
From:  Dimitris Papavasiliou 
Subject:  [Helpgsl] Quaternions anyone? 
Date:  Wed, 29 Mar 2006 01:50:50 +0300 
Useragent:  Mail/News 1.5 (X11/20060228) 
Hello all,this is now the third time I'm attempting to use the GSL for computation in the area of computer graphics. And for the third time I'm stuck with the most important (or rather common) part, namely affine transformations of points and such. Using the blas routines for simple R^3 matrixmatrix and matrixvector multiplications seems to be overkill on one side and too much of a hassle. And since the GSL doesn't have any simple routines for that I though of using quaternions, which might be a better idea anyway.
In case you don't know quaternions are a generalization of complex numbers to four dimensions and have been dead for many decades now (well since their birth is more like it) except for one use: representing rotations and orientation in R^3 and R^4. So I have put together a few routines for handling quaternions in a GSLlike manner (using gsl_vectors to store them and convert them to from gsl_matrices) which are mostly geared towards representing rotations in R^3. Implementing other operations like even, odd, inner or outer products would be easy but I doubt anyone would use them. Maybe physicists could use quaternion pairs to represent rotations in R^4 for relativity and such.
So I was wondering if there might be interest for incorporating such routines into the GSL. As I have said areas of interest may include computer graphics, physics, robotics, control theory etc.
Dimitris P.Finally, to convince you of the usefulness and value of quaternions, here are some quotes:
Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clark Maxwell.  Lord Kelvin, 1892.
. . .quaternions appear to exude an air of nineteenth century decay, as a rather unsuccessful species in the struggleforlife of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions but, alas, such enthusiasm means little to the harderheaded physical scientist.  Simon L. Altmann, 1986
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