Moving a 2D object to a 3D world

[GraemeD]

Hi all,

I like working with computer graphics so I often work between 2D and 3D computer simulations.

For example let’s say you had a square in a XY coordinate system and you wanted to move it to an XYZ coordinate system. Placing it in directly would mean that when viewed along the Z direction the square won’t exist as there is no Z information.

This is fine for a computer simulation but how would this example translate to the “real world”? Could a 2D object appear in 3D space or would it be forced to have a Z dimension making it a cube?

Thanks for any input that you can provide and I hope I posted this question in the correct forum.

Thanks,

Graeme

 

[KLoux]

In the "real world" everything has three spatial dimensions... so no, your 2D square couldn't physically exist. The best you could do is to give it a very small depth (like a piece of paper, which has this depth compared to it's width and height).

Does this answer your question?

-Kerry

 

[GraemeD]

Does this answer your question?

Yes it does, thank you

So I can gain a better understanding do you have any information or links that explains this in more detail? I assume that in theory a 2D object cannot exist in a 3D world but what proof do we have. As I assume this is not something we can prove in a lab somewhere.

 

[KLoux]

What kind of proof are you looking for? An equation? Here's a quick attempt...

The foundation of this proof is that in order for any object to physically exist (so you can touch it or hold it in your hand) it must have mass.

In order for it to have mass, it must have density and volume.

The volume is an integral over three spatial dimensions. If anyone of those dimensions is zero, then you end up with and integral over two dimensions times the third dimension (zero). The volume of a 2D object is zero.

Zero volume times any density gives you zero mass.

Zero mass -> no object.

-Kerry