I need to learn what quaternions are

[enigma]

Hi all,

For a project, I need to learn what quaternions are, and how they are used and manipulated. All I've had in my classes on the subject is: "They are another way of using angles to keep track of orientation, but we won't be covering them here." Same in all my textbooks - they're mentioned in passing, but not covered.

Does anyone know of any good textbooks or online sites which cover the topic?

Thanks

 

[synergy]

Good luck.
Actually, the basics aren't that hard (let me blow the cobwebs off my brain for a second).
Okay, quaternions are similar to imaginaries, BUT...
Instead of just i, you now have i,j,and k.
I think... i*j=k, j*k=i, i*k=-j (or something like that)
but the square of any of them is -1 (again, I'm almost certain, I think).
Anyway, if you look at how i*j=k, it's like multiplying vectors, since each is one unit along a different axis, the product is one unit, and you have a sort of "right-hand rule" for the orientation of the product (point the fingers of your right hand along the positive direction of one axis and curl them in the positive direction of the other axis then your thumb points in the (pos. or neg.) direction of the product). Something like that. That's probably enough to give some understanding, you'll have to find a place to verify the rules I gave, though. You could probably draw a graph and figure them out yourself. Hope this helped.
Aaron
p.s. Notice i*k=-j but k*i=j i.e. they are noncommutative!

 

[enigma]

Originally posted by synergy
Good luck.
Actually, the basics aren't that hard

Thanks for the primer. Unfortunately, I'm going to need to find something a bit more in-depth than that. I will be using them for orientation control on a robot with 6 degrees of freedom for motion.

 

[chroot]

The quaternions are just another way to represent rotations in 3-space -- just like Euler angles, or the axis/angle representation. The quaternions are advantageous mainly because they don't require matrix multiplication, and because they don't suffer from gimbal lock.

Graphics programmers use them somewhat frequently, so you might want to check out websites like gamasutra.com for practical tutorials.

Do sites like mathworld not provide enough information for you? Or is it too hard to digest? Given enough incentive, I could probably write up a reasonably accessible treatise on the quaternions for you.

- Warren

 

[enigma]

Thanks Warren!

That site works - I didn't know about it. I'll check the references listed at the page bottom as well.

 

[grady]

I have this book, it is very good. I think it is just what you need.

 

[chroot]

I don't know why I didn't think of this earlier, but I really should've linked you to my favorite site, the Dr. Math archive:

http://www.mathforum.org/library/drmath/view/51464.html
http://www.mathforum.org/library/drmath/view/51994.html

I am one of the Math Doctors there, and (for shame) I forgot to tell you about my own site!

- Warren