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
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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 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 can obtain a copy of the GNU General Public License from
http://www.gnu.org/copyleft/gpl.html or by writing to
Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%0001 function [a,t]=v_rotqr2ax(q) 0002 %V_ROTQR2AX converts a real quaternion to the corresponding rotation axis and angle 0003 % Inputs: 0004 % 0005 % Q(4,1) real-valued quaternion (with magnitude = 1) 0006 % 0007 % Outputs: 0008 % 0009 % A(3,1) Unit vector in the direction of the rotation axis. 0010 % T Rotation angle in radians (in range 0 to 2pi) 0011 % 0012 % In the quaternion representation of a rotation, and q(1) = cos(t/2) 0013 % where t is the angle of rotation in the range 0 to 2pi 0014 % and q(2:4)/sin(t/2) is a unit vector lying along the axis of rotation 0015 % a positive rotation about [0 0 1] takes the X axis towards the Y axis. 0016 % 0017 % Copyright (C) Mike Brookes 2007-2018 0018 % Version: $Id: v_rotqr2ax.m 10865 2018-09-21 17:22:45Z dmb $ 0019 % 0020 % VOICEBOX is a MATLAB toolbox for speech processing. 0021 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0022 % 0023 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0024 % This program is free software; you can redistribute it and/or modify 0025 % it under the terms of the GNU General Public License as published by 0026 % the Free Software Foundation; either version 2 of the License, or 0027 % (at your option) any later version. 0028 % 0029 % This program is distributed in the hope that it will be useful, 0030 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0031 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0032 % GNU General Public License for more details. 0033 % 0034 % You can obtain a copy of the GNU General Public License from 0035 % http://www.gnu.org/copyleft/gpl.html or by writing to 0036 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0037 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0038 a=q(2:4); 0039 m=sqrt(a'*a); 0040 t=2*atan2(m,q(1)); % avoids problems if unnormalized 0041 if m>0 0042 a=a/m; 0043 else 0044 a=[0 0 1]'; 0045 end 0046 if ~nargout 0047 v_rotqr2ro(q); % plot a rotated cube 0048 end 0049