V_ROTQR2EQ converts a real unit quaternion into the corresponding euler angles
Inputs:
M a string of n characters from the set determining the order of rotation axes
as listed below. Note that the control characters 'rdoOaA' may occur anywhere in the string:
'x','y','z' rotate around the given axis by the corresponding angle
given in e()
'1','2','3' 90 degree rotation around x,y or z axis; doesn't use a value from e()
'4','5','6' 180 degree rotation around x,y or z axis; doesn't use a value from e()
'7','8','9' 270 degree rotation around x,y or z axis; doesn't use a value from e()
'r','d' all angles are given in radians or degrees [default='r']
'R','D' all angles are given in radians or degrees and are negated
'o','O','a','A' selects whether to rotate the object or the coordinate axes and
whether the rotation axes remain fixed in space for consecutive
rotations (extrinsic) or else move with each rotation (intrinsic).
'o' = object-extrinsic [default]
'O' = object-intrinsic
'a' = axes-extrinsic
'A' = axes-intrinsic
Q(4,...) array of quaternions0001 function e=v_rotqr2eu(m,q) 0002 %V_ROTQR2EQ converts a real unit quaternion into the corresponding euler angles 0003 % Inputs: 0004 % M a string of n characters from the set determining the order of rotation axes 0005 % as listed below. Note that the control characters 'rdoOaA' may occur anywhere in the string: 0006 % 'x','y','z' rotate around the given axis by the corresponding angle 0007 % given in e() 0008 % '1','2','3' 90 degree rotation around x,y or z axis; doesn't use a value from e() 0009 % '4','5','6' 180 degree rotation around x,y or z axis; doesn't use a value from e() 0010 % '7','8','9' 270 degree rotation around x,y or z axis; doesn't use a value from e() 0011 % 'r','d' all angles are given in radians or degrees [default='r'] 0012 % 'R','D' all angles are given in radians or degrees and are negated 0013 % 'o','O','a','A' selects whether to rotate the object or the coordinate axes and 0014 % whether the rotation axes remain fixed in space for consecutive 0015 % rotations (extrinsic) or else move with each rotation (intrinsic). 0016 % 'o' = object-extrinsic [default] 0017 % 'O' = object-intrinsic 0018 % 'a' = axes-extrinsic 0019 % 'A' = axes-intrinsic 0020 % 0021 % Q(4,...) array of quaternions 0022 0023 % 0024 % Outputs: 0025 % 0026 % E(K,...) K Euler angles in radians (or degrees if 'd' or 'D' specified) per quaternion where K is the number of 'xyz' characters in M. 0027 % A positive rotation is clockwise if looking along the +ve axis away from the origin or anti-clockwise if 'R' or 'D' is given. 0028 % The x, y, z axes form a right-handed triple. 0029 % 0030 % The string M specifies the seqeunce of axes about which the rotations are performed. There are 12 0031 % possible 3-character sequences that avoid consecutive repetitions. These are 'Euler angles' if 0032 % there is a repeated axis or 'Tait-Bryan angles' if not. Common choices are: 0033 % (1) 'zxz' the most common Euler angle set 0034 % (2) 'xyz' corresponds to 'roll, pitch, yaw' for an aeroplane heading in the x direction with y to 0035 % the right and z down. The intrinsic equivalent is 'Ozyx' corresponding to 'yaw, pitch, roll'. 0036 % (3) 'z1z1z' involves 5 rotations, in which all the non-fixed rotations are around the z axis. 0037 % 0038 % The Euler angles are not, in general, unique. In particular: 0039 % (1) v_roteu2ro('zxz',[a b c]) = v_roteu2ro('zxz',[a+pi -b c+pi]) 0040 % (2) v_roteu2ro('xyz',[a b c]) = v_roteu2ro('xyz',[a+pi pi-b c+pi]) 0041 0042 % 0043 % Copyright (C) Mike Brookes 2007-2020 0044 % Version: $Id: v_rotqr2eu.m 11260 2020-07-18 20:07:58Z dmb $ 0045 % 0046 % VOICEBOX is a MATLAB toolbox for speech processing. 0047 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0048 % 0049 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0050 % This program is free software; you can redistribute it and/or modify 0051 % it under the terms of the GNU General Public License as published by 0052 % the Free Software Foundation; either version 2 of the License, or 0053 % (at your option) any later version. 0054 % 0055 % This program is distributed in the hope that it will be useful, 0056 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0057 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0058 % GNU General Public License for more details. 0059 % 0060 % You can obtain a copy of the GNU General Public License from 0061 % http://www.gnu.org/copyleft/gpl.html or by writing to 0062 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0063 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0064 0065 if nargout 0066 e=v_rotro2eu(m,v_rotqr2ro(q)); 0067 else 0068 v_rotqr2ro(q); % draw a cube 0069 end