The Combinatorial Geometry (CG) used by FLUKA is a modification of the
package developed at ORNL for the neutron and gamma-ray transport
program MORSE [Emm75] which was based on the original combinatorial
geometry by MAGI (Mathematical Applications Group, Inc.) [Gub67,Lic79].
The default input format is fixed, and different from that adopted elsewhere
in the FLUKA code. The input sequence must be completely contained between a
GEOBEGIN and a GEOEND card (see the corresponding description in 7}).
Two concepts are fundamental in CG: bodies and regions.
Originally, MORSE bodies were defined as convex solid bodies (finite
portions of space completely delimited by surfaces of first or second
degree, i.e. planes or quadrics). In FLUKA, the definition has been
extended to include infinite cylinders (circular and elliptical) and
planes (half-spaces). Use of such "infinite bodies" is encouraged since
it makes input preparation and modification much easier and less
error-prone. They also provide a more accurate and faster tracking.
Regions are defined as combinations of bodies obtained by boolean
operations: Union, Subtraction and Intersection. Each region is not
necessarily simply connected (it can be made of two or more non
contiguous parts), but must be of homogeneous material composition.
Because the ray tracing routines cannot track across the outermost
boundary, all the regions must be contained within a surrounding
"blackhole" (an infinitely absorbing material, in MORSE jargon
"external void", designated by the FLUKA material number 1), so that all
escaping particles are absorbed. It is suggested to make the external
blackhole region rather big, so as not to interfere with possible
future modifications of the problem layout. The external blackhole
must be completely surrounded by the boundary of a closed body, and
therefore cannot be defined by means of half-spaces or infinite
cylinders only. Inside such outermost boundary, EACH POINT OF SPACE MUST
BELONG TO ONE AND ONLY ONE REGION.
Note that in MORSE the concept of "region" refers to a portion of space
of homogeneous statistical importance or weight setting, which may
extend over one or several "zones" (homogeneous in material
composition). Since the two MORSE concepts of region and zone coincide in
FLUKA (there is a one-to-one correspondence), the term "region" will be
used here to define "a portion of space of uniform material composition,
obtained by boolean operations on one or more subregions", while "zone"
will indicate one of such subregions, obtained by boolean operations on
one or more geometrical bodies.
Repetition of sets of regions according to symmetry transformations is
possible in FLUKA through the card LATTICE and through a user-written
routine. This allows, for instance, to model in detail only a single cell
of a calorimeter and to replicate it in the entire volume.
Combinatorial Geometry input
CG input must respect the following sequential order:
GEOBEGIN card (in FLUKA standard format, or in free format if requested
by a previous FREE command)
Geometry title (in special format, or in free geometry format if requested
by an initial GLOBAL command)
Body data (in special or free geometry format)
END card (in special or free geometry format)
Region data (in special or free geometry format)
END card (in special or free geometry format)
LATTICE cards (optional, in FLUKA standard format, or in free format if
requested by a previous FREE command)
Region volumes (optional, see Geometry title card)
GEOEND card (in FLUKA standard format, or in free format if requested
by a previous FREE command)
GEOBEGIN card
This card follows the general FLUKA format (see description in 6}).
It can be in free format if the latter has been requested with
option FREE. The rest of the geometry must be in a special fixed
format described below, unless free geometry format has been requested
by a GLOBAL command at the beginning of input.
The meanings of the WHAT and SDUM parameters are:
WHAT(1) : flag for printing geometry error messages:
if >< 0 only a global summary is given
Default: 0.0 (all geometry error messages are printed)
WHAT(2) = used to set the accuracy parameter - reserved for
program development
WHAT(3) = logical unit from which the geometry definition has to be
read. If WHAT(3) is > 0.0 and different from the standard
input unit LUNIN (normally = 5), the name of the
corresponding file must be input on the next card.
Otherwise, the geometry input follows.
WHAT(4) = logical unit to which the geometry output has to be
directed. If WHAT(4) is > 0.0 and different from the
standard output unit LUNOUT (normally = 11), the name of
the corresponding file must be input on the next card.
Otherwise, geometry output is printed on the standard
output.
WHAT(5), WHAT(6): not used
SDUM = must be blank or = COMBINAT
For further information on the use of the GEOBEGIN card, the reader is
referred to GEOBEGIN in the section of option description.
1
Geometry Title card
Three variables are input in the CG Title card: IVOPT, IDBG, TITLE.
The format is (2I5,10X,A60).
The first integer value (IVOPT = Input Volume OPTion) is a flag to
indicate how to normalise the quantities scored in regions by the
FLUKA option SCORE.
IVOPT = 0 means that no normalisation must be performed (output
values are total stars or total energy deposited in each
region).
IVOPT = 1 and IVOPT = 2 have no meaning in FLUKA and are not
allowed.
IVOPT = 3 means that the scores must be normalised dividing by region
volumes input by the user just before the GEOEND card.
The second integer value can be used to modify the format with which
body and region data are read:
IDBG = 0 or 10 : default fixed format for both bodies and regions
= -10 : high-accuracy fixed format for bodies; default fixed region
format
= -100 : high-accuracy fixed format for bodies; region fixed format
allowing more than 10000 regions
= 100 : default fixed format for bodies; region fixed format allowing
more than 10000 regions
Note however that the maximum number of regions is dimensioned to
10000 in INCLUDE file (DIMPAR). To take advantage of the wider format
it is necessary to modify the file and to recompile the program
Any other value should be avoided. The value of IDBG is irrelevant if
free geometry format has been requested (see the GLOBAL command).
The remaining 60 characters can be used for any alphanumeric string at
the user's choice.
If fixed format is not used, the value of IDBG is irrelevant.
