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03 December 2009 @ 08:57 am
2d to 3d  
I was looking at the stripes on a barber shop light from the bus the other day, vaguely remembering how the red stripe has something archaic to do with surgery.

I started wrapping thick straight lines around and realized they would never reconnect on the back side as they were. In my mind, I slid the straight line in a way that allowed it to wrap around the 3d cylinder and connect all the way around.

In what dimension was I sliding that line? "sliding" isn't probably the perfect word. basically instead of just smacking down the 2d object in mass, I was laying down the 2d object one tiny segment at a time and kind of forcing the 2d object boundary's angle to change so I could accomplish the task.

Is there a name for doing something like that?

Probably I need a white board, but I thought I'd ask on the off chance that someone is able to piece together my poorly worded description and voila! answers.

It struck me that there's something interesting that changes between a 2D and a 3D interface - i.e. we can take advantage of the 3D space and dimension to fundamentally change how the 2D object interacts.
 
 
 
yvetteserpentmoon on December 4th, 2009 02:20 am (UTC)
Stop it. You're going to make the world collapse.


Actually, it sounds like you have an Escher barber pole in your head.
Kburgunder on December 4th, 2009 05:06 am (UTC)
Re: Stop it. You're going to make the world collapse.
O:>
Beththepresident on December 4th, 2009 06:39 am (UTC)
my friend tried to explain 4th dimensional euclidean geometry to me but my head asploded. :-(
Varnvarn_ix on December 4th, 2009 07:45 am (UTC)
If I understand this process correctly, you were wrapping an infinite band (finite nonzero width, infinite length) around an infinite cylinder, so that all of the cylinder's surface was covered? (Similar to how you would wrap a longsword hilt with a leather strip.)

This is possible. The surface of an infinite cylinder is a once-non-simply connected manifold without a boundary, locally everywhere homeomorphic ("equivalent") to a plane. In essence, the answer to your question 'in what dimension was I sliding that line' is definitely 2.

Perhaps what is confusing is the fact that the 2-dimensional object (cylinder surface) is nontrivially embedded in a 3-d space, that is, while it's locally equivalent to a plane, globally they are different. On a cylinder surface you can inscribe a circle that goes all the way around the circumference: such a circle can never be contracted to a point while staying on the cylinder surface. On a plane, every circle can be contracted into a point while staying on the plane.

The name I'd say is 'applying texture' or 'texturizing'. This is essentially what the graphic card does to the surfaces of 3-d objects all the time you're playing a 3-d game.