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 matrix-matrix and matrix-vector 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 GSL-like 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 struggle-for-life 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 harder-headed physical scientist. --
Simon L. Altmann, 1986
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