Volume creation

First lets look at an very simple geometry description. The following example just describe a box that contains a sphere.

GEOM
  MODU 0
    TYPE t1 BOX 10. 10. 10.
    VOLU v1 0 t1 material1 0. 0. 0.

    TYPE t2 SPHE 10.
    VOLU v2 v1 t2 material2 0. 0. 0.
  ENDM
ENDG

You can see two kind of entity: the volumes (VOLU) and the types (TYPE) that describe the shape of the volumes. Let’s explaine this two entities.

Volume syntax

The VOLU keyword creates an elementary volume.

Block syntax

VOLU id cont type mat x y z

Input parameter	Description
id	Unique identifier within the current module
cont	A parent volume, i.e. a volume in which it is completely included
type	Corresponding shape
mat_id	Material composition that will fill the volume
x y z	Position within the module (the meaning of the position depends of the `TYPE`)

Note

The type must be declared before the corresponding volume.
The parent volume must be declared before the corresponding volume.

Type syntax

A TYPE is a concept that associates the following quantities within a given entity:

a three-dimensional convex shape (see below).
the dimensions of the shape.

Block syntax

TYPE id shape  args

Input parameter	Description
id	Shape (or Type) identifier
shape	Keywords associated to a predefined shape
args	Arguments related to the shape keyword (see below)

A TYPE is created in a module and is labelled with a unique identifier within the module and can be used multiple times.

Here are some examples:

examples

* Type 1 is a sphere with a radius of 3.2 cm
TYPE  1  SPHE  3.2

* Type 2 is a box with the following dimensions:
* o 40.0 cm along the X-axis;
* o 20.4 cm along the Y-axis;
* o 13.2 cm along the Z-axis.
TYPE  2  BOX   20.  10.2   6.6

* Type 3 is a cylinder parallel to X-axis, with a 12 cm radius and a height of 40.5 cm.
TYPE  3  CYLX  12.  20.25

Available finite shapes

Sphere

The SPHE keyword is used to describe a sphere whose radius is r.

Block syntax

SPHE r

The face identifier of the sphere is always 1.

Ellipsoid

The ELLI keyword is used to describe an ellipsoid where the semi-principal axes align with the reference axes.

Block syntax

ELLI a b c

Input parameter	Description
a b c	Semi-length along the X-axis / Y-axis / Z-axis

The face identifier of the sphere is always 1.

Box

The BOX and LBOX keywords are used to describe a rectangular parallelepiped for which the three sides are aligned with the reference axes.

Block syntax

BOX  a/2  b/2  c/2
LBOX a  b  c

Input parameter	Description
a/2 b/2 c/2	Half-length of the side of the box along the X-axis / Y-axis / Z-axis
a b c	Length of the side of the box along the X-axis / Y-axis / Z-axis

The numbering of the box faces is as follows:

face 1 in the -X-direction;
face 2 in the +X-direction;
face 3 in the -Y-direction;
face 4 in the +Y-direction;
face 5 in the -Z-direction;
face 6 in the +Z-direction.

Cylinder

The CYL(X|Y|Z) keywords are used to describe a cylinder, with one of its axes parallel to a reference axis (respectively X-axis, Y-axis or Z-axis).

Block syntax

CYL(X|Y|Z)  r  h/2

Input parameter	Description
r	Radius
h/2	Half-height

The numbering of the cylinder faces is as follows:

face 1 is the upper flat face;
face 2 is the curved lateral face;
face 3 is the the lower flat face.

Hexagonal-section prism

The HEX(X|Y|Z) keywords describe a hexagonal-section prism, with one of its axes parallel to a reference axis (X-axis, Y-axis, or Z-axis respectively). It can be created specifying:

either the base edge length;
or the diameter of the circle inscribed in the base.

Tip

When defining a lattice with triangular pitch, this second syntax may be more useful, as the diameter of the circle inscribed in the base is equal to the pitch of the lattice)

Block syntax

HEXX  ( a | DIAM d )  h/2  φy
HEXY  ( a | DIAM d )  h/2  φz
HEXZ  ( a | DIAM d )  h/2  φx

Input parameter	Description
a	Base edge length
d	Diameter of the circle inscribed in the base
h/2	Half-heigth of the prism
φ	Azimuth of one of the base vertices relative to the X, Y, or Z reference axis (in degrees)

Please note that the numbering of the faces is as follows:

the lateral faces are numbered from 1 to 6 in the direct (anticlockwise) direction (see figure below);
the lower face is number 7;
the upper face is number 8.

Available infinite shapes

Infinite shapes are defined as shapes that are bounded solely by the external volume of the module they belong to. To further define the boundaries of these shapes, geometric operators utilizing the TRUN and/or INTE keywords must be employed.

Infinite cylinder

The CYLI keyword is used to describe an infinite cylinder along any axis.

