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r 4d objects rotatable?

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SFH2 is not online. SFH2
Joined: 26 Jul 2011
Total Posts: 103
18 Sep 2011 11:06 PM
lol idk
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GoldenUrg is not online. GoldenUrg
Joined: 23 Aug 2009
Total Posts: 6428
18 Sep 2011 11:09 PM
Yes, they have 4 axes of rotation.
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NXTBoy is not online. NXTBoy
Joined: 25 Aug 2008
Total Posts: 4533
19 Sep 2011 01:42 AM
And by axes, you mean planes.
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booing is not online. booing
Joined: 04 May 2009
Total Posts: 6594
19 Sep 2011 07:13 AM
but das imposinbur
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thegenius is not online. thegenius
Joined: 03 Oct 2008
Total Posts: 3838
19 Sep 2011 03:19 PM
Wait...

Rotating...

ON A PLANE?!

*headasplode*
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
Total Posts: 30553
19 Sep 2011 03:20 PM
Thegenius stole what I was gonna say!
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ElectricBlaze is not online. ElectricBlaze
Joined: 18 Jul 2011
Total Posts: 22930
19 Sep 2011 03:21 PM
^


-Like an __AWESOME__ boss
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GoldenUrg is not online. GoldenUrg
Joined: 23 Aug 2009
Total Posts: 6428
19 Sep 2011 03:28 PM
If you wanted a 2D rotation perhaps, but there are more than 4 planes.

You could use a 3D rotation matrix about each axis.
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Danster5oo is not online. Danster5oo
Joined: 27 Aug 2010
Total Posts: 10003
19 Sep 2011 03:32 PM
Four axes: x, y, z, and time.

-The naked old man who is possibly chocolate...
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sdfgw is not online. sdfgw
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Joined: 08 Jan 2009
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19 Sep 2011 04:07 PM
> time

no

pure, undiluted no
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Danster5oo is not online. Danster5oo
Joined: 27 Aug 2010
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19 Sep 2011 04:08 PM
It was a joke, i got that from a comic.

-The naked old man who is possibly chocolate...
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sdfgw is not online. sdfgw
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Joined: 08 Jan 2009
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19 Sep 2011 04:22 PM
where is this comic so that i may burn it
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Danster5oo is not online. Danster5oo
Joined: 27 Aug 2010
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19 Sep 2011 04:25 PM
Internet.

-The naked old man who is possibly chocolate...
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
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19 Sep 2011 04:25 PM
We're talking about spacial dimensions noob.
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EMAN381 is not online. EMAN381
Joined: 27 Nov 2007
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19 Sep 2011 04:27 PM
@Arceus,

What a great way to put that. :P
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
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19 Sep 2011 04:30 PM
And who are you?
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EMAN381 is not online. EMAN381
Joined: 27 Nov 2007
Total Posts: 4300
19 Sep 2011 04:32 PM
I am E MAN.
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thegenius is not online. thegenius
Joined: 03 Oct 2008
Total Posts: 3838
19 Sep 2011 04:36 PM
'E 'AS TEH POWER!

'E-MAN

(Note: Math FTW) (Also, thegenius is insane.)
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EMAN381 is not online. EMAN381
Joined: 27 Nov 2007
Total Posts: 4300
19 Sep 2011 04:38 PM
I know it's should be spelled E-MAN,

but it relates to some blonde superhero in a comic which I don't feel like relating to.
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NXTBoy is not online. NXTBoy
Joined: 25 Aug 2008
Total Posts: 4533
19 Sep 2011 04:39 PM
@GoldenUrg: Not sure you understand:

 * In 2D, you rotate around a point (0D)
 * In 3D, you rotate around a line (1D)
 * So in 4D, you rotate around a plane (2D)

And so on. The dimensionality of the object you rotate around is two fewer than the dimensionality of the coordinate space.
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GoldenUrg is not online. GoldenUrg
Joined: 23 Aug 2009
Total Posts: 6428
19 Sep 2011 05:56 PM
While that's certainly a valid way to do things, but I'm not sure it's adequate.
In 2D you can rotate around a single point and arrive at any orientation.
In 3D you need to rotate around 3 lines.
In 4D can you achieve any orientation by rotation around 6 planes?
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NXTBoy is not online. NXTBoy
Joined: 25 Aug 2008
Total Posts: 4533
20 Sep 2011 02:07 AM
> In 3D you need to rotate around 3 lines.

No you don't. All rotations can be achieved by a single rotation around a single line. I can't prove it to you, but I know it to be true. That's why there's `CFrame.fromAxisAngle`.
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cymru72 is not online. cymru72
Joined: 26 Jan 2008
Total Posts: 4362
20 Sep 2011 08:22 AM
NXTboy wins. If i remember correctly, a 4d object has 4 rotations x, y, z and w?
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NXTBoy is not online. NXTBoy
Joined: 25 Aug 2008
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20 Sep 2011 11:17 AM
@cymru: Not really: A 4d space has 4 *axes*, defined as w, x, y, and z. The sentence "has n rotations" makes no sense.
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cymru72 is not online. cymru72
Joined: 26 Jan 2008
Total Posts: 4362
20 Sep 2011 12:45 PM
Meh, due to the fact that I was mid-lesson and posting from my phone my lack of a logical sentence should be excused.

So, to conclude..

A 4D object rotates on a stationary plane which remains stationary under rotation on any axis. Under rotation, the object rotates around the plane. Difficult to wrap your head around that? Good, this isn't something a 3D being should be able to visualize or understand easily.

Here's a simple analagy,
If you rotated a 2D object on a 3D axis, say the Z axis. A similar effect would occur as it does with 4D rotation. It would appear as if the object was being inversed or turned inside out.

A 4D object has 6 Principal Rotations,
- XW
- YZ
- YW
- XY
- XZ
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