zAxisAngleRadians computes the axis and angle of rotation in an orthogonal matrix R
0001 % zAxisAngleRadians computes the axis and angle of rotation in an 0002 % orthogonal matrix R 0003 0004 function [axis, angle] = zAxisAngleRadians(R) 0005 0006 [v,d] = eig(R); % get eigenvectors and values of R 0007 [y,i] = sort(imag(diag(d))); % sort by imaginary part of eigenvalues 0008 0009 axis = v(:,i(2)); % eigenvector with eigenvalue 1, imag part 0 0010 0011 [y,i] = sort(abs(axis)); % look for largest entries in axis 0012 0013 b = zeros(3,1); % b will be perpendicular to axis 0014 b(i(2)) = axis(i(3)); % use the largest entries in axis 0015 b(i(3)) = -axis(i(2)); 0016 0017 angle = acos((b'*R*b) / (b'*b)) * sign(det([b R*b axis])); 0018 % angle of rotation, signed by rotation 0019 % sense relative to axis of rotation