SFH2
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| Joined: 26 Jul 2011 |
| Total Posts: 103 |
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GoldenUrg
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| Joined: 23 Aug 2009 |
| Total Posts: 6428 |
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| 18 Sep 2011 11:09 PM |
| Yes, they have 4 axes of rotation. |
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NXTBoy
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| Joined: 25 Aug 2008 |
| Total Posts: 4533 |
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| 19 Sep 2011 01:42 AM |
| And by axes, you mean planes. |
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booing
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| Joined: 04 May 2009 |
| Total Posts: 6594 |
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thegenius
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| Joined: 03 Oct 2008 |
| Total Posts: 3838 |
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| 19 Sep 2011 03:19 PM |
Wait...
Rotating...
ON A PLANE?!
*headasplode* |
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| 19 Sep 2011 03:20 PM |
| Thegenius stole what I was gonna say! |
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| 19 Sep 2011 03:21 PM |
^
-Like an __AWESOME__ boss |
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GoldenUrg
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| Joined: 23 Aug 2009 |
| Total Posts: 6428 |
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| 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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| 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
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| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
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| 19 Sep 2011 04:07 PM |
> time
no
pure, undiluted no |
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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
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| Joined: 08 Jan 2009 |
| Total Posts: 41681 |
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| 19 Sep 2011 04:22 PM |
| where is this comic so that i may burn it |
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| 19 Sep 2011 04:25 PM |
Internet.
-The naked old man who is possibly chocolate... |
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| 19 Sep 2011 04:25 PM |
| We're talking about spacial dimensions noob. |
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EMAN381
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| Joined: 27 Nov 2007 |
| Total Posts: 4300 |
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| 19 Sep 2011 04:27 PM |
@Arceus,
What a great way to put that. :P |
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EMAN381
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| Joined: 27 Nov 2007 |
| Total Posts: 4300 |
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thegenius
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| Joined: 03 Oct 2008 |
| Total Posts: 3838 |
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| 19 Sep 2011 04:36 PM |
'E 'AS TEH POWER!
'E-MAN
(Note: Math FTW) (Also, thegenius is insane.) |
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EMAN381
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| Joined: 27 Nov 2007 |
| Total Posts: 4300 |
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| 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
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| Joined: 25 Aug 2008 |
| Total Posts: 4533 |
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| 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
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| Joined: 23 Aug 2009 |
| Total Posts: 6428 |
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| 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
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| Joined: 25 Aug 2008 |
| Total Posts: 4533 |
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| 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
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| Joined: 26 Jan 2008 |
| Total Posts: 4362 |
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| 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
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| Joined: 25 Aug 2008 |
| Total Posts: 4533 |
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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
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| Joined: 26 Jan 2008 |
| Total Posts: 4362 |
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| 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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