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Vicker 2013년 1월 31일 오후 8시 32분
What is the sixth degree of freedom?
The description of this game describes it as having six degrees of freedom. The physicist and chemist in me are sceptical.

A rigid object moving in three dimensions has five degrees of freedom:
Three translational degrees of freedom (i.e. forwards/backwards, left/right, up/down)
Two rotational degrees of freedom (e.g. pitch and roll)

The third axis of rotation is not a degree of freedom. For example, any rotation of yaw can be achieved instead by a combination of pitching and rolling. If you want to yaw by 45deg, you can instead roll right 90deg, pitch up 45deg, and then roll left 90deg. Similarly, a rotation of pitch can be achieved by a combination of yaw and roll, or a rotation of roll can be achieved by a combination of pitch and yaw. The definition of a degree of freedom necessitates that a transformation of that degree of freedom cannot be performed by a combination of the other degrees of freedom. This means that there are only two rotational degrees of freedom, despite there being three axes of rotation.

There are three axes of rotation. There are only two rotational degrees of freedom.

So what is the sixth degree of freedom?
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TUKAN SAM [2098] 2013년 1월 31일 오후 8시 44분 
Wow. I can't tell if this is a troll post or not.... If it isn't, well then it really isn't all that difficult to understand what they meant.

1. Forward
2. Backward
3. Left strafe
4. Right strafe
5. Upward
6. Downward
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ColdEquation  [개발자] 2013년 1월 31일 오후 8시 53분 
Six degrees of freedom is a common term in physics, engineering, and control systems:

It more refers to the flexibility of movement than the possible states of position/rotation. In the game, we give the usual WASD for planar horizontal movement, Space/Shift for vertical, mouse X and Y for yaw and pitch, and QE for roll. Though you never actually need to roll to look somewhere specifically, it makes motion much smoother when performing vertical U-turns and such. In real life situations, an airplane that could not move freely over all rotational axes would put quite a bit of stress on its passengers and crew.
Vicker 2013년 2월 1일 오전 1시 01분 
You know, I think I got my definition of a degree of freedom mixed up with some other random thing. You're right, ColdEquation. A three dimensional rigid body has six degrees of freedom.

I think my weird misconcieved ramble stemmed from an explanation of why ColdEquation is correct even if you use something called Euler angles. My example of rotate right 90deg, pitch up 45deg, and then rotate left 90deg required three steps. The fact that it required three steps means that you have three rotational degrees of freedom, even if you try to describe your system with two Euler angles.

Silly me.
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komninosm 2013년 2월 1일 오전 1시 07분 
The OP is not a Troll, he makes a somewhat valid point.
However try not to think of movement, but of positioning.
What I mean is how many variables are needed to describe an object's (current) position and orientation.
You need x,y,z for position and you need q,p,r for where it's pointing and how.

But even for what he says he's not totally correct. Degrees of freedom are "awarded" for motion "ability" not for ending position capabilities. If you had a robotic arm that could not do roll, but it could still reach all orientations by combining pitch and yaw, it would still be missing 1 degree of freedom.
Freedom Hype-r 2013년 2월 1일 오전 5시 58분 
hey Vickers, this was actually a good topic you brought up. Another example: in your initial train of thought you could also loose 2 translationals and "half" of the left one, plus "half" of the two rotationals, thus you can get anywhere with just a Forward key for translation, a clocwise twist and an upward pitch. :D
Godeke 2013년 2월 1일 오전 7시 01분 
I took an online class in Artificial Intelligence and we had to consider motion of objects in the real world for simulations to control. There were huge forum wars denying the sixth degree of freedom (roll) because they were thinking about vectors (which have no "top" like a physical object like a vehicle).

After teacher intervention, engineering texts cited, and many thousands of bytes wasted on the Internet there remained a group of "sixth degree deniers". I guess I'm thankful for having played Elite all those years ago, since all you have there is Forward, Roll and Pitch, no Yaw or Slide. It made it obvious that you had six degrees of freedom in orientation and location even you only had three degrees of input freedom.
@xi@g@me 2013년 2월 2일 오전 9시 56분 
Yes, you can indeed yaw by using your pitch & rool, but I think that if you have the ability to directly perform the yaw it would make the game easier ;)

(and thus, using 2 degrees of rotation and 1 degree of translation, if I follow your theory, you can place anywhere you want with any rotation you want. In that cas, the two other translation degrees are not bound to be ?)
night 2013년 2월 2일 오전 11시 06분 
On a side note, I don't think this kinda thread would of been in the Miner Wars forum, so maybe I'll check this game out more...
BLTRunner 2013년 2월 2일 오전 11시 08분 
@night YAY! I should be posting a video about the games controls and weapon uses later today. Thanks for considering us!
Freedom Hype-r 2013년 2월 2일 오후 12시 32분 
one thing is certain, that there's no seventh axis/degree that would help you in any slightest way, at least in our daily 3D euclidean sub-lightspeed universe, hehe
SCE_CoconutCat 2013년 2월 2일 오후 1시 21분 
mordock son of eva slayer of teramack
Vicker 2013년 2월 4일 오후 10시 22분 
Well, my later amendment was that there are indeed three rotational degrees of freedom, due to the fact that constructing a yaw out of just pitch and roll would require three steps and not just two.

As Godeke said, if you think of it as a vector, a 3d solid object does not just have a vector indicating its direction its front is pointing; a third angle is required to specify which way the top is pointing.
@xi@g@me 2013년 2월 5일 오전 4시 15분 
@Vicker In video game programming, we need to konw the front and the top vector of an object (and so we can compute the right vector and then the transformation matrix) to be able to draw it with the correct roll. So what you're saying have great sense :)
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Nemesis 2013년 2월 5일 오전 5시 30분 
@xi@g@me 2013년 2월 5일 오전 10시 54분 
WASD for front & side, mouse for yaw & pitch, QE for roll and shift/space for down & up.

That makes 6 ^^
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