VO EA - Vector Operation - Create Doc File Containing Evenly Spaced Angles



Creates doc file listing of three Eulerian angles quasi-evenly spaced on surface of a sphere. This document file can be used to calculate reference projections (operation 'PJ 3Q') for the 3D alignment 'AP SH' operation   Example.


VO NEA [Vector Operation - Create More Uniformly Spaced Angles]
VO MD [Vector Operation - angular Document file from 'AP MD' output]
VO RA [Vector Operation - Rotate Angular doc file]
VO IA [Vector Operation - Find Included Angle]
AP SH [Alignment - multi-reference, exhaustive rotation & shift ||*]
PJ 3Q [Project - 3D volume using Eulerian angles, trilinear interpolation ||]


.OPERATION: VO EA [num-angles]
[This operation can return one optional register variable:
Variable Example Receives
First [num-angles] Number of angular directions created

[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.]

.RANGE OF THETA (0,90): 0.0, 90.0
[Range of theta angle. Default is 0...90, as suitable for use by the the 'AP SH' or 'AP REF' operations with Check mirrored positions?: 1 ]

.RANGE OF PHI (0,359.9): 0.0, 359.9
[Range of phi angle. Default is 0 ... 359.9, as suitable for use by the 'AP SH' or 'AP REF' operations with Check mirrored positions?: 1 ]

[Enter the name of the output angular docfile. The file will contain the Eulerian angles psi, theta, phi needed for input into the 'AP SH' or 'AP REF' operations.]


  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 can be implicitly taken into account in the 'AP SH' or 'AP REF' operation.

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

  3. Numbers of projection directions for default theta and phi ranges:
      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. If the directions are considered on a sphere, then the delta theta sets the number of latitudes and longitudes where the projections are made. I.e. it sets the degrees betwen successive projections directions. The theta range limits the coverage of latitudes, e.g. 0..90 cover the 90 degrees of north latitudes. The phi range sets the longitudinal coverage, e.g. 0..360 covers the entire sphere.

  5. Implemented by P. Penczek





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