Hypercube (4-D analog of a cube)

[UnConeD]

The line you pasted means:

printf("%f %f \n",x1,y1)

Echo the real numbers 'x1' and 'y1' in the format "%f %f \n" (\n is a linebreak) to the screen.

So it's only outputting 2 coordinates... I assume these are pre-transformed to a 2D projection then?

If you want I could whip up a quick Windows program to draw them through basic GDI commands (ugly but works).

Send it to steven at acko dot net (spam proof ).

(By the way, the book you're reading is that a physical or electronic book? In the second case I wouldn't mind getting a copy...)

[dirkdeftly]

No, it's not just outputting 2 coordinates, it's outputting the coordinates for the endpoints of every edge in the object.
And it's supposed to draw the lines...

And the book is a paperback by Clifford A. Pickover (do you suppose he's the same pickover as the one who created the pickover orbital? *looks it up*)

[dirkdeftly]

BTW, I figured out why my hypercube wasn't working right. I was rotating it in a cube of the radius sqrt(3), not sqrt(2). I feel safer now...

[Matt_W74656]

I'm sorry but i just cant get this thing to sork you make it sound so good though. Can plez when you get it to zip up post it here. It doesnt matter if we have to put it in are selves thanks.

[dirkdeftly]

Okiedokie...Matt, the zipped version is in the fourth or fifth post on this thread.

And this is my current application of the hypercube. I'm pretty sure this one is going in my pack.

[Nic01]

Just asking for permission to use yar hypercube...

[dirkdeftly]

Shoot, I forgot to tell everybody this:
DO NOT PUBLISH YOUR PRESET USING MY HYPERCUBE UNTIL THE FORWARD FLOW IS RELEASED ON WINAMP.COM!!!

Anywho, yeah Nic, you can use it

[Zevensoft]

Yada yada, anyone wanting to use me 4D sphere just include credit for me.

Also, if you increase res to 10000, but add n=1000 to the init line, you'll get some cool-looking curves. Use res=1000,n=10000 to be able to clearly see the spheres.

[sonic.blade]

one thing that should be mentioned is that
the concept of dimensioned is not limited
to distances is space.
so you can basicly consider the r, g and b-
values as dimensions.
if we leave our dimensions clamped between 0 and 1
(or -1 and 1(or-999999999999 and +99999999999
(or whatever finite intervall) we can split time
easily into x, y and z-movement eventually h, p and b-rotation
and so on
so u can easily construct a 12-dimensional object in screen-space

jm2c
sonic

[dirkdeftly]

I'm trying to decide whether that was actually a meaningful contribution or just a desperate attempt to sound cool.
The concept of dimensional geometry IS about spacial relationships. The color of an object is a property. It has only to do with it's material configuration. Therefore color is a unidimensional property. Therefore color is not a dimension in itself.
time has been theorized as a fourth spatial dimension, and our movement through it is relative to our movement in 3-space.
And what are h-, b-, and p- rotation? Also remember that a rotation is a perpetually changing movement; it has no constant direction.

And you kind of missed the point of this whole thread; that rotation in higher dimensions and translation between dimensions is extremely easy to program.

[UnConeD]

I'm not sure what you mean sonic.blade...

Of course a space doesn't need to have a spatial meaning... any vector can be used, wether it's a point, a colour, etc.

Maybe you meant that you can use colour to indicate the coordinate of a point in a higher dimension as well?

[Krash]

I know what sonic.blade means, though I'm not sure how well I'll go with explaining it - I haven't done maths of any real sort in years, and multi-dimensional stuff in even longer.

If we first of all think about a unit sphere. The sphere exists for values of x, y, and z between -1 and 1, and does not exist for all other values (outside the function's domain, as it were).
This is a simple concept to grasp, as we deal with three dimensions every day.

If you want to easily comprehend a 4th dimensional unit sphere, the best way is to arbitrarily assign some value to the 4th dimension. Most commonly, people assign time to the 4th dimension.

