PENELOPE 2003 - OECD Nuclear Energy Agency

5.3. Constructive quadric geometry 161
1
1
4
2
3
2
5
3 6
Figure 5.2: Example of simple quadric geometry; an arrow within a sphere (the corresponding
definition file is given in section 5.7). The solid triangles indicate the outside of the surfaces
(side pointer = +1). Numbers in squares indicate bodies.
the new material. To do this, we must determine the intersections of the track segment
r 0 + tˆd (0 < t ≤ s) with all the surfaces that limit the body B (including those that
limit other bodies that limit B), and check if the final position r 0 + sˆd remains in B
or not. The reason for using only quadric surfaces is that these intersections are easily
calculated by solving a quadratic equation.
Notice that bodies can be concave, i.e., the straight segment joining any two points in
a body may not be wholly contained in the body. Hence, even when the final position of
the particle lies within the initial body, we must analyze all the intersections of the path
segment with the limiting surfaces of B and check if the particle has left the body after
any of the intersections. When the particle leaves the initial body, say after travelling a
distance s ′ (< s), we have to locate the point r ′ = r 0 +s ′ˆd. The easiest method consists of
computing the side pointers of all surfaces of the system at r ′ , and determining the body
B ′ that contains r ′ by analyzing the side pointers of the different bodies in ascending
order. It is clear that, for complex geometries, this is a very slow process. We can speed
it up by simply disregarding those elements of the system that cannot be reached in a
single step (e.g. bodies that are “screened” by other bodies). Unfortunately, as a body
can be limited by all the other bodies that have been defined previously, the algorithm
can be improved only at the expense of providing it with additional information. We
shall adopt a simple strategy that consists of lumping groups of bodies together to form
modules.
A module is defined as a connected volume 3 , limited by quadric surfaces, that contains
one or several bodies. A module can contain other modules, which will be referred
to as submodules of the first. The volume of a module is filled with a homogeneous
medium, which automatically fills the cavities of the module (i.e. volumes that do not
3 A space volume is said to be connected when any two points in the volume can be joined by an arc
of curve that is completely contained within the volume.