FLUKA: ROT-DEFIni
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ROT-DEFIni
Defines rotations and translations to be applied to binnings and lattices
See also EVENTBIN, ROTPRBIN, USRBIN, and LATTICE (in Chap. 8})
WHAT(1)
: assigns a transformation index and the corresponding
rotation axis
=< 0.0 : the card is ignored if SDUM
is empty, otherwise SDUM
is
kept as the rotation name, and the first free rotation
number is used
> 1000 : interpreted as j + i * 1000
> 100 and < 1000 : interpreted as i + j * 100
(note the inversion of i and j!)
> 0 and =< 100 : interpreted as i, and j assumed to be = 0
where i = index of the rotation
j = 1 rotation with respect to x axis
= 2 rotation with respect to y axis
= 0 or 3 rotation with respect to z axis
(see Note 4)
Default
= 0.0 (no transformation defined)
WHAT(2)
= Polar angle of the rotation (Theta, 0...180 degrees)
Default
= no default
WHAT(3)
= Azimuthal angle of the rotation (Phi, -180...180 degrees)
Default
= no default
WHAT(4)
= X_offset for the translation
Default
= no default
WHAT(5)
= Y_offset for the translation
Default
= no default
WHAT(6)
= Z_offset for the translation
Default
= no default
SDUM
: name of the transformation
Default
: a name will provided by the program
Default
(option ROT-DEFIni not given): no transformation is defined
Notes:
1) FLUKA binnings (spatial meshes independent of the problem geometry,
designed to score average or event-by-event quantities) are
generally defined as Cartesian structures parallel to the
coordinate axes, or as cylindrical structures parallel to the
z-axis. However, it is possible to define binnings with any
arbitrary position and direction in space, by means of
transformations described by commands ROT-DEFIni and ROTPRBIN.
Command ROT-DEFIni defines rotations/translations to be applied
to binnings (requested by the user by means of EVENTBIN or USRBIN).
Each transformation defined by ROT-DEFIni is assigned a number
WHAT(1)
which can be applied to one or more binnings. The
correspondence between transformation index and binning number
is assigned via option ROTPRBIN.
2) Command ROT-DEFIni can be used also to define roto-translations
to be applied to lattice cells. Command LATTICE (see description
in Chap. 8, Combinatorial Geometry) sets the correspondence between
transformation index and lattice cell.
3) Command ROT-DEFIni can be used also to define roto-translations
to be applied to bodies in the geometry, as requested by the
$Start_transform....$End_transform directive (see Chap. 8,
Combinatorial Geometry).
4) The transformation matrices are:
(cth = cos(Theta), sth = sin(Theta), cph = cos(Phi), sph = sin(Phi))
j = 1 :
| X_new | | cth sth 0 | | 1 0 0 | | X_old+X_offset |
| Y_new | = | -sth cth 0 | | 0 cph sph | | Y_old+Y_offset |
| Z_new | | 0 0 1 | | 0 -sph cph | | Z_old+Z_offset |
j = 2 :
| X_new | | 1 0 0 | | cph 0 -sph | | X_old+X_offset |
| Y_new | = | 0 cth sth | | 0 1 0 | | Y_old+Y_offset |
| Z_new | | 0 -sth cth | | sph 0 cph | | Z_old+Z_offset |
j = 3 :
| X_new | | cth 0 -sth | | cph sph 0 | | X_old+X_offset |
| Y_new | = | 0 1 0 | | -sph cph 0 | | Y_old+Y_offset |
| Z_new | | sth 0 cth | | 0 0 1 | | Z_old+Z_offset |
Rij = Tik Pkj
| X_new | | cph cth sph cth -sth | | X_old+X_offset |
| Y_new | = | -sph cph 0 | | Y_old+Y_offset |
| Z_new | | cph sth sph sth cth | | Z_old+Z_offset |
and the inverse R(^-1)ij = P(^-1)ik T(^-1)kj
| X_old | | cph -sph 0 | | cth 0 sth | |X_new| |X_offset|
| Y_old | = | sph cph 0 | | 0 1 0 | |Y_new|-|Y_offset|
| Z_old | | 0 0 1 | | -sth 0 cth | |Z_new| |Z_offset|
| X_old | | cph cth -sph cph sth | | X_new | | X_offset |
| Y_old | = | sph cth cph sph sth | | Y_new |-| Y_offset |
| Z_old | | -sth 0 cth | | Z_new | | Z_offset |
For example:
(assume zero offset and [x,y,z] = old frame, [x',y',z'] = new frame)
Theta = pi/2, Phi = 0 :
j = 1: x' = y j = 2: x' = x j = 3: x' = -z
y' = -x y' = z y' = y
z' = z z' = -y z' = x
Theta = 0, Phi = pi/2:
j = 1: x' = x j = 2: x' = -z j = 3: x' = y
y' = z y' = y y' = -x
z' = -y z' = x z' = z
That is, the vector which has position angles Theta and Phi
with respect to the j_th axis in the original system, will
become the j_th axis in the rotated system. For the special
case Theta=0 this implies a rotation of Phi in the original
frame. In practice it is more convenient to think about the
inverse rotation, the one which takes the j_th versor into
the versor with Theta and Phi
5) Note that a transformation can be defined recursively,
for example with two cards pointing to the same transformation.
If Pij is the rotation corresponding to the first card and
Tij the one corresponding to the second card, the overall
rotation will be Rij = Tik Pkj
Example (number based):
ROT-DEFI 201.0 0.0 90.0 -100.0 80.0 -500.0
USRBIN 11.0 201.0 70.0 30.0 0.0 1000.0tot-dose
USRBIN 0.0 0.0 0.0 10.0 1.0 6.0&
ROTPRBIN -1.0 1.0 0.0 1.0 1.0 1.0
The same example, name based:
ROT-DEFI 201.0 0.0 90.0 -100.0 80.0 -500. FromZtoX
USRBIN 11.0 201.0 70.0 30.0 0.0 1000.0tot-dose
USRBIN 0.0 0.0 0.0 10.0 1.0 6.0&
ROTPRBIN -1.0 FromZtoX 0.0 tot-dose 0.0 0.0
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