[K.I.L.E.R]

What kind of things do we need to have 4D renderings?

[mat]

time machines
but i heard they are in DX10

[Hyp-X]

I don't know if the question was meant as a serious one, but here we go.

First we should clarify what we'd mean by 4D rendering.

Currently the highest practical rendering takes objects in 3D space projects it into 2D and the rendering is done in 2D.

True 3D rendering is not usually neccesary because of the lack of 3D visualisation devices.

So the analogue of 3D->2D as 4D->3D is not feasible.

It is possible though to project 4D space to 3D, than render the resulting 3D objects using "traditional" rendering.

It has been done before, I have seen a rotating 4D hypercube in one of such a program.

It's really just a form of dynamically creating 3D objects - it looks strange, and I doubt it's particularly useful.

[Nagorak]

Since we see in 3 dimensions, our minds can't really fathom 4D objects anyway (except in the abstract). Rendering 4D down to 3D is more or less a waste of time, because we still see it as 3D. I guess if you're studying 4D it might be useful, but on a wide scale it's practically useless.

[no_way]

temporal AA can be considered as 4D rendering feature, in a way :P
But, our universe is still more commonly regarded as 3+1 dimensional, not 4 dimensional.

[darkblu]

Originally Posted by Nagorak

Since we see in 3 dimensions, our minds can't really fathom 4D objects anyway (except in the abstract). Rendering 4D down to 3D is more or less a waste of time, because we still see it as 3D. I guess if you're studying 4D it might be useful, but on a wide scale it's practically useless.

actually a typical 4d->2d projection yields considerably more occlusion, compared to a 3d->2d projection - this could be useful .. i guess

[Dave B(TotalVR)]

"But, our universe is still more commonly regarded as 3+1 dimensional, not 4 dimensional."

You mean it is more generally perceived as 3 dimensional

[Kristof]

I always thought that time is the extra dimension... currently 3D Rendering matches the world for an infinitly small amount of time, a single perfect snapshot. This is not very realistic, so maybe 4D is when we accurately handle time related issues.

To a certain degree current 3D rendering is 4D since a whole set of images creates animation. So we have X, Y and Z forming the 3D space and T creating the animation. Its all in your definition of that fourth dimension.

K-

[martrox]

Just as long as Robert Lansing doesn't come through my walls....I'm happy!

ACK! Showing my age!!!!

http://www.scifilm.org/reviews/4dman.html

[Saem]

I always thought that time is the extra dimension...

When I clicked on this thread, I thought the discussion would touch upon temporal anti-aliasing.

[Reverend]

Wow, what a topic to discuss on this site!

[Crusher]

http://sprott.physics.wisc.edu/pickover/fourth.html

[fresh]

We can't perceive 4 (spatial) dimensional objects. You can project them into 3D though, just like you can project 3D into 2D (your monitor). You can only ever see a single "slice" of this 4D object in 3D.

To illustrate, imagine you were a 2 dimensional being (a stick man) living on the surface of a piece of paper. You can't see 3D objects, but you could see the shadow of a 3D object. If I (being 3D) was able to reach my hand through the paper you'd see a 2D slice of my hand. You could do some strange things being 3D in a 2D world! You could see inside the stick man. You (or rather your projection/slice) could suddenly appear and disappear in the stick man's 2D universe. 4D objects could do similar things in 3D.

If you want to see what a 4D object looks like in 3D, do a google search on "hypercube" and I'm sure you'll run into many java applets which demonstrate this.

edit : Ack! I just noticed that Crusher put up a link with the exact same analagy I used. I got mine from Michio Kaku's book "Hyperspace" though.

[Vince]

Originally Posted by fresh

I got mine from Michio Kaku's book "Hyperspace" though.

Great book, or if your first getting into this topic, the classic Victorian satire, Flatland, is pretty good as a prerequisite for getting you aquanted with the generalized ideas. Pretty good book on a few levels actually, physics, societal hiarchy, ect.

4D objects could do similar things in 3D.

Just to clearify, as you [being 4D] move threw the 3D 'plane', the 3D entity would see a 'spherical' crossecection [3D] of the 4D one, ect.

Kind of like a xD interpolation of a higher D object, with x being the limits of perception/physics. So, for Fresh's stick guy, x=2 and he'd see a 'circular' represenation. For us, x=3 and we'd see a 'spherical' or 3D crossection.

Cool stuff

[K.I.L.E.R]

So what you guys are saying is that Virtual Reality is a 4d thing?

Damn I just read one of the links and that is scary. Is there such thing as a 4d being? Seriously?

[malcolm]

Would there be any use of living in 4d?
Things that arent possible in 3d? Ofcource everything would be a lot different but actualy still basicaly the same i think if you know what i mean.

[Nagorak]

Think about the advantages we have over a hypothetical creature living in 2D space. We can move and perceive a whole different dimension.

Then again do we have any real advantages or would it be just about the same if we were used to it... hmm

[malcolm]

I also think you cant realy compare moving from 2d to 3d and 3d to 4d when it comes to usefullness.
Is real world 3d actualy 3d ? I mean 3 dimensions put together?
I know thats how we calculate it but is that how it realy is?
Is the universe just a mathematical system then instead of a 'real' universe we can just make (discover) mathematics for to predict it.
I actualy do think its a system, so not 'real' but real is what the system gives you with your senses.
So atoms or the more complex working in attoms are just points with properties (forces and frequencies and whatever else) that determine the way the points interact with the other points.
So basicaly just a system that exists in something (consciousness memory of god? (remember god is just a word, has nothing to do with existing religion, more like what is called all that is sometimes)
Ok this might be of topic but im wondering what you guys think about this.

