For randomly-oriented targets, we wish to compute the orientational average of
a quantity 
:
To compute such averages, all you need to do is edit the file
ddscat.par
so that DDSCAT knows what ranges of the angles 
, 
,
and 
are of interest.
For a randomly-oriented target with no symmetry, you would need to
let run from 0 to 
,
from 0 to 
,
and from 0 to .
For targets with symmetry, on the other hand, the ranges of , ,
and may be reduced.
First of all, remember that averaging over is relatively ``inexpensive",
so when in doubt average over 0 to ;
most of the computational ``cost" is
associated with the number of different values of (,) which
are used.
Consider a cube, for example, with axis 
normal to one of the cube
faces; for this cube need run only from 0 to 
, since the
cube has fourfold symmetry
for rotations around the axis .
Furthermore, the angle need run only
from 0 to , since the orientation
(,,) is indistinguishable from
(, 
, 
).
For targets with symmetry, the user is encouraged to test the significance
of ,, on targets with small numbers of dipoles (say, of
the order of 100 or so) but having the desired symmetry.
It is important to remember that DDSCAT.4b handled even and odd values of
NTHETA differently - see §7 above!
For averaging over random
orientations odd values of NTHETA
are to be preferred, as this will allow use
of Simpson's rule in evaluating the ``integral" over 
.