## OR 3Q - ORientation search - 3D, Eulerian angles ||

(06/01/13)

PURPOSE

Determines relative orientation of two cubic volumes in terms of three Eulerian angles. Rotation is around the SPIDER volume center (NX/2+1, NY/2+1, NZ/2+1).   Example.

 OR 3A [ORientation search - 3D, Eulerian angles, arbitrary center ||]

USAGE

.OPERATION: OR 3Q [phi],[theta],[psi],[cc]
[Find orientation info. This operation can return up to 4 optional register variables:
 Variable Example Receives First [phi] Euler angle: phi Second [the] Euler angle: theta Third [psi] Euler angle: psi Fourth [cc] Cross-correlation coefficient

.REFERENCE VOLUME: VOL001
[Enter name of the file containing the reference volume.]

.EXPERIMENTAL VOLUME: VOL002
[Enter name of the file containing the volume to be matched with the reference file.]

[The correlation coefficient is calculated only inside a sphere of the specified radius.]

.INITIAL EULERIAN ANGLES PHI,THETA,PSI: 76.0, 45.0, 275.0
[Enter three Eulerian angles defining a starting position for optimization procedure.]

NOTES

1. The Eulerian angles agree with the convention used in SPIDER. In particular, to rotate the second volume to the orientation of the reference volume, the command 'RT 3D' must be used with the angles determined by this operation. To rotate the reference volume to the position of the second volume, the following transformation must be applied: phi' = -psi, theta' = -theta, psi' = -phi. The 'primed' angles are then applied to the reference volume in 'RT 3D'.

2. In most cases it is sufficient to use the input volumes interpolated to the smaller dimensions, for example, 2-fold smaller. The accuracy is excellent, and the gain in speed for this example is eightfold. It is recommended that different initial Eulerian angles be tried to verify the results.

3. If two volumes are shifted with respect to one another, the 3D cross-correlation function must be used after (or before) the rotational search, and the whole procedure must be repeated to determine the best orientation.

4. Implemented by P. Penczek.

SUBROUTINES

QALI, QNRF, UQU, FCNQ, AMOEBA

CALLER

UTIL3