You can then imagine that at time t=0, a 4th dimensional unit sphere would look identical to a 3d unit sphere. But if you went back to t=-0.5 (keeping x, y and z at 1, for simplicity's sake), you would see a smaller sphere.
Why?
Well, if you think about a 3d sphere, a 2d cross-section taken at z=-0.5 is a smaller circle than at z=0. So for a 4d sphere, the "cross-section" at t=-0.5 will be a smaller sphere than that taken at t=0.

You can progress this across the entire domain of t (-1 to 1). If you remember that t is time, you can therefore imagine that 4d sphere would appear as nothing before t=-1, at which point it would become an infintesimal sphere. This sphere would grow until it reached unit dimensions at t=0, and would then shrink back to nothingness. Of course, this is just for visualising a 4d shape.

The elegance of this method means that you can assign practically any continuous property to a dimension. You can even use non-continuous properties, provided you limit the domain appropriately.

For example, you can set colour as an example. Colour is actually a value on an electromagnetic frequency spectrum. So if you assign colour to the 5th dimension, and set "red" to c=-1, and "blue" to c=1, with a smooth spectrum in between, you can imagine a 5th dimensional sphere.

This would be a growing/shrinking sphere, as for the 4th dimensional sphere, but the sphere would have an infinite number of spheres inside it, of differing colours. In the center of the 5-hypersphere would be two infintesimal spheres, one red, and one blue. The outside of the sphere when it was at it's maximum size and colour variation (x,y,z,t and c all equal 0) would be green. There would be a smooth gradient opf colour within the sphere, in BOTH directions (green->red and green->blue). Sort of like an everlasting gobstopper...

You can extend this however you like. Assign pitch, yaw and roll to dimensions - that brings us up to 8-d. Assign other properties - luminescence, transparency, roughness... brings us up to 11-d. You can even use non-visual properties (as these properties are simply there to help us understand the shape) such as volume, frequency of a generated noise, etc.

Maybe I've explained this poorly... I don't know... it's been too long.

- Krash

[sonic.blade]

thanx krash and unConeD
i really just wanted to give some imput to the topic and
it was´nt my intention to show off.
Atero: -I just ment the 2-dimensional representation of n-dimensional
objects (not just geometries)
-HPB-rotation means heading-pitch-banking its basicly just
another notation to prevent gimballockup
to explain a bit more scintific why i counsider those
things as (useable) dimensions i want to point out the sence of
distances in space (i hope the translation is OK)
a space is defined by it´s metrik and the only three needs
for a metrik (distance-funktion) d:XxX->R are:
1.) d(x,y)=0 <--> x=y
2.) d(x,y) = d(y,x)
3.) d(x,z)<= d(x,y)+d(y,z)
as far as i know (please correct me if i´m wrong)
a n-dimensional metrik space can be easily constructed
as space is (x1,x2,x3,...,xn) and
metrix is d^n(x^n,y^n)=d(x1,y1)+d(x2,y2)+...+d(xn,yn)
when all properties (x1,x2...xn) are independent
so i consider every property that can be represented as a Real-Number
as a valid dimension.
hope it makes sence
sonic

[dirkdeftly]

I think I'd trust you more if you would spell "meant," "metric ~ics," and "function" correctly.
But in any case, no, you did not make sense.

Krash: Again, that was kind of the point of this thread...

[sonic.blade]

sorry for my bad english, i do all the math-stuff
at the university in german.
i wasn´t supposed to start and endless thread about math
over here i just wanted to give some input.
sonic

[n-D being]

Going back up to zevensoft's hypersphere, *******ns can be represented (approximately) by changing the first three lines of code to
x=cos(i*pi*res)*sin(i*pi*res*res)*sin(i*pi);
y=cos(i*pi*res*res)*sin(i*pi);
z=sin(i*pi*res)*sin(i*pi*res*res)*sin(i*pi);

Layering this scope on top of his original gives a much clearer view of the 4D surface shape.

David

[dirkdeftly]

EEEEEEEAAAAAAARGH

WHY ON EARTH DID YOU REVIVE THIS

IT WAS DAMN NEAR A YEAR OLD!!!

