ROTQR2RO converts a real quaternion to a 3x3 rotation matrix Inputs: Q(4,1) real-valued quaternion (possibly unnormalized) Outputs: R(3,3) Input rotation matrix Plots a diagram if no output specified 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: rotqr2ro.m 5659 2015-02-02 20:21:49Z 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

- rectifyhomog RECTIFYHOMOG Apply rectifying homographies to an image set
- roteu2ro ROTEU2QR converts a sequence of Euler angles to a real unit quaternion
- rotqrvec ROTQRVEC applies a quaternion rotation ot a vector array y=[q,x]

0001 function r=rotqr2ro(q) 0002 %ROTQR2RO converts a real quaternion to a 3x3 rotation matrix 0003 % Inputs: 0004 % 0005 % Q(4,1) real-valued quaternion (possibly unnormalized) 0006 % 0007 % Outputs: 0008 % 0009 % R(3,3) Input rotation matrix 0010 % Plots a diagram if no output specified 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: rotqr2ro.m 5659 2015-02-02 20:21:49Z 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 0039 persistent a b c d e f g 0040 if isempty(a) 0041 a=[1 5 9]; 0042 b=[11 16 6]; 0043 c=[16 6 11]; 0044 d=[4 8 3]; 0045 e=[10 15 14]; 0046 f=[4 2 3]; 0047 g=[2 6 7]; 0048 end 0049 p=2*(q*q.')/(q.'*q); % force normalized 0050 r=zeros(3,3); 0051 r(a)=1-p(b)-p(c); 0052 r(d)=p(e)-p(f); 0053 r(g)=p(e)+p(f); 0054 if ~nargout 0055 % display rotated cube 0056 clf('reset'); % clear current axis 0057 % vv=[0,0,0;1,0,0;0,1,0;0,0,1]*r'; % pyramid 0058 % ff=[1 2 4; 2 1 3; 3 1 4; 4 2 3]; 0059 % cc=[0 1 0; 0 0 1; 1 0 0; 1 1 0]; 0060 vv=[0,0,0;1,0,0;0,1,0;0,0,1;0 1 1; 1 0 1; 1 1 0; 1 1 1]*r'; % cube 0061 ff=[1 2 6 4; 2 7 8 6; 7 3 5 8; 4 5 3 1; 3 7 2 1; 6 8 5 4]; 0062 % cc=[0 1 0; 1 0 0; 0 1 0; 1 0 0; 0 0 1; 0 0 1]; 0063 cc=[1 0 1 0 2 2]'; 0064 pa=patch('Vertices',vv,'Faces',ff,'FaceVertexCData',cc,'FaceColor','Flat'); 0065 colormap([1 0 0; 0 1 0; 0 0 1]); 0066 xlabel('x axis'); 0067 ylabel('y axis'); 0068 zlabel('z axis'); 0069 title(sprintf('qr = [%.2f, %.2f, %.2f, %.2f]'' initial xyz=0 are rgb',q)) 0070 axis([-1 1 -1 1 -1 1 0 1]*sqrt(3)); 0071 grid on 0072 view(3); 0073 axis equal; 0074 end 0075

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