Planetarion Forums

vampire_lestat · 21 Dec 2003, 11:04

aside from the obvious fact that they're four dimentional shapes, what are they? How are they represented in our three dimentional world (or on my monitor)?

Nodrog · 21 Dec 2003, 11:14

4d shapes are represented in 3d the same way 3d shapes are represented in 2d; either via projection or by cross section. Projection involves showing what the object looks like if you were to view it from one specific angle it in a space one dimension 'lower' than that which the object exists in. For instance, any 2d drawing youve ever seen of a cube is a 2d projection of a 3d object. A proper projection of a hypercube would have to be 3 dimensional. Cross sections show what youd get if you cut the n dimensional shape up into infinitely many n-1 dimensional segments. For instance, a 2d cross section of a sphere would be a series of circles which grew from smaller to larger, then back to smaller (because if you 'cut' a slice of a sphere and looked at it in 2 dimensions it would be a circle, and the circle would be larger the closer to the center you cut). A 2d cross section of a cube would be a series of squares. Likewise, a 3d cross-section of a hypersphere would be a series of spheres that went from smaller to larger then back to smaller, and a 3d cross section of a hypercube would be a series of equally sized cubes.

As to what it actually is, http://www.angelfire.com/ultra/nerds...imensions.html

edit: you cant meaningfully represent 4d shapes in 2d (eg on a computer screen) in a way understandable to humans - youd need 3d space to do it properly. Some people compromise on this and try and represent them using various animation gimmicks (search google for examples) with varying degrees of success. You can do it using 2-d projections viewed with 3-d glasses (those things you get as a kid which have 2 lenses, one red and one green, and you look at a picture made up of red and green lines etc) as well I think, though I've never experienced it

vampire_lestat · 21 Dec 2003, 11:21

W · 21 Dec 2003, 15:39

One of the demo's I coded had a regular 2d projection of a hypercube.

MrL_JaKiri · 21 Dec 2003, 15:47

Quote:

Originally Posted by W

One of the demo's I coded had a regular 2d projection of a hypercube.

You can't really make any sense of it though without it being in 3D. I could make a 1D projection of a 3D object, but it wouldn't mean much.

W · 21 Dec 2003, 16:01

Quote:

Originally Posted by MrL_JaKiri

You can't really make any sense of it though without it being in 3D. I could make a 1D projection of a 3D object, but it wouldn't mean much.

It was easilly recognized as a hypercube by most people.

It was wireframe of course, as a projection of a hypersolid hypercube would be identical to a projection of a solid cube.

MrL_JaKiri · 21 Dec 2003, 16:19

Quote:

Originally Posted by W

It was easilly recognized as a hypercube by most people.

That doesn't mean it's a worthwhile representation of a hypercube that will help people visualise it.

W · 21 Dec 2003, 16:22

Quote:

Originally Posted by MrL_JaKiri

That doesn't mean it's a worthwhile representation of a hypercube that will help people visualise it.

And that wasn't my goal. My goal was to make a "wow, cool" effect, so we would get votes in the competition, and not end up last place. It succeeded, we got second-to-last place scoring better than a badly drawn animation of a chicken eating a worm.

I still think it was tho. Obviously not quite as good as a real 3d projection, but close.

MrL_JaKiri · 21 Dec 2003, 16:22

Quote:

Originally Posted by W

And that wasn't my goal. My goal was to make a "wow, cool" effect, so we would get votes in the competition, and not end up last place. It succeeded, we got second-to-last place scoring better than a badly drawn animation of a chicken eating a worm.

Quote:

Originally Posted by W

I still think it was tho. Obviously not quite as good as a real 3d projection, but close.

We'd have to ask someone who deals with this kind of thing

djbass · 21 Dec 2003, 16:53

So far of the drawings I've seen it looks like a cube within a cube???

=[DJ Bass]=

W · 21 Dec 2003, 17:03

Quote:

Originally Posted by djbass

So far of the drawings I've seen it looks like a cube within a cube???

=[DJ Bass]=

Yes, that's how it tends to look, if you keep the distance->smaller projection thing. Of course, animation makes it alot easier to understand.

Nodrog · 21 Dec 2003, 17:34

Quote:

Originally Posted by W

It was easilly recognized as a hypercube by most people.

It was wireframe of course, as a projection of a hypersolid hypercube would be identical to a projection of a solid cube.

they recognise it because they know what its meant to be. If I drew a picture of a tree that looked almost nothing like a tree, the fact that people who had seen trees could recognize it once I'd told them what it was meant to be wouldnt mean that the picture would give someone who had never seen a tree before any information regarding what a tree looked like.

queball · 21 Dec 2003, 22:01

Quote:

Originally Posted by MrL_JaKiri

You can't really make any sense of it though without it being in 3D. I could make a 1D projection of a 3D object, but it wouldn't mean much.

Code:

. .   . .     . .   . .

cheekybru · 22 Dec 2003, 03:03

This thread gave me a headache :/

And the stupid music that plays on that geek site nearly woke everyone in my house up :/

Androme · 22 Dec 2003, 09:28

Quote:

Originally Posted by cheekybru

This thread gave me a headache :/

And the stupid music that plays on that geek site nearly woke everyone in my house up :/

same here. we should all team up like we did when we first came to Jolt''s and met 'them lot' and taken down the nerds this xmas

:smith: :smith: :smith: :smith: :smith: :smith: :smith:

JetLinus · 22 Dec 2003, 16:52

@W: Could I have a look at that demo of yours plz?

vampire_lestat · 22 Dec 2003, 17:01

mmmm, theme hospital music. The mouse thing is cool tho imo.

W · 22 Dec 2003, 18:49

Quote:

Originally Posted by JetLinus

@W: Could I have a look at that demo of yours plz?

It's long since been lost, something I regret deeply. It was produced for the pc demo competition for The Gathering '95, if you're ever able to dig up someone who has an archive of such stuff. For a long while I had it save on a floppy (and even that was an unfinnished version, last touches was made on the actual floppy used to deliver the entry to the competition, 5 minutes before deadline) and the floppy no longer lives.

Cyp · 22 Dec 2003, 18:51

Quote:

Originally Posted by W

..., as a projection of a hypersolid hypercube would be identical to a projection of a solid cube.

How do you orient a solid cube, so that its projection on a plane is an octagon?

W · 22 Dec 2003, 18:54

Quote:

Originally Posted by Cyp

How do you orient a solid cube, so that its projection on a plane is an octagon?

You don't? Are you saying you can with a hypercube? Explain please.

Cyp · 22 Dec 2003, 18:57

Quote:

Originally Posted by W

You don't? Are you saying you can with a hypercube? Explain please.

http://www.angelfire.com/ultra/nerds...imensions.html

Was working out how to describe it, then discovered there was already a picture of it in the second post...

W · 22 Dec 2003, 19:03

Quote:

Originally Posted by Cyp

http://www.angelfire.com/ultra/nerds...imensions.html

Was working out how to describe it, then discovered there was already a picture of it in the second post...

Well, that's not a HYPERSOLID or even solid hypercube.

But I think I see where I went wrong, the very solidness is what can't be projected, any projection of a hypersolid would have to be a projection of a 3D crosssection at best.