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

PURPOSE

Determines orientation between two 3D volumes in terms of three Eulerian angles. Rotation around arbitrary center.

SEE ALSO

OR 3Q	[ORientation search - 3D, Eulerian angles ||]
OR R	[ORientation search - 2D, rotation, remapping into polar coordinates ||]

USAGE

.OPERATION: OR 3A [phi],[theta],[psi],[cc]

[The first three optional register variables will contain the phi, theta and psi Eulerian angles found by the program. The fourth register will contain the value of the correlation coefficient found by the program.]

.REFERENCE 3D FILE: VOL001
[Enter name of the file containing the 3D reference volume.]

.SECOND FILE: VOL002
[Enter name of the file containing the 3D volume to be matched with the reference file.]

.RADIUS OF THE MASK: 14
[The correlation coefficient is calculated only inside a sphere of the specified radius.]

.CENTER OF ROTATION IX, IY: 12,27
[Enter X,Y coordinates of a center of rotation. Volume extends in X from 1 to NX and in Y from 1 to NY.]

.CENTER OF ROTATION NZ: 55
[Enter Z coordinate of a center of rotation. Volume extends in Z from 1 to NZ.]

Initial Eulerian angles:
.PHI, THETA: 76.0,45.0

.PSI: 275.0
[Enter three Eulerian angles defining the 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 3A'.

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. The speed of the calculations is very high (on the order of a few minutes for a 32X32X32 cube and radius 14). 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 croscorrelation function must be used after (or before) the rotational search, and the whole procedure must be repeated to determine the best orientation.

4. Memory requirements: 2*NX*NY*NZ.

5. Implemented by P. Penczek.

SUBROUTINES

QALI, QNRF, UQU, FCNQ, AMOEBA

CALLER

UTIL3