1
Body data
The geometry must be specified by establishing two tables. The first
table describes the type, size and location of the bodies used in the
geometry description. The second table defines the physical regions
in terms of these bodies.
Each body TYPE is referred to by a three-letter code.
There are three kinds of possible body input formats, two fixed and one free.
Free format, if used, implies necessarily also the use of free format in
region input (see below).
FIXED FORMAT BODY INPUT:
Fixed format for both body and region input is the default, unless requested
differently by a GLOBAL command at the beginning of the input file.
In fixed format, each body is defined by: its code, a sequential number, and a
set of floating point numerical parameters defining its size, position and
orientation in space (all in cm).
Default fixed format is the original CG one as used in MORSE and in other
Monte Carlo programs. It expects up to 6 floating point values per line.
High-accuracy fixed format allows to enter numerical data with full precision
(16 significant digits) and accommodates only a maximum of 3 floating point
values per line.
The fixed input format for each body depends on the value of the IDBG variable
given in the Geometry Title card (see above).
If IDBG = 0, 10 or 100, the body input format is (2X, A3, I5, 6D10.3);
if IDBG = -10 or -100, the format is (2X, A3, I5, 3D22.15);
where the 3-letter code in columns 3-5 is one of the following:
ARB BOX ELL PLA RAW RCC REC RPP SPH TRC
WED XCC XEC XYP XZP YCC YEC YZP ZCC ZEC
(columns 3-5 must be left blank in continuation cards).
The integer in columns 6-10 is the body sequential number (if left
blank numbers are assigned automatically, but this is not recommended;
it must be left blank in continuation cards).
The floating-point numbers in columns 11-76 are geometrical quantities
defining the body (their number depends on the body type as explained
below, and can extend over several continuation lines). The presence of the
decimal values in the numerical data is compulsory.
After the last body description, end with a card having the code END
in columns 3-5.
FREE FORMAT BODY INPUT:
Free format is used for both body and region input only if requested by a GLOBAL
command at the beginning of the input file or by the string COMBNAME in the
SDUM field of the GEOBEGIN command.
In free format, each body is defined by: its code, its identifier (an alphanumeric
string of up to 8 characters, with the first character alphabetical) and a set of
numerical parameters defining its size, position and orientation in space (all
in cm).
Free format has been introduced only recently and is expected to supersede soon
the other formats, which will be kept however for reasons of back compatibility.
Its main advantages, in addition to the freedom from strict alignment rules,
are the possibility to modify the input sequence without affecting the region
description (for instance, by inserting a new body) and the availability of
parentheses to perform complex boolean operations in the description of regions.
The input for each body consists of a 3-letter code indicating the body type
ARB BOX ELL PLA RAW RCC REC RPP SPH TRC
WED XCC XEC XYP XZP YCC YEC YZP ZCC ZEC
followed by a unique "body name" (alphanumeric identifier) and a set of
geometrical quantities defining the body (their number depends on the body type
as explained below). The different items, separated by one or more blanks, or by
one of the separators "," "/" ";" "\" ":" can extend over as many lines as needed.
See option FREE for more detailed instructions on the use of separators.
After the last body description, end with a line having the code END
With all input formats, a card having an asterisk (*) in column 1 is treated
as a comment card. Such comment cards can be inserted freely at any point of
Body and Region input, allowing easier identification.
Body types
1. Rectangular Parallelepiped. Code: RPP
An RPP has its edges parallel to the coordinate axes.
It is defined by 6 numbers in the following order:
X_min, X_max, Y_min, Y_max, Z_min, Z_max (minimum and maximum
coordinates which bound the parallelepiped).
An RPP definition extends over one single card in default fixed format,
or over two cards in high-accuracy body fixed format (IDBG = -10 or -100
in the CG Title card, see above).
Example in default fixed format (the comment lines shown are allowed input
lines):
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
RPP 4 -20.0 +20.0 -50.0 +50.0 -38.5 +38.5
* (a parallelepiped centreed on the origin)
The same input, in high-accuracy fixed format, would be:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
RPP 4 -20.0 +20.0 -50.0
+50.0 -38.5 +38.5
The same, in free format:
RPP Smlbrick -20.0 +20.0 -50.0 +50.0 -38.5 +38.5
2. General Rectangular Parallelepiped. Code: BOX
A BOX is also a Rectangular Parallelepiped, but with arbitrary
orientation in space. Its use is generally not recommended, since it
can be replaced by a suitable combination of infinite planes (PLA,
XYP, XZP, YZP). Planes are easier to define, make tracking more
accurate and often only a few are needed in a region description.
A BOX is defined by 12 numbers in the following order:
V_x, V_y, V_z (coordinates of a vertex), H1_x, H1_y, H1_z,
H2_x, H2_y, H2_z, H3_x, H3_y, H3_z (x, y and z components of three
mutually PERPENDICULAR vectors representing the height, width and
length of the box). Note that it is the user's responsibility to
ensure perpendicularity. This is best attained if the user has chosen
high-accuracy input fixed format (IDBG = -10 or -100 in the CG Title card,
see above), or free format, and the value of each vector component is
expressed with the largest available number of significant digits.
