[Halld-offline] fixes to the CDC acceptance holes

[Richard Jones]

Hello Offliners,

I have diagnosed and fixed the bug that Simon and Paul pointed out back in
November, that after my geometry updates related to the Geant4 development,
there appeared large holes in the acceptance for charged tracks at backward
angles in the CDC.  The changes have been checked into subversion.  I
invite anyone who is interested to check out the updated code and verify
that the holes have been healed.  The problem was entirely with Geant3, not
with mcsmear and not with the reconstruction code.

The source of the bug was code that Simone (Gianni, not Taylor) introduced
in Geant321, related to his scheme for virtual divisions.  That code
employed a short-cut for determining the transverse extents of volumes with
cylindrical symmetry when being cut along a cartesian axis.  He assumed
that if the cos(theta) of the rotated volume is greater than 0.99 then it
should be treated as if theta=0.  His code is full of approximations like
this, and in most cases they are conservative ones that result in intervals
that are larger than the actual volume, which is safe.  But in the case of
the stereo straws, we have cos(6 deg) = 0.995, which results in the
projection of the stereo staws onto the x,y plane having a width of only
one straw diameter.  This is wrong by a whole order of magnitude, and
results in straws not being checked for intersections with tracks if the
track intersects the straw layer at a point in x that is far from its
shunken image in x,y.  The image was being taken at the downstream end,
which explains why the problems got worse at the upstream end, but really
there were problems everywhere.

That was one bug I found, and there was another one that I am not sure
impacts us very much, but which I also fixed.

Someone might be wondering what changed to make this bug suddenly impact us
in such a clear way after the recent geometry updates.  The reason is
somewhat arbitrary, because the straws were changed from straight tubes to
"profiled tubes" in order to make them "neck down" to the diameter of the
feedthroughs where they punch through the end plates.  This change made the
code form the "shunken image" of the straw x-y profile (that I referred to
above) at the downstream end instead of in the middle of the straw, as it
did formerly.

We were LUCKY THIS HAPPENED, because the bug was always there in the
simulation code, but the effects were more subtle before, and were only
happening near the two end plates, which made them more difficult to notice
and diagnose.  Now with this fix, any bogus inefficiencies that were seen
in the stereo layers near the end-plates are now removed.

Thanks to all of you for your patience with this.  We might have gotten
away with ignoring it and moving forward with the G4 development, but I
think that would have been a mistake.  We need both simulations to work
during the transition period, and this information may be useful for
explaining artifacts in prior simulations that were never fully understood.

-Richard Jones
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