tr2eul.m

Robot tool box - provides many functions that are useful in robotics including such things as kinem

%TR2EUL Convert a homogeneous transform matrix to Euler angle form
%
%	[PHI THETA PSI] = TR2EUL(M)
%
% Returns a vector of roll/pitch/yaw angles corresponding to M, either a rotation
% matrix or the rotation part of a homogeneous transform.
% The 3 angles correspond to rotations about the Z, Y and Z axes respectively.
%
% See also:  EUL2TR, TR2RPY

% Copyright (C) 1993-2008, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for Matlab (RTB).
% 
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
% 
% RTB 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 Lesser General Public License for more details.
% 
% You should have received a copy of the GNU Leser General Public License
% along with RTB.  If not, see <http://www.gnu.org/licenses/>.

function euler = tr2eul(m)
	
	s = size(m);
	if length(s) > 2,
		euler = [];
		for i=1:s(3),
			euler = [euler; tr2eul(m(:,:,i))];
		end
		return
	end

	euler = zeros(1,3);

	% Method as per Paul, p 69.
	% phi = atan2(ay, ax)
	% Only positive phi is returned.
	if abs(m(1,3)) < eps & abs(m(2,3)) < eps,
		% singularity
		euler(1) = 0;
		sp = 0;
		cp = 1;
		euler(2) = atan2(cp*m(1,3) + sp*m(2,3), m(3,3));
		euler(3) = atan2(-sp * m(1,1) + cp * m(2,1), -sp*m(1,2) + cp*m(2,2));
	else
		euler(1) = atan2(m(2,3), m(1,3));
		sp = sin(euler(1));
		cp = cos(euler(1));
		euler(2) = atan2(cp*m(1,3) + sp*m(2,3), m(3,3));
		euler(3) = atan2(-sp * m(1,1) + cp * m(2,1), -sp*m(1,2) + cp*m(2,2));
	end