**PURPOSE**- Computes projection(s) of a 3D volume according to the three
Eulerian angles. Creates a "Circular Rings File" for use by
'AP REF' or other 'AP' operations. This may be usefull for
speeding up alignment.

(See align_overview.html for info on 'AP' operations.)

**SEE ALSO****PJ 3Q**[Project - 3D volume using Eulerian angles, trilinear interpolation ||] **RT SQ**[Rotate and Shift - image, Quadratic interpolation ||] **AP REF**[Alignment - multi-reference, rotation & shift ||*]

**USAGE**- .OPERATION: PJ 3Q RR

- .3-D INPUT FILE: vol001

[Enter the name of the volume whose projections are to be computed. This should be a cube!].RADIUS OF THE OBJECT: 90.0

[The projections are computed only for the object inside the sphere of the given radius.].ANGLE NUMBERS OR SELECTION DOC. FILE NAME: 1-700 or SEL001

[Enter selected angle numbers or name of a document file containing the selected angle numbers. Projections will only be calculated for the selected sets of angles from the following angles doc. file. (If you use a selection doc. file hee then the selected numbers are taken from the first register in the doc. file.)].ANGLES DOC. FILE: ANGLES

[Enter the name of the document file containing the Eulerian angles for the projections. The angles have to be given in the order: psi, theta, phi. The meaning of the angles is the same as in operation 'RT SQ'. Projections will be calculated for every entry specified in the previous question.].FIRST, LAST RING, & RING SKIP: 5,80, 1

[Only rings with radii in the range 5-80 will be analyzed. If skip=0 or 1, then every ring between 5 and 80 will be taken; for skip=2, every second ring; etc.].TEMPLATE FOR 2-D PROJECTIONS: PRJ****

[Enter the template for the output files which will contain the 2-D projections.].REFERENCE RINGS FILE: ref_rings

[Enter the template for the output files which will contain the reference rings (polar coordinate representation) of the 2-D projections. This file can be used by 'AP REF'.]

**NOTES**

- Memory requirements: NX*NY+12*R**3+15*R**2, where R is the
radius, but no more than: 6*NX*NY + NX*NY*NZ
- The projection file has always dimensions NX x NY.
- For a projection of the whole volume (not the internal
sphere only) give a radius larger than any linear
dimension of the volume. Please note that usually
such a projection is incorrect and the program takes
much longer!
- Implemented by: P.Penczek & A. Leith.
- Psi, theta, & phi angles are placed in projection file header
starting at location: 100
- Use: 'MD' with option 'FBS ON' to get higher resolution projection than the linear interpolated default operation.

**SUBROUTINES**- PJ3Q_N, PREPCUB, WRITPRO_N, WPRO_N, WPRO_FBS, FBS3

**CALLER**- VTIL2

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