## Copyright (c) 1998, 2000, 2005, 2007 Auburn University.
## Copyright (c) 2011 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
##
## This program is free software: you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega})
## Derivative of a quaternion.
##
## Let Q be a quaternion to transform a vector from a fixed frame to
## a rotating frame.  If the rotating frame is rotating about the
## [x, y, z] axes at angular rates [wx, wy, wz], then the derivative
## of Q is given by
##
## @example
## Q' = diff(Q, omega)
## @end example
##
## If the passive convention is used (rotate the frame, not the vector),
## then
##
## @example
## Q' = diff(Q,-omega)
## @end example
## @end deftypefn

## Adapted from: qderiv by A. S. Hodel <a.s.hodel@eng.auburn.edu>

function qd = diff (q, Omega)

  if (nargin != 2)
    print_usage ();
  endif

  if (! isa (q, "quaternion") || ! isscalar (q.w))
    error ("quaternion: first argument '%s' must be a scalar quaternion", inputname(1));
  endif

  Omega = vec (Omega);

  if (length (Omega) != 3)
    error ("quaternion: second argument '%s' must be a length 3 vector", inputname(2));
  endif

  qd = 0.5 * quaternion (Omega(1), Omega(2), Omega(3)) * q;

endfunction

%!shared q
%! q = quaternion(3,1,0,0);

%!assert(quaternion(0,0,0.5,1.5) == diff(q,[0 0 1]))
%!assert(quaternion(0,0,2,1) == diff(q,[0 1 1]))