Block syntax

CYLI  r   xa  ya  za  xb  yb  zb

Input parameter	Description
r	Radius
xa ya za	Corrdinates of a point A located on the axis of the cylinder
xb yb zb	Corrdinates of a point B located on the axis of the cylinder

Example of using infinite cylinder

GEOM
    MODU 0

    * Type 1 is an infinite cylinder 
    * - with a 7.5 cm radius;
    * - inclined at a 45-degree angle relative to each of the three reference axes. 
    * Delimiting infinite shapes
    * This example shows how to delimit any infinite cylinder. In this case, a
    * cylinder inclined at a 45-degree angle relative to each of the three reference
    * axes is delimited by two planes:
    * - one with the equation X=0 cm;
    * - one with the equation X=10 cm.
    TYPE 10  BOX   20.  20.  20.
    TYPE 11  PLAX  0.  10.
    TYPE 12  CYLI  7.5   1.  1.  1.   2.  2.  2.
    VOLU  20   0  10  m1  0. 0. 0.                 * external volume
    VOLU  21  20  11  m2  0. 0. 0.                 * fictitious volume
    VOLU  22  20  12  m3  0. 0. 0.  INTE  1   21   * cylinder
* Volume 21 is fictitious; it exists only in relation to volume 22, in order to
* reduce its space. Furthermore, its material is not included in the calculation.
    ENDM
ENDG

Cone

The CON(X|Y|Z) describe a cone with its axis parallel to a reference axis (X-axis, Y-axis, or Z-axis). Two syntaxes are available:

the first one utilizes the tangent value of the half-angle at the vertex of the cone;
the second option requires defining a value for this half-angle.

Block syntax

CON(X|Y|Z)    ( tan(α)  | ANGL   α )

Input parameter	Description
tan(α)	Tangent value of the half-angle at the vertex of the cone
α	Half-angle at the vertex of the cone (in degrees)

The following figure illustrates the use of the CONZ keyword to create a Type.

Specifying tan(α) or α, the orientation of the cone is defined as follow:

if tan(α) > 0, then the opening of the cone is oriented towards the positive axis;
if tan(α) < 0, then the opening of the cone is oriented towards the negative axis.

Plan

The PLA(X|Y|Z) keywords describe a convex space delimited by one or two planes parallel to one of the reference axes (respectively X-axis, Y-axis or Z-axis). The syntaxe allows to select two space definitions:

either a half-space above (using the SUPE keyword) or below (using the INFE keyword) the specified plane altitude alt;
or a space located between two planes whose altitudes are alt-1 and alt-2.

Block syntax

PLA(X|Y|Z)  ( ( SUPE  |  INFE )  alt  |  alt-1  alt-2  )

Input parameter	Description
`SUPE`	Selects the half-space located above the plane altitude alt
`INFE`	Selects the half-space located below the plane altitude alt
alt	Plane altitude along the (X\|Y\|Z)-axis
alt-1	First plane altitude along the (X\|Y\|Z)-axis
alt-2	Second plane altitude along the (X\|Y\|Z)-axis

Note

If the volume/hole centre is not (0,0,0) the type is translated around the volumes/holes center.

The following figure illustrates the use of the PLA and INFE keywords:

Example of defining plans

GEOM
    MODU 0

    TYPE a BOX 10. 10. 10.
    VOLU a 0 a m1 0. 0. 0.

    * Definition of two types using the PLAX keyword
    TYPE  1  PLAX  SUPE  5.
    TYPE  2  PLAX  2.    4.

    * Volume 1 is the half-space x ≥ 8 along the X-axis through the reference point
    * of the module (it is truncated by another volume using the TRUN keyword).
    VOLU  1  a  1  m2  3.  0.  0.  TRUN  ( a )

    * Volume 2 is the space between x=5 and x=7 along the X-axis through the
    * reference point (it is truncated by another volume using the TRUN keyword).
    VOLU  2  a  2  m3   3.  0.  0.    TRUN  ( a ) 

    ENDM
ENDG

Group of planes

The MPLA keyword describes a convex space defined by p planes, each defined by 3 non-collinear points ai, bi, and ci.

Block syntax

MPLA  p  x-a1  y-a1  z-a1  x-b1  y-b1  z-b1  x-c1  y-c1  z-c1
        (…)
        x-ai  y-ai  z-ai  x-bi  y-bi  z-bi  x-ci  y-ci  z-ci
        (…)
        x-ap  y-ap  z-ap  x-bp  y-bp  z-bp  x-cp  y-cp  z-cp
        xi yi zi

Input parameter	Description
p	Number of planes delimiting the space
x-ai y-ai z-ai	Coordinates of a point A located on the plane i
x-bi y-bi z-bi	Coordinates of a point B located on the plane i
x-ci y-ci z-ci	Coordinates of a point C located on the plane i
xi yi zi	Coordinates of an internal point I within the delimited space

Note

When using an “MPLA-type” within a volume, the type is moved so that the internal point aligns with the corresponding volume center.

In the following figure, the arrows depict the normal vectors for each plane, indicating the inward direction of the space determined by the internal point I.

The faces are numbered in the same order as specified in the MPLA definition.