**PURPOSE**- Determines relative orientation of two cubic volumes in terms of three Eulerian angles. Rotation around arbitrary center. Example.

**SEE ALSO****OR 3Q**[ORientation search - 3D, Eulerian angles ||] **OR R**[ORientation Search - 2D, rotation, uses polar coords. ||]

**USAGE**- .OPERATION: OR 3A [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.].MASK RADIUS: 14

[The correlation coefficient is calculated only inside a sphere of the specified radius.].ROTATION CENTER X, Y, Z: 12, 27, 55

[Enter X,Y & Z coordinates of a center of rotation.].INITIAL EULERIAN ANGLES PHI,THETA,PSI: 76.0, 45.0, 275.0

[Enter three Eulerian angles defining a starting position for optimization procedure.]

**NOTES**

- 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'.
- 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.
- 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.
- Implemented by P. Penczek.

**SUBROUTINES**- QALI, QNRF, UQU, FCNQ, AMOEBA

**CALLER**- UTIL3

SUBROUTINES: QALI, QNRF, UQU, FCNQ, AMOEBA CALLER: UTIL3

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