A BOX definition extends over 2 cards in default fixed format, or
over 4 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
BOX 18 0.0 0.0 0.0 7.0710678 7.0710678 0.0
-14.142136 14.142136 0.0 0.0 0.0 30.0
* (a parallelepiped with a corner on the origin, with edges 10, 20 and
* 30 cm long, rotated counterclockwise by 45 degrees in the x-y plane)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
BOX 18 0.0 0.0 0.0
7.071067811865475 7.071067811865475 0.0
-14.14213562373095 14.14213562373095 0.0
0.0 0.0 30.0
The same, in free format:
BOX tiltslab 0.0 0.0 0.0 7.071067811865475 7.071067811865475 0.0
-14.14213562373095 14.14213562373095 0.0 0.0 0.0 30.0
3. Sphere. Code: SPH
A SPH is defined by 4 numbers:
V_x, V_y, V_z (coordinates of the centre), R (radius)
A SPH definition extends over one single card in default fixed format,
or over two cards in high-precision body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
SPH 002 5.0 -30.0 27.0 528.2
* (a sphere centreed at point x=5, y=30, z=27, with a radius of 528.2 cm)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
SPH 002 5.0 -30.0 27.0
528.2
The same, in free format:
SPH TheBall 5.0 -30.0 27.0 528.2
4. Right Circular Cylinder. Code: RCC
An RCC can have any orientation in space. It is limited by a
cylindrical surface and by two plane faces perpendicular to its
axis. (If the cylinder axis is parallel to one of the coordinate
axes, it is worth considering instead the use of an infinite
cylinder XCC, YCC or ZCC (see below), leading to increased tracking
speed).
Each RCC is defined by 7 numbers:
V_x, V_y, V_z (coordinates of the centre of one of the circular
plane faces), H_x, H_y, H_z (x, y and z components of a vector
corresponding to cylinder height, pointing to the other plane face),
R (cylinder radius).
An RCC definition extends over 2 cards in default fixed format, or over
3 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
RCC 07 5.0 5.0 5.0 57.735027 57.735027 57.735027
37.
* (a circular cylinder 100 cm long and of 37 cm radius, with base
* centred at point x=5, y=5, z=5, its axis making equal angles to
* the coordinate axes).
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
RCC 07 5.0 5.0 5.0
57.73502691896258 57.73502691896258 57.73502691896258
37.
The same, in free format:
RCC BYGCYL 5.0 5.0 5.0 57.73502691896258 57.73502691896258
57.73502691896258 37.
5. Right Elliptical Cylinder. Code: REC
A REC can have any orientation in space.
It is limited by a cylindrical elliptical surface and by two plane
faces perpendicular to its axis. (If the cylinder axis is parallel
to one of the coordinate axes, it is worth considering instead the
use of an infinite cylinder XEC, YEC or ZEC (see below), leading to
increased tracking speed).
Each REC is defined by 12 numbers:
V_x, V_y, V_z (coordinates of the centre of one of the elliptical
plane faces), H_x, H_y, H_z (x, y and z components of a vector
corresponding to cylinder height, pointing to other plane face),
R1_x, R1_y, R1_z (components of a vector corresponding to the minor
half-axis of the cylinder elliptical base), R2_x, R2_y, R2_z
(ditto for the major half-axis).
A REC definition extends over 2 cards in default fixed format, or over
4 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
REC 1 -10.0 12.0 7.0 0.0 58.0 0.0
9. 0.0 0.0 0.0 0.0 17.0
* (an elliptical cylinder 58 cm long parallel to the y axis, with minor
* half-axis 9 cm long parallel to the x coordinate axis, major
* half-axis 17 cm long parallel to the z axis, base centreed at point
* x=-10, y=12, z=7)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
REC 1 -10.0 12.0 7.0
0.0 58.0 0.0
9. 0.0 0.0
0.0 0.0 17.0
The same, in free format:
REC pipesurf -10.0 12.0 7.0 0.0 58.0 0.0 9.0 0.0 0.0 0.0 0.0 17.0
6. Truncated Right Angle Cone. Code: TRC
A TRC can have any orientation in space.
It is bounded by a conical surface and by two circular plane faces
perpendicular to the axis of the cone.
Each TRC is defined by 8 numbers:
V_x, V_y, V_z, (coordinates of the centre of the major circular
base), H_x, H_y, H_z (components of a vector corresponding to the
TRC height, directed from the major to the minor base), R1 (radius
of the major base), R2 (radius of the minor base)
A TRC definition extends over 2 cards in default fixed format, or over
3 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
TRC 102 0.0 0.0 -130.0 0.0 0.0 1000.0
600. 150.0
* (a truncated cone 1000 cm long parallel to the z axis, with the
* larger circular base 600 cm in radius located at z = -130 and the
* smaller base 150 cm in radius located at z = 870)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
TRC 102 0.0 0.0 -130.0
0.0 0.0 1000.0
600. 150.0
The same, in free format:
TRC NewCone 0.0 0.0 -130.0 0.0 0.0 1000.0 600. 150.0
7. Ellipsoid of Revolution. Code: ELL
An ELL is a prolate (cigar-shaped) ellipsoid, obtainable by
revolution of an ellipse around its major axis, and having any
orientation in space.
Each ELL is defined by 7 numbers:
F1_x, F1_y, F1_z, F2_x, F2_y, F2_z, (coordinates of the two foci
on the major ellipsoid axis), L (full length of the major axis).
An ELL definition extends over 2 cards in default fixed format, or over
3 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
ELL 003 -400.0 0.0 0.0 400.0 0.0 0.0
1000.
* (an ellipsoid obtained by revolution around the x axis of an ellipse
* centred at the origin, with major axis parallel to x 1000 cm long and
* minor axis 600 cm long).
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
ELL 003 -400.0 0.0 0.0
400.0 0.0 0.0
1000.
The same, in free format:
ELL TheCigar -400.0 0.0 0.0 400.0 0.0 0.0 1000.0
8. Right Angle Wedge. Code: WED or RAW
A WED is the half of a BOX (see), cut by a plane passing through
its centre and through four corners. Its use, like that of the BOX,
is now mostly superseded by the availability of infinite planes
(XYP, XZP, YZP and PLA).
