to represent a 4 dimensional-space object (In fact, I think it would be easier to do on a 2-D limited screen because it don't think it would be possible to show the player the whole object at once.) About moving in extra dimensions:

You have 3 spacial dimensions:
The Forward-Backward dimension
The Right-Left dimension
The Up-Down dimension

and then we have
The Future-Past dimension

So if a video game were made that played in 4 spacial dimensions you would have to figure out what the 4th way of movement would be.

Anyway, this is one interesting topic.

The 4th dimension would be represented with a full screen motion blur ;)

Yes I did notice, which was why I included it in the Quote. But you are still wrong.
Look see. Imagine that this "Wrap back to the begining space isnt very big, then when you look forwards, (or any direction really) you can see the back of yourself.
Whereas in an unbounded one you cannot. This is not analgus to your crumpelled paper example, it is analgus to your torus example. In the torus example if whatever lived there had good eyesight, and the torus was small enough it too would be able to see that back of its head.
In the Space game the shear act of going forwards in the GameSpace is moving you in a forth dimention. And when you get back to the Same space station that you left, the you realise that you have traveled so. Irrelevent of if this GameSpace has been crumpeled up or not.

Hahaha, should I have used a flatWorm? The Analogy works perfectly if you pertend that the snake cannot go or see up and down. The point being that we know of no 2d animal to use in the example, so what is used is always a ground based animal. Preferably a ground hugging one, so that people dont claim it would notice the curvature of whatever it lived on

See Above.
And if you think that thats a stupid answer, please remember that we can now "nearly" see half the Universe, (Ok so it half in age, and as it expaned quiker when it was young its not half the distance, but you see were the point is going).
So when we can look out and see half the distace of the Universe would we not see the same thing in all directions? Well if we dont, then we know that its Undounded 3d in 3d. And if we do then we know that is bounded 3d in 4d. (Which I think it is)

Well yes.
Thats either just before the Big Bang created the space for the Universe to start to be created in. (And as its waiting for Time to be created in it as well, just before is very subjective)
Or Just before God said whatever the Word was. (Depending)
Its like the Not space between you and other people on the Metro, then you let one rip, and space is created.

It actually is - the concept is the same (warping of lower dimensions in higher dimension). The only difference is that with a torus/sphere, the ends of the paper meet. Sure, in the torus example you could theoretically see your own back (btw, this is impossible in your snake example), but I don't see what this has to do with my point.

My point is simple: No matter how your universe is warped/twisted/torused/crumpled, you're stuck in that universe, unless you hit an "edge" or a "tear" in that universe, or have some scientific way of rotating yourself out of that universe.

What I'm saying is there's no use for Full 4-dimensional space in a 3D game, unless the viewer is restricted to 3D or 2D views. A 4D renderer (as in the original topic) would be useless, because humans don't have 4D eyes.

As I said, you might be able to represent the player's view as a cross-section of the 4D world, where they could move into parallel universes, but content creators have enough trouble creating 1 universe, much less 100+.


Yeah, if the 4th dimension is time.

I think it would be really interesting if there was a game where you could time-travel - where you could go back and observe your previous actions. Then if you interrupt yourself, the AI would have to take over as though you're actually interacting with yourself. But then if you interact too much you may change your actions which brought you here, and you would never have met yourself, which means you didn't change your actions, which means you will meet yourself, which means you'll change your actions, etc. I think this "infinite loop" is called a time paradox :)


What I meant was "A nothingness where everything that is or everything that could have been, can never be or will never be." Pure nothingness, no laws of physics, no nothing.

No.
There is a fundimental differance on the topology of the shape if the "Ends connect" or if its just a crumpled shape. For example the Gas/water/Electricity to three houses problem without crossing the connections, cannot be solved on a piece of paper (2d surface), no matter how crumpled (NOT folded),it is. But is can be solved on a torus, because they are mathematicaly different shapes. And no, its not impossible in the snake example. (Because its analgus, not the same as; The universe is the 2d plane/Tourus)

Unless its "Shaped" so as not to have an edge, and loops round the same way as your torus. (Klien Bottle) In which case it is a diffent shape to a Universe that doesnt loop round

And what I am saying is if you travel in one direction and it loops back to your start possition, then it is already 4D. And as Ive said the original topic was not implicetly about a 4D render, just Dimentions.

Yes, that could mean that it's 4D (although in most cases you hard-code the looping behavior, rather than implementing actual 4D simulation).


You're right - I misread it; somehow I though Mr. Picklesworth was referring to 4D renderers in addition to 4D coordinates.

I actually mean 2D and 3D, with 4D and 5D (What is this screaming I hear?) being sort of extras that become possible with the then existing framework :b

An interesting discussion, though...

Already done: Legend of Zelda: Ocarina of Time

I know it's not exactly what you wanted but it's a start ;)

And yet again, you fail to specify that you mean 4d/5d spacial dimentions. If a shape has mass, and a coofficient of friction and a colour, and a err .. shape, (assume round) and a position thats 9D

Athough I was a bit flippent about it. This is what was there before the Universe. When the Big Bang happened the first thing it did was create the Space for it to happen in. Before that there was no Anything, where nothing that was or anything that could have been. There was Pure Nothingness, includeing nowhere for the Nothingness to be, no laws of Physics, no anything. Including Time.