Texturing for 3D CI

Higher-dimensional geometry (previously "Polyshapes").

Texturing for 3D CI

Postby Fariel » Tue Jan 27, 2004 5:34 pm

Hi folks.

One of my hobbies is making 3D computer images. Recently, I began to understand that mapping the surface of a 3D object into 2D was an exercise in some other dimension.

There are certain mapping problems that cannot be resolved without approximation. What I'm referring to can best be described by referring to a familiar mapped and textured object--the globe. All the maps you see of the "peeled" globe (interrupted projections) are approximations because the peeling itself (being rounded) must be stretched or compressed in places to lay flat in 2D.

I am usually dealing with planar maps of a spherical projection of a 3D body.

When everything is laid flat, you can see all the surfaces of the body at the same time. This reminded me of a painting I once saw of a table with all four legs visible. I think the painting was an exploration of that concept of stepping into another dimension. (Does anyone have links to paintings like that?)

It took me a while to be able to "see" the body in those projections, but now I can see it almost as well as in 3D space. Still lots of surprises though. Most of the times I guess "wrong" on the placement of a feature in that interrupted projection, it is because the map was skewed in order to make a curved surface lie flat.

How does this exercise fit into tetraspace theories?
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Postby Geosphere » Tue Jan 27, 2004 7:11 pm

It really doesn't.

It's simple architecture. Plan/Elevation/Profile can describe a 3d solid. The pictures of mars from the rovers are 360, but we see it incorrectly as a flat plane. Seeing something from all angles is simply compiling projections.

I work a lot in 3d images for marketing. Yeah, you train to look at a sheet of cardboard with lines on it and understand what the folded box will look like. Its the distortion of mapping just like you said. Not much more.
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Postby Fariel » Tue Jan 27, 2004 8:08 pm

OK.

But what about the mental exercise of viewing all sides at once; isn't that a 4D perception?
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Postby Geosphere » Tue Jan 27, 2004 9:05 pm

Not even remotely. That's a Draftsman perception.
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Postby Fariel » Tue Jan 27, 2004 10:35 pm

Okay then, explain this:

If you were in an actual place where you could see all sides at once, where would you be?
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Postby alkaline » Tue Jan 27, 2004 11:29 pm

In order to see all of the external and internal points of an object at the same time, you would have to view the object from at least one dimension higher. To conceptualize all of the internal and external points at once in your mind (as opposed to actually seeing them), you don't actually have to be in a higher dimension, you just have to be capable of visualizing such things. Thus, visualizing the view from the fourth dimension is possible for us, but not physically seeing the images that fourth dimension beings would see.
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Postby Geosphere » Wed Jan 28, 2004 1:08 am

To see all sides at once, you just need enough mirrors.
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unwrapped surfaces

Postby Fariel » Wed Jan 28, 2004 2:08 am

Geo wrote: . . . you just need enough mirrors.


:D

All right. I give.

Can 4D be mapped in a 3D projection, as we map 3D into 2D? And what gets thrown out?
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Postby Aale de Winkel » Wed Jan 28, 2004 11:51 am

A realm space mercator projection I gather;

It's just what kind of mapping on chooses.
the articles here show polar coordinates that maps IR[sup]4[/sup] into IR[sup]3[/sup] (θ variables).
just as the simular polar coordinate mapping one dimension lower.
see pe: 4-d coordinate system for the discussion I had with alkaline.
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Postby alkaline » Wed Jan 28, 2004 7:25 pm

I discovered a bunch of referrals from a forum at http://www.psychodogstudios.net/forums/ and discovered that Fariel posted a link to here from there. now i know just what you think of us: "I'm not that crazy. Or at least I'm not as crazy as the guys on that forum. " :-) The post: http://www.psychodogstudios.net/forums/viewtopic.php?p=32192&highlight=fourth+dimension#32192
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Postby RQ » Fri Jan 30, 2004 7:05 am

I thought that the way we see 3D is via the intensity of light (lux) which is inversely proportional to the square of the distance between the light source and the object that's being illuminated, which is actually seen or rather unseen as shadow.
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Postby alkaline » Fri Jan 30, 2004 6:16 pm

I was assuming that to see a 3d object from tetraspace, you'd have to shine tetronian light on it, so the light would dim with the inverse cube of the distance.
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Postby Geosphere » Fri Jan 30, 2004 8:11 pm

Distance measured tetronian or realmic?
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Postby alkaline » Sun Feb 01, 2004 10:42 pm

well this is tetronian light i'm talking about, so it would be tetronian distance of course.
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