Anybody have any idea how to convert between 4D and 3D points?? I already have something to convert 3D to 2D... once I can do that extra step I will have a perfectly-working 4D engine!!

(x,y,z) -> (x,y,z,time) :) you would have to set it up to draw things at set times ;)

Nope. Fourth dimension != time.

AAARGHHHH! NOT C!
Fourth dimension <> time

AARRGGHHH! NOT BASIC!

not("Fourth dimension".eq("time"))

AGGGH! Who cares?
4th dimension DOES NOT EQUAL time!
g33z.

AARRGGHHH! Not English!
(Can't think of alternative ...)

Le "fourth dimension" c'est pas "time" (I dunno, I'm only in my 3rd year of french)

Here's Spanish: la dimensión cuarta no iguala tiempo

hetay ourthay imensionday isway otnay imetay.

Just one question, what would be the purpose behind a 4D engine? I'm confused as to how a 4D program would be useful ...

No, the fourth dimension is NOT time. It hasn't even been proven that time is linear, so how could it be a dimension? any given dimesion can only be

positive, negative, or zero.

and no, 3D games are not 4D, or you would be able to move *back* in time in them, according to your theory.

anyway, here's a brief rundown on 4D geometry.

0D space is a point. It has no size.

In 1D space, the only figure you can have is a line, formed by taking a point and moving it along a dimension to another point. It has one edge, which is

1-dimensional, and 2 points, which are 0-dimensional 'faces'.

In 2D space, the 'generic' figure is a square - four line segments connected at right angles. You can form it by taking a line and moving it along a second

dimension. It has four zero-dimensional points, four one-dimensional edges, as well as a two-dimensional edge (a face).

In 3D space, the cube is the 'generic' figure. It is formed by taking a square and moving it along a third dimension. It has eight zero-dimensional points,

eight one-dimensional edges, six two-dimensional faces, and one three-dimensional face (the cube itself). Since the only way to represent a 3D object on a

flat surface is to project it from some angle, this is equivalent to saying that you are drawing the 2D shadow of a 3D object.
<end part 1>

Notice the pattern yet? In a generic figure in n-dimensional space, the number of edges equals the number of points, which equals 2^n, and there are 2*n

faces, with each face being a (n-1)D figure. Thus, in 4D space, a generic figure (which is commonly called the 'hypercube', or 'tesseract') has 16 points, 16

edges, and 8 faces. These faces, as can be expected, are (n-1)D, which means they are 3D. The eight faces of a hypercube are cubes themselves. To represent a

4D object, the only thing we can do is to draw the 2D shadow of the 3D shadow of the object, since we can't physically construct 4D objects.

The appearance of a 4D object can be quite confusing. Example #1:
http://www.cogsci.indiana.edu/ farg/harry/phy/4dmat09.gif
sorry about the big image.

The sphere in that picture is NOT changing size, or technically even shape. It is a 4D sphere, moving along the 4th dimension. You might call this the result

of 4-dimensional 'perspective', of a sort: when you watch someone pass by you on the street, they may appear to be shaped or even sized differently, but this

is only because of the 3-dimensional distance between the two of you. Similarly, a 4D object appears to change shape depending on your 4D distance from it.

The only problem is that when you watch it in 3D space, it seems almost undeniable that it *is* changing shape.
(note: if you visit the web site I got that image from, you'll notice they constantly refer to the 4th dimension as 'time'. however, they don't really mean

it *is* time. they simply used time as a way to introduce a fourth variable. it would be the same as using four embedded 'for' loops, say with variables

w,x,y, and z, to represent the position of a 4D object. time is simply a convenient way for mathematicians to take 3D snapshots of a 4D object as it moves

through 4D space.)
<end part 2>

Another way to visualize why it seems to change shape is this:

When a line intersects with 0D space - a point - the entire intersection is that single point.
When a plane intersects with 1D space - a line - the entire intersection is that line.
When a cube intersects with 2D space - a plane, or square, or whatever - that intersection can be a square or a triangle (maybe something else, but it's 2:50

AM and I'm damn tired).
When a hypercube intersects with 3D space - any 3-dimensional object or area - it can be assumed that there are an immense number of 3D shapes - in most

cases, an infinite number - which its intersection can form. these shapes don't even have to follow the laws of what we consider reality. for example, a 4D

tube could intersect with 3D space at one end, and the opening of the tube could hang in midair. when you go to the other side of the hole - which may be

infinitely deep, or whatever you'd call the fourth dimension - there might not even *be* another side. it could just be empty air.

OK. I know I said this would be brief, but I'm rambling. The main points I'm trying to make:
1. time is *not* the fourth dimension
2. representing 4D objects on a 2D plane is possible, but it requires complex mathematical formulas
3. I'm tired

Hope this clears evertyhing up.

--lord_nightrose

P.S. For a better explanation than the one I've given, check out http://home.san.rr.com/ slawek/Tata/Math/4DGeom.html .

P.P.S. http://www.cs.mu.oz.au/ ~amb/4d/ has a huge library of 4D and ND related links. Check it out. There's java!! ooo!
<end part 3>

Eep. Those were all under the wrong post.

Anyway, the purpose of a 4D engine would be to model 4D objects. Duh. :-p

Nah. I just figured that, if I can write a 3D graphics engine, I should relatively easily be able to write a 4D one... but it's not turning out so simple after all.

Of course I realized that a 4D engine would be used to model 4D objects. I just wanted to know what are the practical applications of such an engine.
Your explanation is making my head spin ... I think I'll stay with 3D for now, thank you very much. :)

Funny, the response has been pretty much the same from everyone I've given that explanation to :-p

anyway, there aren't many practical applications I can name, but mathematicians don't really need practical applications... if one doesn't exist, they just make it up.

someone monitored water influx into a bay in the Gulf of Mexico using 4D graphing... of course, they decided to use time as the fourth dimension... grr...

someone wrote a credit card verification routine that somehow uses 4D matrices, but that's not really 4D graphics...

to quote some college chemistry class' web site:
"The four-dimensional variational data assimilation algorithm (4D-var) recently introduced in chemical data assimilation holds promise to exploit observations with beneficial impact for analyses of non observed species, which are chemically closely related to observed constituents."

I have no idea what that means.

Apparently they also can be used in quaternion frame fields and to plot 3D data as mountains on 4D terrain... and I have no idea what quaternion frame fields are.

so there aren't many practical applications that I could find; I just think it's fun to research.

I figured that there wouldn't be too many practical applications of a 4D engine. But of course one can always do it for the FUN of it. :P

holy crap, you typed a lot! Go to calcsoft.tk, go to forum, and look until Rendering 4D Engine (I'm reading that right now!) He typed a lot on that there too.

it was the same thing.

d'oh! You're kidding! It looks like there's more here (except for that image)

You scare me.

Wow, he typed three extremely long posts in about two minutes?!?!??!!? Wow...

He is talented! (if you scroll up, he says he copied+pasted)