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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = rotation3dToEulerAngles(mat, varargin)
%ROTATION3DTOEULERANGLES Extract Euler angles from a rotation matrix.
%
% [PHI, THETA, PSI] = rotation3dToEulerAngles(MAT)
% Computes Euler angles PHI, THETA and PSI (in degrees) from a 3D 4-by-4
% or 3-by-3 rotation matrix.
%
% ANGLES = rotation3dToEulerAngles(MAT)
% Concatenates results in a single 1-by-3 row vector. This format is used
% for representing some 3D shapes like ellipsoids.
%
% ... = rotation3dToEulerAngles(MAT, CONVENTION)
% CONVENTION specifies the axis rotation sequence. Default is 'ZYX'.
% Supported conventions are:
% 'ZYX','ZXY','YXZ','YZX','XYZ','XZY'
% 'ZYZ','ZXZ','YZY','YXY','XZX','XYX'
%
% Example
% rotation3dToEulerAngles
%
% References
% Code from '1994 - Shoemake - Graphics Gems IV: Euler Angle Conversion:
% http://webdocs.cs.ualberta.ca/~graphics/books/GraphicsGems/gemsiv/euler_angle/EulerAngles.c
% (see rotm2eul, that is part of MATLAB's Robotics System Toolbox)
% Modified using explanations in:
% http://www.gregslabaugh.net/publications/euler.pdf
% https://www.geometrictools.com/Documentation/EulerAngles.pdf
%
% See also
% transforms3d, rotation3dAxisAndAngle, createRotation3dLineAngle,
% eulerAnglesToRotation3d
%
% ------
% Authors: David Legland, oqilipo
% E-mail: david.legland@inrae.fr
% Created: 2010-08-11, using Matlab 7.9.0.529 (R2009b)
% Copyright 2010-2023 INRA - Cepia Software Platform
p = inputParser;
validStrings = {...
'ZYX','ZXY','YXZ','YZX','XYZ','XZY',...
'ZYZ','ZXZ','YZY','YXY','XZX','XYX'};
addOptional(p,'convention','ZYX',@(x) any(validatestring(x,validStrings)));
logParValidFunc = @(x) (islogical(x) || isequal(x,1) || isequal(x,0));
addParameter(p,'IsRotation', 1, logParValidFunc);
valTol = @(x) validateattributes(x,{'numeric'},{'scalar', '>=',eps(class(mat)), '<=',1});
addParameter(p,'tolerance', 1e-8, valTol);
parse(p,varargin{:});
convention=p.Results.convention;
isRotation = p.Results.IsRotation;
tolerance = p.Results.tolerance;
if isRotation
if ~isTransform3d(mat(1:3,1:3), 'rotation', 1, 'tolerance', tolerance)
warning(['Rotation matrix contains reflection or scaling ' ...
'tested with a tolerance of ' num2str(tolerance) '.' newline ...
'Calculation of euler angles might be incorrect.'])
