possible alternative to quaternions?
Author
I've been reading about quaternions as used in game programming, and was wondering how the following type of 3D hypercomplex number might work out for representing rotations:
The numbers are of the form
A + By + Cz
There is a real-number axis, and two imaginary ones whose units are y and z. The multiplication rules are
y^2 = z
z^2 = -y
yz or zy = -1
Multiplying by the unit y rotates any number in one direction, touching both sides of every axis, and similarly the unit -z (note the minus) rotates in the other direction.
Would it be any use in games programming in 3D?
[Edited by - rrrr on August 19, 2006 11:58:37 AM]
z^2 = -y <=> z^3 = -yz <=> z^3 = 1 <=> z = 1 <=> y = -1
Therefore "A + By + Cz" simply diminishes to "A - B + C" and there's nothing complex about them.
Coming up with a quantity that can be used to represent 3d rotations is not a trivial task.
Oops, of course not. I replied in a rush and forgot the other 2 roots.
Yes, it could also be -(-1)^(1/3) and (-1)^(2/3)
I just wanted to point out that numbers with that properties are not imaginary units.
Yes, it could also be -(-1)^(1/3) and (-1)^(2/3)
I just wanted to point out that numbers with that properties are not imaginary units.
Author
Well, we would differ on that. Assuming I am right, I would be very interested to have game developers try out these numbers and see if perhaps they might be a contender for expressing rotations.
Anyone want to give it a "whirl"?
Anyone want to give it a "whirl"?
So what number would you use to represent a 90 degree rotation about the x-axis? The y-axis? The z-axis?
My algebra knowledge is not that solid, but doesn't this solution (z = 1, y = -1) mean it's isomorphic to (and thus no more interesting to represent rotations in than) the real numbers?
Author
Quote:Original post by SiCraneActually that's the sort of question I was hoping others more proficient in math than I am might want to tackle.
So what number would you use to represent a 90 degree rotation about the x-axis? The y-axis? The z-axis?
However, I'll see what I come up with. Am a bit busy at the moment though. Anyone else is welcome to try.
EDIT: Turns out to be very easy. Will post when I have time.
[Edited by - rrrr on August 19, 2006 5:56:25 PM]
I'm willing to give it a try,
i just got my quaternion camera set up, so no biggie to try it out. If i could just get my head straight on how to implement it.
EDIT: will this be able to rotate over all 3 axes?
Greetings.
[Edited by - Limitz on August 19, 2006 8:28:00 PM]
i just got my quaternion camera set up, so no biggie to try it out. If i could just get my head straight on how to implement it.
EDIT: will this be able to rotate over all 3 axes?
Greetings.
[Edited by - Limitz on August 19, 2006 8:28:00 PM]
This topic is closed to new replies.
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