[gking]

Dimensionality is a really abstract concept (you encounter it frequently in higher-level math). It refers to the number of independently varying parameters in any function.

Rather than referring strictly to object positions (conventional 3D), the higher dimensions could refer to light directions, viewer stimulus response, or pretty much anything else.

One application of 4D rendering is a lightfield -- instead of rendering one image, every possible viewer and light direction are rendered into an array of images. Subsequently, the original data can be reconstructed/interpolated very quickly. This technique is primarily interesting for software rendering engines; however, I've had a couple of ideas for shader-based lightfield-style rendering/reconstruction that could make for some very interesting effects.

[Gollum]

How's this for a spaced-off topic for once, kinda cool actually. I dunno about others here, but I haven't delved too much into the hyperspace side of things that was brought up here. Would be interesting to read up on this, any worthwhile book reccomendations?

My view of the world is based mainly off Eintein's "Raumzeit" (Spacetime) where we have the 3 dimensions of space and the 4th dimension of time. I am vaguely familiar with the quantum theory, heard some basics about superstring theories and their up to over 10 dimensions. Now once we get there I totally loose any kind of image of how things would "be like", its just too abstract. So basically I'm aware that in high physics and maths dimensions can be a lot more complex and take on different functions, but that's about it. Coming back to the more conventional theories - what do we talk about when we mean 4D? Time as in the Raumzeit or something else? In Einstein's world I'd kind of expect a 4D object or being would look to us kind of like a "normal" 3D object does, its 4th dimension for me would refer to its ability to be able to move through the 4th dimension, time, just as we can move throuh space? It all depends on how you define the dimensions I guess...

If we take a different construct than Einstein's Spacetime I fail to have a basis for comparison, as I don't know the theories such a universe would be based upon and what a 4th dimesnions would or could represent. However, even so I think its too simple to draw comparisons between how a 3D -> 2D representation works/appears and conclude on the 4D -> 3D relationship from there, IMHO the whole thing would be vastly more complex and much harder to explain than these 3D -> 2D analogies try to convey. And how all of this could be translated into hardware rendering technolohy is beyond me, hehe...

[malcolm]

Originally Posted by gking

Dimensionality is a really abstract concept (you encounter it frequently in higher-level math). It refers to the number of independently varying parameters in any function.

Rather than referring strictly to object positions (conventional 3D), the higher dimensions could refer to light directions, viewer stimulus response, or pretty much anything else.

One application of 4D rendering is a lightfield -- instead of rendering one image, every possible viewer and light direction are rendered into an array of images. Subsequently, the original data can be reconstructed/interpolated very quickly. This technique is primarily interesting for software rendering engines; however, I've had a couple of ideas for shader-based lightfield-style rendering/reconstruction that could make for some very interesting effects.

Yes i know about dimensions in math calculations but i think here they were talking about a 4dimensional environment with 4dimensional movement and 4dimensional spherical vision (3d projected image)

Ive also been thinking about doing something like lightfield youre talking about (i think).
I think you can do real geometry bumpmapping so there are shadows in it.
Would be good especialy for things where the geometry details are much smaller than the screen pixels because you lose the small detail bumps there when you render it real time and the lighting result is very different.
With that technique you could render out different view angle textures and also the average geometry direction and reflectiveness per pixel for each mipmap for the real time specular calculation.
Some examples ive been thinking of are a cloth for a pooltable and asphalt for a racing simulation.

[Fred]

The temporal field as an added dimension is interesting to me.

It does not make sense to me mathematically to represent 3d graphics signature as standard 3 + 1 (for comparison our universe is actually +3 -1 technically). That is just an approximation, a hack so to speak.

Since we are dealing in reality with a quantized temporal field in 3dgraphics it should naturarly necessitate a different metric tensor, probably living in fourier transform space.

It should be possible to represent things in a precise way using this approach, and I suspect could lead to quite a few interesting results if done rigourously.

Whether its possible for realtime renderers, or even warranted by virtue of the extra overhead is anyone's guess.

[elimc]

http://pw1.netcom.com/~hjsmith/WireF...tesseract.html

[g__day]

I was half expecting a post on M-theory, 11 dimensional space, string theory, and super-gravity.

As a mathematican it is easy to transform an N dimensional object in an N dimensional (linear) space into its best fit in a lower dimensional (linear) space. That's just second year University Pure linear algebra maths. The equations are straight forward once you realise you are determining the best way of describing the axis's of a N dimensional space onto the axis's of a space with fewer dimensions. Its a one line formulea for each axis.

With a maxtrix transform it'd probably be require one matrix multiply to change a N dimension object into its best equivalent form in a space of fewer dimensions. (easy peasy)! So N equations to set up the matrix and one multiply to change any object in an N dimensional space to its N-A target space. 4 dimensions to 3 dimensions, simple.

But why would you want to do this? What real world use does someone have for this need?