Numerically stable methods for converting rotation matrices to Euler parameters

Euler parameters have several advantages over other methods of parameterising rotations. A selection of methods for extracting Euler parameters from a rotation matrix are presented, and their computational efficiency and accuracy are compared. One commonly accepted method is shown to suffer from loss of significance when rotations are close to pi +/- 2k pi radians. This paper also presents an original mettled based on the eigendecomposition of the rotation matrix.