Quaternions

So are you saying, " what's a quaternion " ?

Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions. This avoids the problem of "gimbal-lock" and allows for the implementation of smooth and continuous rotation.

In effect, they may be considered to add a additional rotation angle to spherical coordinates ie. Longitude, Latitude and Rotation angles.

A Quaternion is defined using four floating point values |x y z w|. These are calculated from the combination of the three coordinates of the rotation axis and the rotation angle.

Simple, isn't it ?

If not : Link 1 Link 2

U_P

Yes, quaternions are used to decrease the computational mathematics required in attitude determination on the ISS.

I was the author of the system brief that is used on console by the ADCO's for the program.

It has surprised, since I have gone back out into industry that quaternions are virtually unknown and have yet to "take off" in areas they could truly make an impact in. For instance, I have not looked into whether NC programming logic has incorporated quaternions yet, but if they haven't I won't be surprised. And if they haven't, they are remiss!

Not only do quaternions result in significantly decreased mathematical operations over using Cosine Matrices for the same calculations, BUT they have no singularities as the alternative Euler angles do!

I was pleasantly surprised to see your thread title.

Originally posted by Valhall

I was pleasantly surprised to see your thread title

.

You're lucky Valhall, I've a strong sense of humour.

Also, I've many hobbies. I don't like ONLY Hunting down commies. I like also physics and maths.

Anyway, thank you.

P.S. To those interested in this topic: The four elements of a quaternion are as follows:

the first is the scalar magnitude of the rotation angle vector (cos (mu/2)
and the next three are the unit vectors of the rotation angle w(x)sin(mu/2), w(y)sin(mu/2) and w(z)sin(mu/2) where mu is the angle of rotation and w is the axis of rotation.

p.s.s. Hope you didn't take my comment of being pleasantly surprised as being that YOU posted this. I meant I was pleasantly surprised to see quaternions mentioned at all! LOL!



[Edited on 7-11-2003 by Valhall]

Ok Valhall. I've read AND understood what were the quaternions.

First I did in English then in French , just to be sure that I wasn't doing an understanding error. You know what ? I wasn't doing an error.

[Edited on 7-11-2003 by ultra_phoenix]

Yes, I appreciated your physical analogy to the singularities that can come up in these calculations when using Euler angles by referring to them as "gimbal lock". That is a nice way of illustrating the problem.

Like...oh my gersh! My calculations just went into gimbal lock! LOL!

But not anymore, somehow there is this abstract reasoning issue now,everything is abstracted through reason and makes less sense after I...............
POOF.

Originally posted by Valhall
I was the author of the system brief that is used on console by the ADCO's for the program.

WAY cool!!! (I sound so fannish, but I do think that's wonderful!) However, I do admit that my brain hurts trying to go through all that. I'm not terribly mathematical.

Originally posted by Byrd

Originally posted by Valhall
I was the author of the system brief that is used on console by the ADCO's for the program.

WAY cool!!! (I sound so fannish, but I do think that's wonderful!) However, I do admit that my brain hurts trying to go through all that. I'm not terribly mathematical.

I want to build my own little flying saucer. I think quaternions can be very usefull for this job. ( I'll let you know if it fly or not )

Gimbal Lock is a problem encountered in 3D animation too. I know of at least one program that uses quaternions (Alias Maya) to calculate rotation values. And seeing how Autodesk (3D Studio Max, Autocad) recently aquired Alias (Maya, MotionBuilder, Studio Tools), they're bound to be everywhere in those design tools soon, if not already.

Thanks for putting that topic list up, Valhall, very handy. It's how I found this thread

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[edit on 9-11-2005 by fingapointa]