<p>The length of the axis is irrelevant and so you can remove one degree of freedom.</p>

CC BY-SA 3.0
2016-10-05T14:25:28.713Z
2016-10-05T14:25:28.713Z
Simon F
<p>It is only 3 degrees of freedom (when talking about a rotation around the origin).</p>

<p>An arbitrary axis can be specified by 1 3D vector however the length doesn't matter so it only takes 2 degrees of freedom. Then you add the rotation angle to it and you have 3 degrees of freedom.</p>

<p>If you mean a rotation around a arbitrary point other than the origin then that point takes up 3 additional degrees of freedom for a total of 6.</p>

CC BY-SA 3.0
2016-10-05T16:02:44.307Z
2016-10-06T11:50:11.057Z
2016-10-06T11:50:11.057Z
ratchet freak
<p>I have been trying to figure out why does rotation about an arbitrary axis have degree of freedom 6. I know that it takes two points, each take 3 values to determine in a 3-D space. But what about the rotation angle? Wouldn't that make the degree of freedom increase by 1 to get 7?</p>

<opengl>
Why does rotation about an arbitrary axis have degree of freedom 6
Louis Kuang
# Why does rotation about an arbitrary axis have degree of freedom 6

(Asked by: username_0 on 2016-10-05)

I have been trying to figure out why does rotation about an arbitrary axis have degree of freedom 6. I know that it takes two points, each take 3 values to determine in a 3-D space. But what about the rotation angle? Wouldn't that make the degree of freedom increase by 1 to get 7?

**Tags:** opengl


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## 2 answers

### Answer by username_1 on 2016-10-05. Score: 4

The length of the axis is irrelevant and so you can remove one degree of freedom.


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### Answer by username_2 on 2016-10-05. Score: 3

It is only 3 degrees of freedom (when talking about a rotation around the origin).

An arbitrary axis can be specified by 1 3D vector however the length doesn't matter so it only takes 2 degrees of freedom. Then you add the rotation angle to it and you have 3 degrees of freedom.

If you mean a rotation around a arbitrary point other than the origin then that point takes up 3 additional degrees of freedom for a total of 6.


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