Program to demonstrate rotation according to quaternion values

Question

On the Wolfram|Alpha website, I type quaternion(1,1,1,1) into the search field. Wolfram|Alpha shows a 3D transformation of the quaternion values representing the orientation of an object.

I have 9 more quaternion values other than quaternion(1,1,1,1).

I would like to ask how can I visualize the 3D transformation of the remaining 9 quaternion values, but without using the Wolfram|Alpha website and opening 9 more tabs and keying in the additional values into search fields.

I hope, rather, to write a Mathematica program to demonstrate rotation according to my 10 quaternion values. Every rotation will take 1 second, so in total the demonstration will take 10 seconds for all 10 rotations.

Can anyone help me how I can write the code for my proposed demonstration?

Do you want to do this with Wolfram|Alpha, the website, or with Mathematica, the desktop software? — Szabolcs, Aug 02 '15 at 11:20
You can convert the quaternion to a rotation matrix, then use GeometricTransformation and AffineTransform. — Szabolcs, Aug 02 '15 at 11:41
Maybe you can help me. I have quartenion code here. http://demonstrations.wolfram.com/downloadauthornb.cgi?name=FromQuaternionTo3DRotation — Jimmy Lee Jing-yi, Aug 02 '15 at 12:14
This may be helpful: http://mathematica.stackexchange.com/a/51487/1997 — ubpdqn, Aug 02 '15 at 23:26

hmilton · Answer 1 · 2015-08-02T20:17:05.173

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Kind of a part answer: It is quite easy to convert a quaternion to a Mathematica RotationMatrix. First normalize the quaternion. The first element will then be the cosine of half the rotation angle. The last 3 elements together describes the axis of rotation.

q = Normalize@{1, 1, 1, 1}
rm = RotationMatrix[2 ArcCos[First@q], Rest@q]

edited Aug 02 '15 at 20:17

answered Aug 02 '15 at 19:52

hmilton

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Program to demonstrate rotation according to quaternion values

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