4D hypercube?

[3DModelerMan]

Since it's possible to project a 3D representation of an object, onto a 2D screen. Shouldn't it be possible to project a 4D representation of an object(maybe a hypercube?), into a 3D voxel, or model, or something like that, then render that in 2D?

[terier]

Maybe you should take a look at this:
http://en.wikipedia.org/wiki/File:8-cell-simple.gif
http://www.superliminal.com/cube/cube.htm
I guess it's possible, but not really practical...

[stefbuet]

Ok let's say you got a 4D object which fourth dimention is time.
Display the object on the sceen and change it's color in function of the time.
That it you got your 4D object on your 2D screen just like you had your 3D object. Seriously, your question is non sence, what do u call a dimention ? object position, time, color, velocity ?
If your object have a,b,c,d property in 4D and you want it in 1D you just do a+b+c+d to get an 1D property

[ent1ty]

Since it's possible to project a 3D representation of an object, onto a 2D screen. Shouldn't it be possible to project a 4D representation of an object(maybe a hypercube?), into a 3D voxel, or model, or something like that, then render that in 2D?

By that theory, a 2D image could be displayed as a 1D.. what?

and imho 4D object is just like a 3D one, but animated

[Iyad]

Since it's possible to project a 3D representation of an object, onto a 2D screen. [...]

It is only possible to draw elements that are 1 Dimension lower than our actual dimension. You said it, you only "project" and a projection is in 2D (or 1D). You can represent what is 4D dimension but you can never access it. You also represent what is a 3D dimension, but you could never draw something in 3D (you can only if you can create matter).

Dont think your 3D engine draw 3D, the rastizer actually calculate everything and draw a 2D projection.

[ent1ty]

It is only possible to draw elements that are 1 Dimension lower than our actual dimension. You said it, you only "project" and a projection is in 2D (or 1D).

But how are you going to draw a rectangle in 1D? At first i thought that maybe just a line that is <rectangles circumference> long, but line is also 2D, isn't it?

[Iyad]

There cant be rectangle in 1D, you can only draw lines in 1D and in only 1 relatif axis (positif and negatif). So you can only draw 1 line from right to left or from left to right if you are taking the X axis.

0D is no axis, so only 1 point can be drawn. 1D means that drawing only support 1 axis (and 2 directions, right and left). 2D is 2 axis (X and Y and 4 directions). 3D is 3 axis (X,Y,Z and 6 directions). 4D is 4 axis (X,Y,Z,W and 8 directions).

To summary, each dimension is an interpolation of the its dimension-1. So 4D is a serie of 3D aligned in 1 axis, As 3D is a serie of 2D aligned in 1 axis.

[ent1ty]

Thanks for clarification

To summary, each dimension is an interpolation of the its dimension-1. So 4D is a serie of 3D aligned in 1 axis, As 3D is a serie of 2D aligned in 1 axis.

Yes, that i realized a while ago when i was thinking about this

but imho 0D doesn't exist.. how do you want to draw 1D in 0D.. there's no way. Two lines, one long 10, second 20 units, would look exactly same in 0D.
There can't exist anything in 'nothing dimension'.

[nathanf534]

[ent1ty]

oh, snap

[Iyad]

A point (no space) has absolutly no dimension. It has no direction to move on, nor space around it and it haves a volume of 0. Its mostly representative, I dont explicitly means that it exists, its mostly theorical. I just red this, take a look at it :

http://en.wikipedia.org/wiki/Dimension

EDIT:

btw : nathanf534, i have no Ph.D in astrophysics lol . if ive said something wrong, im srry, i will fix it.

[stefbuet]

The polynomial 0 dimension is : -infiny
But I can draw 0 on a peace of paper.
I converted a -infiny to 2 dimention representation

[nathanf534]

nathanf534, i have no Ph.D in astrophysics lol . if ive said something wrong, im srry, i will fix it.

That wasn't directed at you, just how everyone is arguing over this. I think its funny

[3DModelerMan]

Yeah, I meant 4 spatial dimensions. Speaking of 4 spatial dimensions did you know that the pythagorean theorem works to get the diagonal of a hypercube if you just add extra terms?