A WED is defined by 12 numbers:
V_x, V_y, V_z (coordinates of one of rectangular corners), H1_x,
H1_y, H1_z, H2_x, H2_y, H2_z, H3_x, H3_y, H3_z (x, y and z
components of three mutually PERPENDICULAR vectors corresponding
to the height, width and length of the wedge). Note that it is the
user's responsibility to ensure perpendicularity. This is best attained
if the user has chosen high-accuracy input fixed format (IDBG = -10 or -100
in the CG Title card, see above), or free format, and the value of each
vector component is expressed with the largest available number of
significant digits.
The face defined by vectors 1 and 3 and that defined by vectors 2
and 3 are rectangular; the 2 faces defined by vectors 1 and 2 are
triangular; the fifth face is rectangular with two edges parallel
to vector 3 and two edges parallel to the hypotenuse of the
triangle made by vectors 1 and 2.
A WED definition extends over 2 cards in default fixed format, or over
4 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
WED 97 0.0 0.0 0.0 7.0710678 7.0710678 0.0
-14.142136 14.142136 0.0 0.0 0.0 30.0
* (the bottom half of a parallelepiped with a corner on the origin,
* with edges 10, 20 and 30 cm long, rotated counterclockwise by 45
* degrees in the x-y plane)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
WED 97 0.0 0.0 0.0
7.071067811865475 7.071067811865475 0.0
-14.14213562373095 14.14213562373095 0.0
0.0 0.0 30.0
The same, in free format:
WED halfbox1 0.0 0.0 0.0 7.071067811865475 7.071067811865475
0.0 -14.14213562373095 14.14213562373095 0.0 0.0 0.0 30.0
9. Arbitrary Convex Polyhedron of 4, 5, or 6 sides. Code: ARB
An ARB is a portion of space bounded by 4, 5 or 6 plane faces.
Its use is rather complicated and is now superseded by the
availability of infinite planes (XYP, XZP, YZP and PLA).
For completeness, however, a description of input will be reported
here.
Assign an index (1 to 8) to each vertex. For each vertex, give
the x, y, z coordinates on 4 cards (8 cards in high-accuracy body
fixed format), with 6 numbers on each card (3 numbers per card in
high-accuracy fixed format):
V1_x, V1_y, V1_z, V2_x, V2_y, V2_z,
V3_x, V3_y, V3_z, V4_x, V4_y, V4_z,
V5_x, V5_y, V5_z, V6_x, V6_y, V6_z,
V7_x, V7_y, V7_z, V8_x, V8_y, V8_z
The vertices not appearing in face descriptions are ignored, but
eight must always be supplied. The above vertex cards are followed
by one card describing the faces (two cards in high-accuracy fixed format).
Each face is described by a four-digit number in floating point format,
such that each digit gives the indices of the three or four vertex
points of that face. These indices must be entered in the same order
for each face (i.e. all clockwise or all counterclockwise).
When the number of the faces is less than 6, the remaining face
description(s) must be zero, and must appear at the end of the
list. If a face has three vertices, the omitted position may be
either 0 or a repeat of one of the other vertices.
An ARB definition extends over 5 cards in default fixed format, or over
10 cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
ARB 5 -44.2 -36.5 3572.0 -44.2 -33.5 3572.0
-37.1 -31.0 3572.0 -37.1 -39.0 3572.0
-44.2 -36.5 0.0 -44.2 -33.5 0.0
-37.1 -31.0 0.0 -37.1 -39.0 0.0
1234. 1562. 5876. 1485. 4378. 6732.
* (a right prism of trapezoidal base, of height 3572 cm parallel to the
* z axis)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
ARB 5 -44.2 -36.5 3572.0
-44.2 -33.5 3572.0
-37.1 -31.0 3572.0
-37.1 -39.0 3572.0
-44.2 -36.5 0.0
-44.2 -33.5 0.0
-37.1 -31.0 0.0
-37.1 -39.0 0.0
1234. 1562. 5876.
1485. 4378. 6732.
The same, in free format:
ARB oddbody -44.2 -36.5 3572.0 -44.2 -33.5 3572.0 -37.1 -31.0 3572.0 -37.1
-39.0 3572.0 -44.2 -36.5 0.0 -44.2 -33.5 0.0 -37.1 -31.0 0.0 -37.1
-39.0 0.0 1234. 1562. 5876. 1485. 4378. 6732.
10. Infinite half-space delimited by a coordinate plane. Code: XYP, XZP, YZP
There are 4 kinds of infinite half-spaces. Three of them are delimited by
planes perpendicular to the coordinate axes:
Delimited by a plane perpendicular to the x-axis. Code: YZP
or by a plane perpendicular to the y-axis. Code: XZP
or by a plane perpendicular to the z-axis. Code: XYP
Each of these half-spaces is defined by a single number:
V_x (resp. V_y, or V_z), the coordinate of the plane on the
corresponding perpendicular axis.
The half-space "inside the body" is the locus of points for
which x < V_x (resp. y < V_y, or z < V_z).
An YZP, XZP, XYP definition, in fixed format, extends always over
a single card.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
YZP 71 -44.2
XZP 72 108.0
XYP 73 0.0
* (respectively, all points having x < -44.2, those having y < 108,
* and those having z < 0).
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
YZP 71 -44.2
XZP 72 108.0
XYP 73 0.0
The same example in free format:
YZP horizPla -44.2
XZP vertPla1 108.0
XYP vertPla2 0.0
11. Generic infinite half-space. Code: PLA
Each PLA is defined by 6 numbers:
H_x, H_y, H_z (x, y and z components of a vector of arbitrary length
perpendicular to the plane), V_x, V_y, V_z (coordinates of any point
lying on the plane).
