VO EA - Vector Operation - Create Evenly Spaced Angles Document file

PURPOSE

Create angular document file containing three Eulerian angles defining quasi-evenly spaced projection directions. This document file can be used to calculate reference projections (operation 'PJ 3Q') for the 'AP SH' operation (3D Projection Alignment).

SEE ALSO

VO MD	[Vector Operation - angular Document file from 'AP MD' output]
VO RA	[Vector Operation - Rotate Angular document file]
AP SH	[Alignment - multi-reference, exhaustive rotation & shift ||*]

USAGE

.OPERATION: VO EA [num-angles]

[[num-angles] is an optional register variable which will receive the number of angular directions for the angular step specified (see note 3).]

.DELTA THETA: 2.0
[The angular step for the theta angles. The angular step for the phi angle is adjusted according to the equation
d(phi) = d(theta)/sin(theta)
to create quasi-evenly spaced directions. X21 is an optional register which will contain the number of angular directions for the angular step specified (see note 3).]

.RANGE OF THETA (0,90): 0.0, 90.0
[Range of theta angle. Default is 0,90, as required by the 'AP MD' command.]

.RANGE OF PHI (0,359.9): 0.0, 359.9
[Range of phi angle. Default is 0, 359.9, as required by the 'AP MD ' command.]

.ANGULAR DOCUMENT FILE NAME: ANGFULL
[Enter the name of the output angular docfile. The file will contain the Eulerian angles psi, theta, phi as required by the 'AP SH' or 'AP REF' operations.]

NOTES

1. The default range of angles covers only half of the full angular range of directions. The full range would require 0<theta<180, but the projections with theta>90 are mirrored versions of projections with theta<90; this is implicitly taken into account in the 'AP MD' operation.

2. For symmetric structures the ranges of angles must be adjusted properly (depending on the symmetry).

3. Numbers of directions for default angular range:

    
            Delta theta               number of directions 
               15.0                            84 
               10.0                           195 
                5.0                           799 
                2.5                          3248 
                2.0                          5088 
                1.5                          9076 
                1.0                         20489 
          

   4. Implemented by P. Penczek

SUBROUTINES

VOEA

CALLER

DRIV1