From: Alberto Fasso' (fasso@SLAC.Stanford.EDU)
Date: Thu Jun 30 2005 - 17:34:53 CEST
On Wed, 29 Jun 2005, Silvia Muraro wrote:
> Is there the possibility of having a torus in the FLUKA combinatorial
> geometry?
> Silvia Muraro
This question comes back from time to time. I copy here below an
answer I gave a couple of years ago.
Other people have recently expressed the wish to have the possibility
to use a torus in the geometry. I think that finding the intersection
point is not a problem: I have already the routine who does this
analytically, and sorting out the smallest of the real roots of the
4th degree equation looks rather easy. The problem, as explained below,
is the numerical accuracy: the solution of a 4th degree equation in double
precision is not always very accurate.
When Alfredo finds some free time after the next FLUKA release, I
would like to discuss this with him.
Alberto
**********************************************************************
**********************************************************************
>From fasso@slac.stanford.edu Thu Jun 30 08:23:29 2005
Date: Wed, 31 Jan 2001 15:05:29 -0800 (PST)
From: Alberto Fasso' <fasso@slac.stanford.edu>
To: Alfredo Ferrari <alfredo.ferrari@cern.ch>
Subject: Re: FLUKA: Geometry (fwd)
Hello everybody,
It looks that Alfredo didn't notice that his reply was directed to the
list... so I better translate it.
**********************************************************************
No chance!
Tori (which are 4th degree surfaces and therefore require a very
different logic and math because the equation solution besides
being complicated gives 4 roots instead of 2) have never been
implemented (Alberto was supposed to do it a loooong time ago).
Similar problems have always been solved by making "polygonal"
tori: depending on your mood you can make them with as many faces
you want.
**********************************************************************
Since I have been mentioned, I would like to add some more information.
It is true that a looooong time ago I have been preparing a TOR body (not
arbitrarily oriented but with the main circle lying on a plane parallel to
one coordinate plane - not a big deal to add a rotation, though).
The routine with the 4 analytical roots of the 4th-degree equation was
made and tested to work correctly. However, the solutions were not stable
numerically. Even in double precision, the accuracy with which the
trajectory-surface intersection points were found was very variable
depending on the distance and on the size of the torus.
I had found a way to improve the solution by iteration, but then I
realized that perhaps it would have been more effective to skip altogether
the lengthy analytical calculation and to do the iteration from the
beginning, similar to what is done with boundary crossing in magnetic
fields.
Here I stopped, but maybe it is time to come back to it.
Concerning the "polygonal" approximation, the simplest and not too bad
can be obtained with cylinders and truncated cones, as follows:
_________________________________________________
/ \
/ + \ TRC 1
/_____________________________________________________\
_______________________
\ /
\ - / TRC 2
\_________________/
______________________________________________________
| |
| + | XCC 1
|______________________________________________________|
________________
| |
| - | XCC 2
|________________|
etc...
_____________......................._____________
/ \ / \
/ \ / \
/ \ / \
| | | |
| | | |
| | | |
\ / \ /
\ / \ /
\_____________/.....................\_____________/
I hope it is clear enough...
Alberto
On Wed, 31 Jan 2001, Alfredo Ferrari wrote:
> No chance!
>
> I tori (che sono superfici di 4o grado e quindi richiedono una logica
> e una matematica parecchio diversa perche' la soluzione delle equazioni
> oltre che complicata da 4 soluzioni invece di due) non sono mai stati
> implementati (doveva farlo Alberto taaaanto tempo fa). Problemi simili
> sono stati sempre risolti facendo tori "poligonali", in dipendenza dalla
> voglia si possono fare con quante facce si vuole.
>
> Ciao
> Alfredo
>
> > A question from Yann. Best,
> >
> >
> > Federico Carminati
> >
> > ---------- Forwarded message ----------
> > Date: Tue, 30 Jan 2001 16:12:25 +0100
> > From: foucher <yann.foucher@psi.ch>
> > To: Federico.Carminati@cern.ch
> > Subject: Geometry
> >
> > Hello Mr Carminati,
> >
> > I would like to define a circular torus which axis is parralel to the z
> > axis.
> > I succed to do this shape with mcnp.
> > the card for mcnp is:
> > tz 0 0 0 8.8 1.8 1.8
> > Is it possible to get the equivalent geometry with FLUKA.
> > If yes, what is the input card ?
> > Thanks for answering.
> >
> > Best reagrds
> >
> > Yann FOUCHER
> > Paul Scherrer Institut (CH)
> > SINQ group
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