ROTEU2QR converts a sequence of Euler angles to a real unit quaternion Inputs: M(1,n) a string of n characters from the set {'x','y','z'} or, equivalently, a vector whose elements are 1, 2, or 3 T(n,1) n rotation angles. A positive rotation is clockwise if looking along the axis away from the origin. Outputs: R(3,3) Input rotation matrix Plots a diagram if no output specified The string M specifies the axes about which the rotations are performed. You cannot have the same axis in adjacent positions and so there are 12 possibilities. Common ones are "ZXZ" and "ZYX". A positive rotation is clockwise if looking along the axis away from the origin; thus a rotation of +pi/2 around Z rotates [1 0 0]' to [0 1 0]'. Inverse conversion: If m has length 3 with adjacent characters distinct, then rotro2eu(m,roteu2ro(m,t))=t. Inverse rotation: roteu2ro(m,t)*roteu2ro(fliplr(m),-fliplr(t))=eye(3)

- roteu2qr ROTEU2QR converts a sequence of Euler angles to a real unit quaternion
- rotqr2ro ROTQR2RO converts a real quaternion to a 3x3 rotation matrix

0001 function r=roteu2ro(m,t) 0002 %ROTEU2QR converts a sequence of Euler angles to a real unit quaternion 0003 % Inputs: 0004 % 0005 % M(1,n) a string of n characters from the set {'x','y','z'} 0006 % or, equivalently, a vector whose elements are 1, 2, or 3 0007 % T(n,1) n rotation angles. A positive rotation is clockwise if 0008 % looking along the axis away from the origin. 0009 % 0010 % Outputs: 0011 % 0012 % R(3,3) Input rotation matrix 0013 % Plots a diagram if no output specified 0014 % 0015 % The string M specifies the axes about which the rotations are performed. 0016 % You cannot have the same axis in adjacent positions and so there are 12 0017 % possibilities. Common ones are "ZXZ" and "ZYX". A positive rotation is clockwise 0018 % if looking along the axis away from the origin; thus a rotation of +pi/2 0019 % around Z rotates [1 0 0]' to [0 1 0]'. 0020 % 0021 % Inverse conversion: If m has length 3 with adjacent characters distinct, 0022 % then rotro2eu(m,roteu2ro(m,t))=t. 0023 % 0024 % Inverse rotation: roteu2ro(m,t)*roteu2ro(fliplr(m),-fliplr(t))=eye(3) 0025 0026 % 0027 % Copyright (C) Mike Brookes 2007-2012 0028 % Version: $Id: roteu2ro.m 2171 2012-07-12 07:33:03Z dmb $ 0029 % 0030 % VOICEBOX is a MATLAB toolbox for speech processing. 0031 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0032 % 0033 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0034 % This program is free software; you can redistribute it and/or modify 0035 % it under the terms of the GNU General Public License as published by 0036 % the Free Software Foundation; either version 2 of the License, or 0037 % (at your option) any later version. 0038 % 0039 % This program is distributed in the hope that it will be useful, 0040 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0041 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0042 % GNU General Public License for more details. 0043 % 0044 % You can obtain a copy of the GNU General Public License from 0045 % http://www.gnu.org/copyleft/gpl.html or by writing to 0046 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0047 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0048 r=rotqr2ro(roteu2qr(m,t));

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