source: proiecte/pmake3d/make3d_original/Make3dSingleImageStanford_version0.1/image3dstiching/useful/Rotation2Q.m @ 37

% *  This code was used in the following articles:
% *  [1] Learning 3-D Scene Structure from a Single Still Image, 
% *      Ashutosh Saxena, Min Sun, Andrew Y. Ng, 
% *      In ICCV workshop on 3D Representation for Recognition (3dRR-07), 2007.
% *      (best paper)
% *  [2] 3-D Reconstruction from Sparse Views using Monocular Vision, 
% *      Ashutosh Saxena, Min Sun, Andrew Y. Ng, 
% *      In ICCV workshop on Virtual Representations and Modeling 
% *      of Large-scale environments (VRML), 2007. 
% *  [3] 3-D Depth Reconstruction from a Single Still Image, 
% *      Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng. 
% *      International Journal of Computer Vision (IJCV), Aug 2007. 
% *  [6] Learning Depth from Single Monocular Images, 
% *      Ashutosh Saxena, Sung H. Chung, Andrew Y. Ng. 
% *      In Neural Information Processing Systems (NIPS) 18, 2005.
% *
% *  These articles are available at:
% *  http://make3d.stanford.edu/publications
% * 
% *  We request that you cite the papers [1], [3] and [6] in any of
% *  your reports that uses this code. 
% *  Further, if you use the code in image3dstiching/ (multiple image version),
% *  then please cite [2].
% *  
% *  If you use the code in third_party/, then PLEASE CITE and follow the
% *  LICENSE OF THE CORRESPONDING THIRD PARTY CODE.
% *
% *  Finally, this code is for non-commercial use only.  For further 
% *  information and to obtain a copy of the license, see 
% *
% *  http://make3d.stanford.edu/publications/code
% *
% *  Also, the software distributed under the License is distributed on an 
% * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either 
% *  express or implied.   See the License for the specific language governing 
% *  permissions and limitations under the License.
% *
% */
function [axisAngle, q] = Rotation2Q(R)
% if rotation matrix is left-handed, then pass in R'

s = warning('off');

if size(R,2) == 9       %rotation matrix
   R = reshape(R, 3,3);
end

q       = [(sqrt( max( 0, 1 + R(1,1) + R(2,2) + R(3,3) ) ) / 2);
           (sqrt( max( 0, 1 + R(1,1) - R(2,2) - R(3,3) ) ) / 2);
           (sqrt( max( 0, 1 - R(1,1) + R(2,2) - R(3,3) ) ) / 2);
           (sqrt( max( 0, 1 - R(1,1) - R(2,2) + R(3,3) ) ) / 2)];

angle = acos( (R(1,1)+R(2,2)+R(3,3)-1 )/2 );

x  = (R(3,2)-R(2,3)) / sqrt( (R(3,2)-R(2,3))^2 + (R(1,3)-R(3,1))^2 + (R(2,1)-R(1,2))^2 );
y = (R(1,3)-R(3,1)) / sqrt( (R(3,2)-R(2,3))^2 + (R(1,3)-R(3,1))^2 + (R(2,1)-R(1,2))^2 );
z = (R(2,1)-R(1,2)) / sqrt( (R(3,2)-R(2,3))^2 + (R(1,3)-R(3,1))^2 + (R(2,1)-R(1,2))^2 );

axisAngle = [x, y, z, angle]; 

s = warning('on');

return;