/me sobs uncontrollably

[BigBob]

I can not see Zensoft's Hypersphere, am I suppose to do something beside copy and paste?

[mikm]

not if its is a digital clock

you should copy each part into the correct 'section' of the superscope and make sure you have it set to lines, not dots (or vice versa)

[dirkdeftly]

somebody whack this thread >_<

[BigBob]

I got it now!

[BigBob]

Would it be possible to make any object in the forth demension, like a cylinder or a rectangle?

[mikm]

use the edit button!!!

well a rectangle is obviously very easy. take the hypercube code and stretch it along the axes. a hypercylinder is harder, although possible (look at the 3d sphere code and play w/ that).

basically, 4d works more or less like 3d, except you have 4 axes to work with.

so, you would be typing w1=...;y1=...;z1=...;x1=...; then use the rest of the engine to convert it to 2d.

i second atero's request for a lock

[sidd]

weell.. if you looking at basic shapes like rectangles etc. It can be a bit confusing. By definition, a rectangle rectangular prism is a shape that has at least one set of sides a different size. So you have to work out how 'long' you 4th dimention is going to be. Same deal with cylinders, only evern more complicated, as a cylinder is definable only as a 3d object, something like (sqrt(x*x+y*y)*z). To put it in 4d you have to really use your imagination.

For example a 4d cylender could be like an infinate 'shaft' of spheres heading off along the 4th dimention. Or and infinate series of tunnels heading off in parrallel to the first tunnel. Although these descriptions are using 3d terms, so you have to try to imagine it like that in 4d.

[Zevensoft]

Well siddhartha, the best way to think of it is that a 3D cylinder is an 'Extruded Circle', therefor the 3D version of circle is sphere, that makes the 4D cylinder an 'Extruded Sphere'.

[sidd]

nice one..
the problem is obviously that we are used to thinking in terms of 3d geometry. but when in gets to 4d, its hard to imagin what properties the fourth dimention should take on. Unless you are talking about figures that have equal properties on all axes (like cubes and spheres) you have to make up the 4th axis from what seems to be the logical way.

[Wiser87]

Help... I think my head's gonna explode...

[mikm]

going off of what Zvensoft said:

you start with a point- the first dimension. You choose an arbitrary direction and translate that point and connect them with a line. You then take those two points and extend them in another arbitrary direction and connect them with a line. This is 2D. Take those four points and extend them in another arbitrary dimension, and connect them with a line. This is the third dimension. Now you can take those eight points and extend them in an arbitrary dimension, connecting them with lines. This is the 4th dimension. You can continue doing this forever.

Try drawing this (you need a pencil and a lot of room)

[dirkdeftly]

okay, what you all need to do is shut the fuck up, read the annotated flatland, then flatterland, and go away >_<

[Wiser87]

Originally posted by Atero
okay, what you all need to do is shut the fuck up, read the annotated flatland, then flatterland, and go away >_<

Hehe... I have flatland. Quite interesting.

[WHCode RED]

2 days isnt old right? .... after reading some of these posts I am having a hard time recognizing sentences... especially...

Originally posted by UnConeD
(By the way, the book you're reading is that a physical or electronic book? In the second case I wouldn't mind getting a copy...)

It took me 3 re-reads to understand "physical or electronic book". Im.. so ... disoriented.

*electronic buzzing coming from head*

[dirkdeftly]

but one year is. and it was almost dead again. and you revived it, again. fuckers >_<

[mikm]

notice the person who revived it never came back.

somebody lock this.

[WHCode RED]

almost dead??? maybe, but the AVS forums are going so slow it was the third thread from the top

[mikm]

just STFU and stop posting in this thread. there is no point in keeping this alive any longer. i will banish the next person who posts here (unless it is a mod locking it) to hell ( i am a minister...a friend was bored during study hall and found a site that ordains you for free, so i got ordained just for kicks. i am not very religious or anything in fact, i don't believe much in religion)

[Rovastar]

Locked but please chill people