PENELOPE 2003 - OECD Nuclear Energy Agency

162 Chapter 5. Constructive quadric geometry
correspond to a body or to a submodule); these filled cavities are considered as a single
new body. A body that is connected and limited only by surfaces can be declared either
as a body or as a module. For the sake of simplicity, modules are required to satisfy
the following conditions: 1) the bodies and submodules of a module must be completely
contained within the parent module (i.e. it is not allowed to have portions of bodies or
submodules that lie outside the module) and 2) a submodule of a module cannot overlap
with other submodules and bodies of the same module (this is necessary to make sure
that a particle can only enter or leave a module through its limiting surfaces). Notice
however, that the bodies of a module are still assumed to be defined in ascending order,
i.e. a body is limited by its surfaces and by the previously defined bodies of the same
module, so that inclusions and interpenetrating bodies can be easily defined. Of course,
overlapping bodies must be in the same module.
A module (with its possible submodules) can represent a rigid part (e.g. a radioactive
source, an accelerator head, a detector, a phantom, etc.) of a more complex material
system. To facilitate the definition of the geometry, it is useful to allow free translations
and rotations of the individual modules. The definition of a module (see below) includes
the parameters of a rotation R(ω, θ, φ) and a translation T (t), which are optional and
serve to modify the position and orientation of the module (and its submodules) with
respect to the laboratory reference frame. As before, the rotation is applied first. All
submodules and bodies of the same module are shifted and rotated together.
In practical simulations, it may be useful to limit the region of space where particles
have to be transported. For instance, to simulate the response of a detector with a given
photon source, it is advisable to stop the simulation of a particle when it is far enough
from the detector. This can be done automatically by considering an “enclosure” of
the material system, which is defined as a module that contains the complete system.
If such a covering module is not explicitly defined, the subroutines set the enclosure
as a sphere of 10 15 cm radius. It is assumed that there is perfect vacuum outside the
enclosure, and in any inner volume that is not a part of a body or of a filled module.
Hence, particles that leave the enclosure are lost and will never return to the material
system.
For programming purposes, it is useful to imagine each module as the mother of its
bodies and submodules, and as the daughter of the module that contains it. We thus
have a kind of genealogical tree with various generations of modules and bodies (see fig.
5.3). The first generation reduces to the enclosure (which is the only motherless module).
The members of the second generation are bodies and modules that are daughters of
the enclosure. The n-th generation consists of modules and bodies whose mothers
belong to the (n − 1)-th generation. Each module is defined by its limiting surfaces
(which determine the border with the external world) and those of their descendants
(which determine the module’s internal structure); this is not true for bodies (childless
members of the tree), which can be limited either by surfaces, by other sister bodies or
by a combination of both. A body that is limited only by surfaces can be defined as a
module, which has the advantage of allowing free rotation and translation.