end
end
switch convention
case 'ZYX'
% extract |cos(theta)|
cy = hypot(mat(1,1), mat(2,1));
% avoid dividing by 0
if cy > 16*eps
% normal case: theta <> 0
phi = atan2( mat(2,1), mat(1,1));
theta = atan2(-mat(3,1), cy);
psi = atan2( mat(3,2), mat(3,3));
else
phi = 0;
theta = atan2(-mat(3,1), cy);
psi = atan2(-mat(2,3), mat(2,2));
end
case 'ZXY'
cy = hypot(mat(2,2), mat(1,2));
if cy > 16*eps
phi = -atan2( mat(1,2), mat(2,2));
theta = -atan2(-mat(3,2), cy);
psi = -atan2( mat(3,1), mat(3,3));
else
phi = 0;
theta = -atan2(-mat(3,2), cy);
psi = -atan2(-mat(1,3), mat(1,1));
end
case 'YXZ'
cy = hypot(mat(3,3), mat(1,3));
if cy > 16*eps
phi = atan2( mat(1,3), mat(3,3));
theta = atan2(-mat(2,3), cy);
psi = atan2( mat(2,1), mat(2,2));
else
phi = 0;
theta = atan2(-mat(2,3), cy);
psi = atan2(-mat(1,2), mat(1,1));
end
case 'YZX'
cy = hypot(mat(1,1), mat(3,1));
if cy > 16*eps
phi = -atan2( mat(3,1), mat(1,1));
theta = -atan2(-mat(2,1), cy);
psi = -atan2( mat(2,3), mat(2,2));
else
phi = 0;
theta = -atan2(-mat(2,1), cy);
psi = -atan2(-mat(3,2), mat(3,3));
end
case 'XYZ'
cy = hypot(mat(3,3), mat(2,3));
if cy > 16*eps
phi = -atan2( mat(2,3), mat(3,3));
theta = -atan2(-mat(1,3), cy);
psi = -atan2( mat(1,2), mat(1,1));
else
phi = 0;
theta = -atan2(-mat(1,3), cy);
psi = -atan2(-mat(2,1), mat(2,2));
end
case 'XZY'
cy = hypot(mat(2,2), mat(3,2));
if cy > 16*eps
phi = atan2( mat(3,2), mat(2,2));
theta = atan2(-mat(1,2), cy);
psi = atan2( mat(1,3), mat(1,1));
else
phi = 0;
theta = atan2(-mat(1,2), cy);
psi = atan2(-mat(3,1), mat(3,3));
end
case 'ZYZ'
cy = hypot(mat(3,2), mat(3,1));
if cy > 16*eps
phi = -atan2(mat(2,3), -mat(1,3));
theta = -atan2(cy, mat(3,3));
psi = -atan2(mat(3,2), mat(3,1));
else
phi = 0;
theta = -atan2(cy, mat(3,3));
psi = -atan2(-mat(2,1), mat(2,2));
end
case 'ZXZ'
cy = hypot(mat(3,2), mat(3,1));
if cy > 16*eps
phi = atan2(mat(1,3), -mat(2,3));
theta = atan2(cy, mat(3,3));
psi = atan2(mat(3,1), mat(3,2));
else
phi = 0;
theta = atan2(cy, mat(3,3));
psi = atan2(-mat(1,2), mat(1,1));
end
case 'YZY'
cy = hypot(mat(2,3), mat(2,1));
if cy > 16*eps
phi = atan2(mat(3,2), -mat(1,2));
theta = atan2(cy, mat(2,2));
psi = atan2(mat(2,3), mat(2,1));
else
phi = 0;
theta = atan2(cy, mat(2,2));
psi = atan2(-mat(3,1), mat(3,3));
end
case 'YXY'
cy = hypot(mat(2,3), mat(2,1));
if cy > 16*eps
phi = -atan2(mat(1,2), -mat(3,2));
theta = -atan2(cy, mat(2,2));
psi = -atan2(mat(2,1), mat(2,3));
else
phi = 0;
theta = -atan2(cy, mat(2,2));
psi = -atan2(-mat(1,3), mat(1,1));
end
case 'XZX'
cy = hypot(mat(1,3), mat(1,2));
if cy > 16*eps
phi = -atan2(mat(3,1), -mat(2,1));
theta = -atan2(cy, mat(1,1));
psi = -atan2(mat(1,3), mat(1,2));
else
phi = 0;
theta = -atan2(cy, mat(1,1));
psi = -atan2(-mat(3,2), mat(3,3));
end
case 'XYX'
cy = hypot(mat(1,2), mat(1,3));
if cy > 16*eps
phi = atan2(mat(2,1), -mat(3,1));
theta = atan2(cy, mat(1,1));
psi = atan2(mat(1,2), mat(1,3));
else
phi = 0;
theta = atan2(cy, mat(1,1));
psi = atan2(-mat(2,3), mat(2,2));
end
end
% format output arguments
if nargout <= 1
% one array
varargout{1} = rad2deg([phi theta psi]);
else
% three separate arrays
varargout = cellfun(@rad2deg, {phi theta psi},'uni',0);
end
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