Re: Interest for quaternions (and octonions)?

From: Hubert.Holin_at_[hidden]
Date: 2000-12-21 17:40:29

paris (U.E.), le 21/12/2000

--- In boost_at_[hidden], "Reid Sweatman" <borderland_at_u...> wrote:
> I'd be interested.  I've got my own quaternion class, but I'm always willing
> to see if someone can show me something better, and it'd be nice to have it
> in Boost.  Like Gary, I use them a lot in games (ex-Sierra myself).  It
> would be nice if it could build on stuff already in the STL or Boost.  I'd
> really like to see a general high-quality *fast* numeric library in Boost.

        The file I uploaded is not fast. It is one branch of a private 
research program. I do believe this can be a good place to improve on 
various programmers tricks.

        In particular, as I wrote this file for clarity, I did not 
implement some known techniques which speed up multiplications (just as 
there are for some matrix multiplication). I guess they could be put in 
if desired.

> As I said, I've got my own stuff, but it isn't exactly portable, being an
> odd mix of generative programming techniques that use valarray, other
> containers, and custom assembler that's CPU-specific.  Else I'd have offered
> it to Boost by now.
> 
> I can just guess, though, that someone will shortly tell me that I should
> just use Blitz++ or something <g>.  Well, I'm keeping my eye on it, but my
> currently favorite compiler (no, not that one, so don't start <g>) won't
> compile parts of it.  But I well understand Dave's comment, because
> *accurate* / *fast* numeric stuff takes an expert to get right.
> 
> Just out of curiosity, what are "octonions?" (I can sort of guess, but I'm a
> mathematician by training, and I ain'ta never heerd of 'em).  Could you
> suggest a book or even better, an online paper that gives the gist?  Thanks.
> 
> Reid Sweatman
> Software Engineer
[SNIP]

        Well, octonions are built from quaternions in the same way 
quaternions are built from complexes, which is the same way complexes 
are built from reals.They see some use in theoretical physics.

        Reals, complexes, quaternions and octonions are the only real-
based division algebras. They are kin to Clifford Algebras.

        One (mandatory) reference is Bourbaki-Algebra. One excellent 
online ressource is "http://www.7stones.com/Homepage/history.html".

                Hubert Holin
                Hubert.Holin_at_[hidden]