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 Version: $Id: rotqr2ax.m 713 2011-10-16 14:45:43Z 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 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]=rotqr2ax(q) 0002 %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 0018 % Version: $Id: rotqr2ax.m 713 2011-10-16 14:45:43Z 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

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