gusucode.com > 《MATLAB图像与视频处理实用案例详解》代码 > 《MATLAB图像与视频处理实用案例详解》代码/第 19 章 基于语音识别的信号灯图像模拟控制技术/voicebox/rotro2pl.m
function [u,v,t]=rotro2pl(r) %ROTRO2PL find the plane and rotation angle of a rotation matrix [u,v,t]=r % Inputs: % % R(n,n) Rotation matrix % % Outputs: % % U(n,1) and V(n,1) are orthonormal vectors defining a plane in n-dimensional space % T is the rotation angle in radians from U towards V with 0<=T<=pi. If T % is omitted it U and V will be separated by T instead of being orthogonal % % Copyright (C) Mike Brookes 2007 % Version: $Id: rotro2pl.m,v 1.1 2007/11/24 14:38:29 dmb Exp $ % % 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% n=size(r,1); [q,e]=schur(r); [m,i]=max(abs(e(2:n+1:n^2))); z=e(i+1,i)<0; % =1 if negative uv=q(:,i+z:1-2*z:i+1-z); u=uv(:,1); % the following code selects unique values of u and v % v=uv(:,2); % f=u.*v; % maximize inner product of u.^2 and v.^2 % g=(v+u).*(v-u); % t=atan2(sum(f.*g),sum(g.^2/4-f.^2))/4; % c=cos(t); % s=sin(t); % uv=uv*[c s; -s c]; % a=sum(uv)<0; % uv=uv*[1-a(1)-a(2) a(2)-a(1); a(1)-a(2) 1-a(1)-a(2)]; % u=uv(:,1); if nargout>2 v=uv(:,2); t=atan2(abs(e(i+1,i)),e(i,i)); else [s,c]=atan2sc(abs(e(i+1,i)),e(i,i)); v=uv*[c;s]; end