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rotparams.m

## Copyright (C) 2002 Etienne Grossmann.  All rights reserved.
##
## 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 2, or (at your option) any
## later version.
##
## This 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.

## -*- texinfo -*-
## @deftypefn{Function File} {@var{[vstacked, astacked]} = } rotparams ( rstacked ) 
## @cindex  
##  The function w = rotparams (r)            - Inverse to rotv().
##  Using, @var{w}    = rotparams(@var{r})  is such that
##  rotv(w)*r' == eye(3). 
##
##  If used as, [v,a]=rotparams(r) ,  idem, with v (1 x 3) s.t. w == a*v.
## 
##     0 <= norm(w)==a <= pi
## 
##     :-O !!  Does not check if 'r' is a rotation matrix.
##
##  Ignores matrices with zero rows or with NaNs. (returns 0 for them)
##
## @seealso{rotv}
## @end deftypefn

## Author:        Etienne Grossmann <etienne@cs.uky.edu>

function [vstacked, astacked] = rotparams (rstacked)

N = size (rstacked,1) / 3;

## ang = 0 ;
## if length(varargin),
##   if strcmp(varargin{1},'ang'),    ang = 1;  end
## end
ok = all ( ! isnan (rstacked') ) & any ( rstacked' );
ok = min ( reshape (ok,3,N) );
ok = find (ok) ;
## keyboard
vstacked = zeros (N,3);
astacked = zeros (N,1);
for j = ok,
  r = rstacked(3*j-2:3*j,:);
  [v,f] = eig (r); 
  f = diag(f);

  [m,i] = min (abs (real (f)-1));
  v = v(:,i);

  w = null (v');
  u = w(:,1);
  a = u'*r*u;
  if a<1,
    a = real (acos (u'*r*u));
  else
    a = 0;
  end
  ## Check orientation
  x=r*u;
  if v'*[0 -u(3) u(2); u(3) 0 -u(1);-u(2) u(1) 0]*x < 0,  v=-v; end 


  if nargout <= 1,   v = v*a; end
  vstacked(j,:) = -v';
  astacked(j) = a;
end

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