ROTPL2RO find matrix to rotate in the plane containing u and v r=[u,v,t] Inputs: U(n,1) and V(n,1) define a plane in n-dimensional space T is the rotation angle in radians from U towards V. If T is omitted it will default to the angle between U and V Outputs: R(n,n) Rotation matrix

- atan2sc ATAN2SC sin and cosine of atan(y/x) [S,C,R,T]=(Y,X)

0001 function r=rotpl2ro(u,v,t) 0002 %ROTPL2RO find matrix to rotate in the plane containing u and v r=[u,v,t] 0003 % Inputs: 0004 % 0005 % U(n,1) and V(n,1) define a plane in n-dimensional space 0006 % T is the rotation angle in radians from U towards V. If T 0007 % is omitted it will default to the angle between U and V 0008 % 0009 % Outputs: 0010 % 0011 % R(n,n) Rotation matrix 0012 0013 % 0014 % Copyright (C) Mike Brookes 2007 0015 % Version: $Id: rotpl2ro.m 713 2011-10-16 14:45:43Z dmb $ 0016 % 0017 % VOICEBOX is a MATLAB toolbox for speech processing. 0018 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0019 % 0020 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0021 % This program is free software; you can redistribute it and/or modify 0022 % it under the terms of the GNU General Public License as published by 0023 % the Free Software Foundation; either version 2 of the License, or 0024 % (at your option) any later version. 0025 % 0026 % This program is distributed in the hope that it will be useful, 0027 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0028 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0029 % GNU General Public License for more details. 0030 % 0031 % You can obtain a copy of the GNU General Public License from 0032 % http://www.gnu.org/copyleft/gpl.html or by writing to 0033 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0034 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0035 0036 u=u(:); 0037 n=length(u); 0038 v=v(:); 0039 l=sqrt(u'*u); 0040 if l==0, error('input u is a zero vector'); end 0041 u=u/l; % normalize 0042 q=v-v'*u*u; % q is orthogonal to x 0043 l=sqrt(q'*q); 0044 if l==0 % u and v are colinear or v=zero 0045 [m,i]=max(abs(u)); 0046 q=zeros(n,1); 0047 q(1+mod(i(1),n))=1; % choose next available dimension 0048 q=q-q'*u*u; % q is orthogonal to x 0049 l=sqrt(q'*q); 0050 end 0051 q=q/l; % normalize 0052 if nargin<3 0053 [s,c]=atan2sc(v'*q,v'*u); 0054 r=eye(n)+(c-1)*(u*u'+q*q')+s*(q*u'-u*q'); 0055 else 0056 r=eye(n)+(cos(t)-1)*(u*u'+q*q')+sin(t)*(q*u'-u*q'); 0057 end 0058

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