The half-space "inside the body" is that from which the vector is pointing
(i.e., the vector points "outside").
A PLA definition extends over a single card in default fixed format, and
over two cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
PLA 74 0.0 1.0 1.0 200.0 -300.0 240.0
* (all points "below" a plane at 45 degrees in the y-z projection which
* passes through the point x=200, y=-300, z=240 - note that for such a
* plane the x value of the point is completely irrelevant - )
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
PLA 74 0.0 1.0 1.0
200.0 -300.0 240.0
The same example in free format:
PLA tiltPla 0.0 1.0 1.0 200.0 -300.0 240.0
12. Infinite Circular Cylinder parallel to a coordinate axis. Code: XCC, YCC, ZCC
A XCC (YCC, ZCC) is an infinite circular cylinder parallel to the
x (y, z) axis.
Each XCC (YCC, ZCC) is defined by 3 numbers:
A_y, A_z (A_z, A_x for YCC, A_x, A_y for ZCC) (coordinates of the
cylinder axis), R (cylinder radius)
An XCC (YCC, ZCC) definition, in fixed format, extends always over one
single card.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
XCC 013 -480.0 25.0 300.0
* (an infinite cylinder of radius 300 cm, with axis defined by y=-480,
* z=25)
ZCC 014 0.0 0.0 2.5
* (an infinite cylinder of radius 2.5 cm, with axis equal to the z axis)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
XCC 013 -480.0 25.0 300.0
ZCC 014 0.0 0.0 2.5
The same, in free format:
XCC Column -480.0 25.0 300.0
ZCC Tunnel 0.0 0.0 2.5
13. Infinite Elliptical Cylinder parallel to an axis. Code: XEC, YEC, ZEC
A XEC (YEC, ZEC) is an infinite elliptical cylinder parallel to the
x (y, z) axis, and with the axes of the ellipse parallel to the other
two coordinate axes. !!! In which order??? !!!
Each XEC (YEC, ZEC) is defined by 4 numbers:
A_y, A_z (A_z, A_x for YEC, A_x, A_y for ZEC) (coordinates of the
cylinder axis), L_y, L_z (L_z, L_x for YEC, L_x, L_y for ZEC)
(semiaxes of the ellipse).
A XEC (YEC, ZEC) definition extends over one single card in default
fixed format, and over two cards in high-accuracy body fixed format.
Example in default fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
ZEC 101 15.0 319.0 33.0 80.0
* (an infinite elliptical cylinder, centreed on x=15, y=319, with the
* ellipse minor semi-axis parallel to x, 33 cm long, and the major
* semi-axis parallel to y, 80 cm long)
The same example in high-accuracy body fixed format:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7....+.
ZEC 101 15.0 319.0 33.0
80.0
The same body, described in free format:
ZEC ChimneyA 15.0 319.0 33.0 80.0
NOTE
+---------------------------------------------------------------------+
| Whenever it is possible, the following bodies should be preferred: |
| PLA, RPP, SPH, XCC, XEC, XYP, XZP, YCC, YEC, YZP, ZCC, ZEC |
| These should indeed make tracking faster, since for them extra |
| coding ensures that unnecessary boundary intersection calculations |
| are avoided when the length of the next step is smaller than the |
| distance to any boundary of the current region. |
+---------------------------------------------------------------------+
Body END card
Body definitions must be terminated by a card with the string END (in
column 3-5 if fixed format is used).
1
Region data
The various regions are described in terms of differences, intersections
and unions of bodies. As in the case of body description, the user has the
choice between free format and two kinds of fixed format. One of the latter
is the traditional format used by the original Combinatorial Geometry as
implemented for example in MORSE. The other fixed format is similar to it, but
has been extended to allow body numbers larger than 10000. Both fixed
formats are now superseded by the more convenient free region input format,
recently introduced. Free format is based on body mnemonic "names" instead
of sequential numerical identifiers and allows the use of parentheses to
perform more complex boolean operations. However, the two fixed formats are
still available for back compatibility reasons.
With any input format, a line having an asterisk (*) in column 1 is
treated as a comment card.
FIXED FORMAT REGION INPUT:
Each region is described as a combination of one or more bodies, by means
of the three operator symbols:
-, +, OR
referring respectively to the boolean operations of subtraction (or
complement), intersection and union.
Each body is referred to by its sequential number in the body description
table (see above the description of fixed format body input).
Input for each region extends on one or more cards, in a format which
depends on the value of IDBG on the Geometry Title card (see above).
If IDBG = 0, 10 or -10, region input format is (2X,A3,I5,9(A2,I5));
if IDBG = 100 or -100, region input format is (2X,A3,I5,7(A2,I7));
=> where the 3 characters in columns 3-5 are:
- on the first input card of a given region, an arbitrary non-blank
string chosen by the user (it can be used, together with optional
comment cards, to help identifying the region or the region
material).
Note that regions are identified in the code by an integer number
corresponding to the order of their input definition: therefore it
can be useful (but not mandatory) to have that number appearing in
the string. For instance, if the 5th region is air, it could be
labelled AI5.
- on all continuation cards, columns 3-5 must be blank.
=> the integer in columns 6-10 (variable NAZ) is the number of regions which
can be entered by a particle leaving any of the bodies defined for the
region being described (leave blank in continuation cards). The NAZ
number is used to allocate memory for this so-called "contiguity list",
and it is not essential that it be exact (if left blank, it is set to 5).
Any number is accepted, but if the final sum of these integers is close to
the actual sum, tracking speed can be slightly improved.
