Mathematical/Geometrical conventions in EMAN

Perversely, we decided to add yet another Euler angle convention to the EM community (we did have a good reason at the time). However, on the bright side, the EMAN library has routines to convert to other conventions. EMAN uses a Z,X,Z’ convention. That is, first there is a rotation about the Z axis, then about X, then about the new Z axis. When viewing projections, the convention is to look along the Z axis, so a 0,0,0 projection will be a ‘top’ view of the particle. The three rotations are given the names azimuth, altitude and phi. In projection, phi represents rotation in the plane of the projection. Alt=90 will produce a ‘side’ view of the particle, and azimuth will rotate through the various possible side views.

The corresponding rotation matrix is:

For symmetry, the convention is for the axis with the highest symmetry to be aligned along Z. So, for a D8 symmetry, the 8-fold axis lies along Z, and the asymmetric triangle spans alt=[0,90] and az=[0,45]. For icosahedral symmetry, the 5-fold lies along Z.