quaternions as orientation

cold_storm · 2006-01-05T20:28:49

Anybody know how to use quaternions to orient a mesh in OpenGL?? It does not make sense to me how 3 imaginary numbers and a real number can represent the orientation of a mesh.

Math and Physics Programming

Started by cold_storm January 01, 2006 07:27 PM

60 comments, last by GameDev.net 18 years, 4 months ago

SiCrane

11,840

January 04, 2006 09:53 AM

Quote:Original post by Anonymous Poster
You said "As I mentioned earliers, quaternions form a four dimensional normed division algebra over the real numbers" is sufficient but what I stated is not? Can you give an example of something that forms "a non-commutative normed associative finite dimensional division algebra with identity over the field of reals" that is not a quaternion or at the very least isomorphic to it?

Sorry, I missed "over the real numbers" when I read your post the first time.

Anonymous

January 05, 2006 04:32 PM

A quaternion is defined as just any other complex number, it's just that the imaginary part is a Vector3. How hard can it be to get that? How you use them does not change the definition, does it?

/f

Anonymous

January 05, 2006 06:20 PM

My impression was that a quaternion was a point on the surface of a 4 dimensional sphere.

Q0^2 +Q1^2 + Q2^2 +Q3^2 = R^2

If this is that case then the roll of the q is no specified, how can you decide which is the imaginary and which is real?
On an imaginary number it is clear which the real part and which the imaginary part, in a quaternion any of the Q can be the real part and the other Qs can be the vector.

I am a noob so do not be too hard on me

Sneftel

1,788

January 05, 2006 06:26 PM

Quote:Original post by Anonymous Poster
A quaternion is defined as just any other complex number, it's just that the imaginary part is a Vector3.

Not "just" that. Quaternion operations are much more nuanced than that.

Sneftel

1,788

January 05, 2006 06:28 PM

Quote:Original post by Anonymous Poster
My impression was that a quaternion was a point on the surface of a 4 dimensional sphere.

unit quaternions (those with a magnitude of 1) can be thought of as points on the surface of a hypersphere. Arbitrary quaternions can be thought of as points in 4-space.

Quote:Q0^2 +Q1^2 + Q2^2 +Q3^2 = R^2

If this is that case then the roll of the q is no specified, how can you decide which is the imaginary and which is real?

You're going to have to explain what you mean by "roll". And what you mean by "Q0" and the others. (Do you mean x,y,z, and w components of the quaternion?) And what you mean by R.

Anonymous

January 05, 2006 06:56 PM

Quote:Original post by Sneftel
Quote:Original post by Anonymous Poster
A quaternion is defined as just any other complex number, it's just that the imaginary part is a Vector3.

Not "just" that. Quaternion operations are much more nuanced than that.

Yes, but still, please show me a paper written within 50 years after the original one that states something else. The operations were defined to match the behaviour of a "normal" complex-number. The guy didn't even found quaternions useful at all. Anybody who implements quaternions today will soon found out that they can be interpretated and extended in various ways but that doesn't change the original definition.

/F

Sneftel

1,788

January 05, 2006 07:07 PM

Quote:Original post by Anonymous Poster
please show me a paper written within 50 years after the original one that states something else.

Heh.... you mean, in the 1800s? Sorry, I don't think any of my OCLC databases go back that far. [wink] In any case, considering quaternions as a real and a 3-vector of imaginary numbers doesn't even give you multiplication.

nilkn

960

January 05, 2006 07:21 PM

A quaternion is not defined solely as a tuple (v, w), with v Î R3 and w Î R; it can merely be so represented.

Each way of representing quaternions (for example, in the above tuple form or as a linear combination of the basis quaternions 1, i, j, and k) has it's own strengths and weaknesses.

This (previously mentioned I think) MathWorld article should help clear things up.

Anonymous

January 05, 2006 07:53 PM

Quote:Original post by nilkn
A quaternion is not defined solely as a tuple (v, w), with v Î R3 and w Î R; it can merely be so represented.

Each way of representing quaternions (for example, in the above tuple form or as a linear combination of the basis quaternions 1, i, j, and k) has it's own strengths and weaknesses.

This (previously mentioned I think) MathWorld article should help clear things up.

Well, one problem with Mathworld is that is constantly updated with explainations that just wasn't around when it all went down. I wouldn't be surprised that an explaination to why there are infinite numbers of primes totally excludes that the original proof was totaly geometric.

If you evalate quaternions by hand (like in 1800), you better do it with a + Bi.

Sneftel

1,788

January 05, 2006 08:01 PM

So you don't want to consider any quaternion operations that don't operate on pure quaternions as "actual" quaternion operations, despite the fact that they're necessary for using quaternions as rotations? Any point to this tangent, or are you just being argumentative?

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