=> in columns 11-73, alternate as many 2-character fields ('OR' or
blank) and integer fields (body numbers preceded by + or - sign),
as are needed to complete the description of that region (see below
for an explanation of symbol meaning). If one card is not sufficient,
any number of continuation cards can be added (identified by a
blank field in column 3-5).
After the last region description, end with a card having the code END
in columns 3-5.
- If a body number appears in a zone description preceded by a +
operator, it means that the zone being described is wholly contained
inside the body (boolean intersection).
- If a body number appears in a zone description preceded by a -
operator, it means that the zone being described is wholly outside
the body (boolean complement).
Obviously, in the description of each region the symbol + must appear at
least once. Examples:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7..
BA1 4 +7 +3
* (the above zone is the part of space common to body 7 and 3)
MU2 7 +3 -4 -7 +20
* (the above zone is the part of space common to body 3 and 20,
* excluding however that which is inside body 4 and that which is
* inside 7)
AIR 5 +19
* (the latter zone coincides entirely with body 19)
- In some instances a region may be described in terms of subregions
(or "zones") lumped together. The OR operator is used as a boolean union
operator in order to combine subregions (partially overlapping or not).
Subregions (also called "zones" in this manual) are formed as
intersections or differences as explained above, and then the region is
formed by a union of these subregions. When OR operators are used there
are always two or more of them, and they refer to all body numbers
following them until the next OR or the end of the region description,
each body being preceded by its + or - sign.
Examples:
*...+....1....+....2....+....3....+....4....+....5....+....6....+....7...
SA7 11OR +4 +6 -7 -8OR +6 +3 -21
* <---- first subregion -----><- second subregion ->
G18 2OR +9OR +15OR +1OR +8 -2OR +8 -3OR +8 +18
* < 1st >< 2nd >< 3rd ><--- 4th ----><--- 5th ----><--- 6th ---->
OR +12 -10 -11 -13 -14
*< blank ><---- 7th and last subregion -----> (continuation line)
Region END card
Region data must be terminated by a card with the string END in
column 3-5.
FREE FORMAT REGION INPUT:
Each region is described as a combination of one or more bodies, by means
of the three operator symbols:
-, +, |
referring respectively to the boolean operations of subtraction (or
complement), intersection and union.
Each body is referred to by its "name" (an alphanumeric string of up to
8 characters, the first character being alphabetical) in the body description
table (see above the description of free format body input).
Input for each region starts on a new line and extends on as many continuation
lines as are needed. It is of the form:
REGNAME NAZ boolean zone expression
or
REGNAME NAZ | boolean zone expression | boolean zone expression | ...
where REGNAME, NAZ and the remaining part are separated by one or more blanks.
- REGNAME is the region "name" (an arbitrary unique alphanumeric character
string chosen by the user). The region name must begin by an
alphabetical character and must not be longer than 8 characters.
- NAZ is an integer indicating (approximately) the number of regions which
can be entered by a particle leaving any of the bodies appearing in the
region description that follows. The NAZ number is used to allocate memory
for this so-called "contiguity list", and it is not essential that it be
exact. Any number is accepted, but if the final sum of these integers is
close to the actual sum, tracking speed can be slightly improved. If the
input value of NAZ is equal to 0, it is set equal to 5.
- "boolean zone expression" is a sequence of one or more body names preceded
by the operators + (intersection) or - (complement or subtraction). A zone
expression can be contained inside one or more sets of left and right
parentheses. Several zone expressions can be combined by the union
operator | (corresponding to OR in fixed format input).
When | operators are used there are always two or more of them, and they
refer to all bodies following them until the next | or the end of the
region description, each body being preceded by its + or - sign.
In evaluating the expressions, the highest operator precedence is given to
parentheses (the most inner ones first), followed by the | operator.
In each zone expression, at least one body name preceded by + must be
present. If one line is not sufficient, any number of continuation lines
can be added. Blanks are ignored.
Meaning of the operators:
- If a body name is preceded by a + operator in an expression describing a
zone (or a zone component surrounded by parentheses) it means that the zone
or zone component being described is wholly contained inside the body (boolean
intersection).
- If a body name is preceded by a - operator in an expression describing a
zone (or a zone component surrounded by parentheses) it means that the zone
or zone component being described is wholly outside the body (boolean
complement).
Obviously, in the description of each region the symbol + must appear at least
once. The same is true for each zone (subregion delimited by | operators) and
for each zone component (subzone delimited by parentheses)
Examples of regions consisting of a single zone:
lastlayr 4 +bigball +slab
* Region "lastlayr" is the part of space common to body "bigball" and body
* "slab"
MidVacuu 7 +cylind2 -slit -sqrhole +Plane1
* Region "MidVacuu" is the part of space common to bodies "cylind2" and
* "Plane1", excluding however that which is inside body "slit" and that which
* is inside body "sqrhole"
H2Osphere 5 +marble
* Region "H2Osphere" coincides entirely with body "marble"
Examples of regions consisting of the union of several zones, possibly (but
not necessarily) partially overlapping:
Corners 6 | +dice +topNorth | +dice +topEast | +dice +topSouth |
+dice +topWest | +dice +botNorth | +dice +botEast | +dice +botSouth | +dice
+botWest
* Region "Corners" is made of the 8 corners of a cube, each of which is
* obtained by the intersection of a cubic body "dice" and a tilted plane
* described by vector pointing to the centre of the cube
twoparts 0 | +leftpart -outerbox | +rghtpart +topplane
* Region "twoparts" is the sum of two parts of space: the space points which
* are inside body "leftpart" but not inside body "outerbox", plus those which
* are common to bodies "rghtpart" and "topplane"
Examples of a region defined as a single zone by means of parentheses:
AirAroun 5 + tunnel + Column - (+outrpipe-innrpipe)
* Region "AirAroun" contains the space points located inside the intersection
* of body "tunnel" and body "Column", with the exception of those which are
* inside body "outrpipe" but not inside body "innrpipe"
CmplexRg | +longcyl + (+shortcyl +vertPla1 -vertPla2) | (+Brick | + ceeling
- floor)
* Region CmplexRg is the union of two zones. The first zone is the
* intersection of body "longcyl" with a portion of space contained inside
* both bodies "shortcyl" and "vertPla1" but not inside body "vertPla2".
