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View Full Version : 4d tesseract/polyhedra in Lightwave?



Carl333
11-03-2004, 03:26 PM
I am interested in creating 4d animations known as tesseracts or polyhedra. Does anyone have any idea how to do this in Lightwave? Here is a guy who figured out a way in 3dMax: HERE (http://www.cgtalk.com/showthread.php?t=121378)

Here is an example of what I'm talking about:
example (http://www.physics.hku.hk/~tboyce/ap/topics/tesseract/mpegs/tesseract2.gv.mpg)

Dodgy
11-03-2004, 05:23 PM
Very interesting ;)

illusory
11-03-2004, 06:05 PM
Yes, I'm doing that right now, as I read your post!

the animation you uploaded would be simple, considering the rendering is simple --the objects he made for it seem easy enough to model, and he isn't worrying about artifacts from intersecting geometry.

If that's what you are looking for, then it sounds like all that's left is to get information about the structure of the tesseract. You can find that many places. Here are some:

this one's interactive:

http://www.geocities.com/hjsmithh/WireFrame4/tesseract.html

this one is too, and shows you the process as it unfolds:

http://www.geom.uiuc.edu/docs/outreach/4-cube/

The visual idea to remember behind the tesseract is, briefly, something like this...
We are used to the idea of representing 3d space on a 2d surface (especially LW'ers)
Likewise 4 dimensions can be represented in three dimensions.
So, we can make that 3D model of 4D space, and represent THAT in 2d.
Of course it's all an illusion, but hey, we are accustomed to that.

There's a neat little book called "Projective Ornament" by Claude Bragdon, which is useful on this, and cheap (and kind of funny cause it was originally pub. in 1915...), I'm sure there are many others.

good luck,
NJ

Carl333
11-03-2004, 10:24 PM
Ok, cool. So, how are you actually going about doing it?

illusory
11-03-2004, 10:56 PM
That's a pretty general question, but maybe this is what you're asking...

I'm not working on an animation at this point, more a hypercube representation in 3d space.

Basically, the idea is to :

*create a cube,

*copy and paste it to TWO other layers -- do the movement in one of those layers "into the 4th dimension", and determine how far in the x, y and z directions you want to move the cube. There is more than one way to do this.(Use the stable cube as a background layer to visualize)

*next, work on extruding EACH face of the ORIGINAL cube SEPARATELY that same x, y and z distance

*cut and paste the cubes you moved into other layers into the 1st layer. (Your original cube from the 1st layer will be gone due to extruding all its faces.)
*this will create your 8 intersecting cubes that make up the hypercube, or tesseract (6 from the sides of the cube you extruded, plus the two others you pasted in which represent the non-distorted original and final position)

How you work with the model geometry after that is up to you! Needless to say, you will have duplicate and intersecting sides, and they will be one poly thick. Best to make them double-sided in order to see what 's going on.

I'd like to see what you come up with.

hope this helps,
NJ

Carl333
11-05-2004, 05:44 PM
Does anyone know if Lscript is powerful enough to do this?