function [a,t]=v_rotqr2ax(q)
%V_ROTQR2AX converts a real quaternion to the corresponding rotation axis and angle
% Inputs: 
%
%     Q(4,1)   real-valued quaternion (with magnitude = 1)
%
% Outputs:
%
%     A(3,1)   Unit vector in the direction of the rotation axis.
%     T        Rotation angle in radians (in range 0 to 2pi)
%
% In the quaternion representation of a rotation, and q(1) = cos(t/2) 
% where t is the angle of rotation in the range 0 to 2pi
% and q(2:4)/sin(t/2) is a unit vector lying along the axis of rotation
% a positive rotation about [0 0 1] takes the X axis towards the Y axis.
% 
%      Copyright (C) Mike Brookes 2007-2018
%      Version: $Id: v_rotqr2ax.m 10865 2018-09-21 17:22:45Z dmb $
%
%   VOICEBOX is a MATLAB toolbox for speech processing.
%   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   This program is free software; you can redistribute it and/or modify
%   it under the terms of the GNU Lesser 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 Lesser General Public License for more details.
%
%   You can obtain a copy of the GNU Lesser General Public License from
%   https://www.gnu.org/licenses/ .
%    See files gpl-3.0.txt and lgpl-3.0.txt included in this distribution.
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a=q(2:4);
m=sqrt(a'*a);
t=2*atan2(m,q(1));      % avoids problems if unnormalized
if m>0
    a=a/m;
else
    a=[0 0 1]';
end
if ~nargout
    v_rotqr2ro(q); % plot a rotated cube
end
    