* The second zone is the union of the space points inside body "Brick"
* and the space points contained by body "ceeling" but located outside
* body "floor".
Region END card
Region data must be terminated by a line with the string END.
Region Volumes
This is an optional set of cards which must be input if (and only if)
flag IVOPT in the CG Title card has been given a value 3. As many volume
definition cards must be given as is needed to input a volume for every
region. The input variable is an array VNOR(I) = volume of the
Ith region. The format is (7E10.5). Volume data are used by FLUKA only
to normalise energy or star densities in regions requested by the
SCORE command.
1
LATTICE card
This is an optional card for modular geometries. Its use needs some
more effort and preparation:
- The basic unit of the geometry, composed by an arbitrary number of
regions, must be described in full detail in the body and region data.
- Additional body and region data must also be provided to describe
"container" regions representing the "boxes", or lattice cells, wherein
the basic unit has to be replicated. No material assignment is needed for
these lattice-cell regions.
- A roto-translation must be defined (option ROT-DEFI) and
associated with each lattice to provide the transformation bringing from
any point and direction inside each lattice cell to the corresponding
point and direction in the basic unit. Alternatively, a user routine
(LATTIC, see 13}) can be written for the same purpose.
- The LATTICE card itself identifies the lattice cells and establishes the
correspondence between region number and lattice cell number, where the
region number is the sequential number in the region table, and the
lattice cell number is that used in the tracking to address the
transformation routine, and is chosen by the user. Contiguous numbering
is recommended for memory management reasons, but is not mandatory.
Non-contiguous numbering can be done using several LATTICE cards.
In the LATTICE card, the meanings of the WHAT parameters are:
WHAT(1) = "Container-region" number of the first lattice cell
("From region WHAT(1)...")
No default
WHAT(2) = "Container-region" number of the last lattice cell
("...to region WHAT(2)...")
Default = WHAT(1)
WHAT(3) = step length in assigning "Container-region" numbers
("...in steps of WHAT(3)").
Default = 1.
WHAT(4) = lattice number of the first lattice cell, assigned to
region WHAT(1)
No default
WHAT(5) = lattice number of the last lattice cell, assigned to
region WHAT(2)
WHAT(6) = step length in assigning cell numbers
("...in steps of WHAT(6)").
Default = 1.
SDUM = possible index of transformation associated with this lattice.
Exceptionally, here SDUM can contain an integer number, in free
format, following any of the strings "ROT#", "Rot#", "rot#",
"RO#", "Ro#", "ro#. If any one of such strings is present, an
integer identifying the associated roto-translation is read in
the following characters. If no such string is found, the LATTIC
user routine will beg called whenever a transformation is
required.
A single geometry can be a mixture of modular areas, described by lattices,
and "normal" areas, described by standard regions.
Many different LATTICE cards may be issued in the same geometry,
when different symmetries are present in different areas. In principle,
any analytical symmetry transformation can be implemented
(rotation, translation, reflection, or combination of these).
Care must be taken to ensure that any region in the basic unit is fully
contained (after coordinate transformation) in any lattice cell
belonging to its symmetry transformation. Regions falling across two
different lattice cells would lead to unpredictable behaviour.
The basic unit does not need necessarily to describe a "real" geometry
region, but can as well be used only as a prototype to reproduce in
any number of "copies".
NOTE: The lattice cell regions do not need to be included in the other input
option cards. Materials, thresholds, etc, must be assigned ONLY to the
regions contained in the basic unit. Of course, this implies that all
copies of a same basic unit share the same material, setting and biasing
properties.
1
GEOEND card
A card with the string GEOEND in column 1-6 must terminate the
combinatorial geometry input.
Geometry debugger:
The GEOEND card can be used also to activate the geometry debugger,
using the WHAT and SDUM parameters. In this case, a second GEOEND
card (continuation) may be necessary. It is recommended that a STOP
card should follow immediately, avoiding to start transport when
debugging is completed.
1st GEOEND card:
WHAT(1) = X_max of the geometry region to be debugged (no default)
WHAT(2) = Y_max of the geometry region to be debugged (no default)
WHAT(3) = Z_max of the geometry region to be debugged (no default)
WHAT(4) = X_min of the geometry region to be debugged (no default)
WHAT(5) = Y_min of the geometry region to be debugged (no default)
WHAT(6) = Z_min of the geometry region to be debugged (no default)
SDUM: must be = DEBUG to activate the debugger
2nd (optional) GEOEND card:
WHAT(1) = Number of steps in the x-direction between
X_min and X_max (default: 20)
WHAT(2) = Number of steps in the y-direction between
Y_min and Y_max (default: 20)
WHAT(3) = Number of steps in the z-direction between
Z_min and Z_max (default: 20)
WHAT(4,5,6) : not used
SDUM = & in any position in column 71 to 78
See the Notes to GEOEND option for more details and instructions.
1 Voxel Geometry
--------------
It is possible to describe a complex geometry in terms of "voxels" (tiny
parallelepipeds forming a 3-dimensional grid). In principle this can be
done with any geometry but it is especially useful when translating a CT scan
of a human body into a dosimetry phantom [Zan01]. Therefore, we will use
loosely the word "organ" to indicate a contiguous group of voxels (or even
more than one group) made of the same material. The code handles each organ as a
Combinatorial Geometry region, possibly in addition to other conventional
"non-voxel" regions defined by the user, and assigns automatically to each
organ a new region number.
