V_ROTQR2MR converts a matrix of real quaternion vectors to quaternion matrices
Inputs:
QR(4m,n,...) mxn matrix of real quaternion vectors (each 4x1)
Outputs:
MR(4m,4n,...) mxn matrix of real quaternion matrices (each 4x4)
In matrix form, quaternions can be multiplied and added using normal matrix
arithmetic. Each element of an mxn matrix of quaternions is itself a 4x4 block
so the total dimension of MR is 4m x 4n.0001 function mr=v_rotqr2mr(qr) 0002 %V_ROTQR2MR converts a matrix of real quaternion vectors to quaternion matrices 0003 % Inputs: 0004 % 0005 % QR(4m,n,...) mxn matrix of real quaternion vectors (each 4x1) 0006 % 0007 % Outputs: 0008 % 0009 % MR(4m,4n,...) mxn matrix of real quaternion matrices (each 4x4) 0010 % 0011 % In matrix form, quaternions can be multiplied and added using normal matrix 0012 % arithmetic. Each element of an mxn matrix of quaternions is itself a 4x4 block 0013 % so the total dimension of MR is 4m x 4n. 0014 0015 % 0016 % Copyright (C) Mike Brookes 2000-2018 0017 % Version: $Id: v_rotqr2mr.m 10865 2018-09-21 17:22:45Z dmb $ 0018 % 0019 % VOICEBOX is a MATLAB toolbox for speech processing. 0020 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0021 % 0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0023 % This program is free software; you can redistribute it and/or modify 0024 % it under the terms of the GNU General Public License as published by 0025 % the Free Software Foundation; either version 2 of the License, or 0026 % (at your option) any later version. 0027 % 0028 % This program is distributed in the hope that it will be useful, 0029 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0030 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0031 % GNU General Public License for more details. 0032 % 0033 % You can obtain a copy of the GNU General Public License from 0034 % http://www.gnu.org/copyleft/gpl.html or by writing to 0035 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0037 persistent a b c 0038 if isempty(a) 0039 a=[1 2 3 3 1 2]; % destination row of +ve entries (from 0) 0040 b=[1 2 3 2 3 1]; % destination col of +ve entries (from 0) 0041 c=[0 0 0 1 2 3]; % source row of +ve entries (from 0) 0042 end 0043 s=size(qr); 0044 m=s(1); 0045 mr=repmat(reshape(qr,s(1),[]),4,1); 0046 n=size(mr,2); 0047 mn=s(1)*n; 0048 j=repmat(4*m*(0:n-1),m/4,1); 0049 i=repmat((1:4:m)',n,1)+j(:); 0050 ni=length(i); 0051 i6=repmat(i,1,6); 0052 mr(i6+repmat(a+m*b,ni,1))=mr(i6+repmat(c,ni,1)); 0053 mr(i6+repmat(c+m*b,ni,1))=-mr(i6+repmat(a,ni,1)); 0054 s(2)=4*s(2); % output array size 0055 mr=reshape(mr,s); 0056 if ~nargout 0057 qr=qr(1:4); 0058 v_rotqr2ro(qr(:)); % plot a rotated cube 0059 end