To describe a voxel geometry, the user must:
1) Assign an organ to each voxel. Each organ is identified by a unique integer
=< 32767. The numbering does not need to be contiguous, i.e. "holes"
in the numbering sequence are allowed. One of the organs must have number 0
and plays the role of the medium surrounding the voxels (usually vacuum or
air).
The assignment is done via a special file where the organ corresponding to
each voxel is listed sequentially in Fortran list-oriented format, with the
x coordinate running faster than y, and y running faster than z.
In practice the file is always written by a program similar to the one
reported below. The user will need to modify the values of the parameters
DX, DY DZ, NX, NY, NZ (respectively voxel size and number of voxels for
each coordinate), and possibly some other more trivial things (file names,
title, reading from the original CT scan file).
The following program takes also care of recompacting the original organ
numbers by eliminating all gaps in the sequence, and writes a translation
table to the screen:
WRITE(*,'(A,2I10)')' New number, old number: ', NO, IC
After having modified the program (assumed to be in a file writegolem.f),
compile it:
fff writegolem.f
link it with the FLUKA library:
lfluka -o writegolem writegolem.o
execute it:
writegolem
The result will be a file golem.vxl (or equivalent name chosen by the user)
which will be referred to by a special command line in the geometry input
(see below).
*------------------------------------------------------------------------------
PROGRAM WRITEGOLEM
INCLUDE '(DBLPRC)'
INCLUDE '(DIMPAR)'
INCLUDE '(IOUNIT)'
* COLUMNS: FROM LEFT TO RIGHT
* ROWS: FROM BACK TO FRONT
* SLICES: FROM TOP TO BOTTOM
PARAMETER ( DX = 0.208D+00 )
PARAMETER ( DY = 0.208D+00 )
PARAMETER ( DZ =-0.8D+00 )
PARAMETER ( NX = 256 )
PARAMETER ( NY = 256 )
PARAMETER ( NZ = 220 )
DIMENSION GOLEM(NX,NY,NZ)
INTEGER*2 GOLEM
CHARACTER TITLE*80
DIMENSION IREG(1000), KREG(1000)
INTEGER*2 IREG, KREG
*
CALL CMSPPR
DO IC = 1, 1000
KREG(IC) = 0
END DO
OPEN(UNIT=30,FILE='ascii_segm_golem',STATUS='OLD')
READ(30,*) GOLEM
NO=0
MO=0
DO IZ=1,NZ
DO IY=1,NY
DO IX=1,NX
IF (GOLEM(IX,IY,IZ) .GT. 0) THEN
IC = GOLEM(IX,IY,IZ)
MO = MAX (MO,IC)
DO IR=1,NO
IF (IREG(IR) .EQ. IC) GO TO 1000
END DO
NO=NO+1
IREG(NO)=IC
KREG(IC)=NO
WRITE(*,'(2I10)')' New number, old number: ', NO, IC
1000 CONTINUE
END IF
END DO
END DO
END DO
* NO = number of different organs
* MO = max. organ number before compacting
WRITE(*,*) ' NO,MO',NO,MO
OPEN(UNIT=31,FILE='golem.vxl',STATUS='UNKNOWN',FORM='UNFORMATTED')
TITLE = 'Golem'
WRITE(31) TITLE
WRITE(31) NX,NY,NZ,NO,MO
WRITE(31) DX,DY,DZ
WRITE(31) GOLEM
WRITE(31) (KREG(IC),IC=1,MO)
STOP
END
*----------------------------------------------------------------------
2) Prepare the usual FLUKA input file. The geometry must be written like
a normal Combinatorial Geometry input (in any of the allowed formats,
as part of the normal input stream or in a separate file), but
in addition must include:
* A VOXELS card as a first line, before the Geometry title card,
with the following information:
WHAT(1), WHAT(2), WHAT(3) = x, y, z coordinates chosen as the
origin of the "voxel volume", i.e. of a region made of a
single RPP body which contains all the voxels
WHAT(4), WHAT(5), WHAT(6): not used
SDUM = name of the voxel file (extension will be assumed to be .vxl).
* The usual list of NB bodies, not including the RPP corresponding to the
"voxel volume" (see VOXELS card above). This RPP will be generated and
added automatically by the code as the (NB+1)th body, with one corner in
the point indicated in the VOXELS card, and dimensions NX*DX, NY*DY
and NZ*DZ as read from the voxel file.
* The usual region list of NR regions, with the space occupied by body NB+1
(the "voxel volume") subtracted. In other words, the NR regions listed
must cover the whole available space, excepted the space corresponding to
the "voxel volume". This is easily obtained by subtracting body NB+1
in the relevant region definitions, even though this body is not
explicitly input at the end of the body list.
The code will automatically generate and add several regions:
- a region NR+1: this is a sort of "cage" for all the voxels. Nothing
(energy etc.) should ever be deposited in it: the user shall assign
vacuum to it.
- a region NR+2 containing all voxels belonging to organ number 0.
There must be at least 2 of such voxels, but in general they should
be many more. Typical material assignment to region NR+2 is air.
- NO additional regions, where NO = number of non-zero organs:
region NR+3 corresponding to organ 1
region NR+4 corresponding to organ 2
.......................................
region NR+2+NO corresponding to organ NO
The assignment of materials shall be made by command ASSIGNMAt
(and in a similar way other region-dependent options) referring to
the first NR regions in the usual way, and to the additional regions
using the correspondence to organs as explained above.
