Consider the situation shown in
Figure 4,
where we trace a particle from
** **
to
** **
in a simple
enclosure with 14 surfaces.
The intersection calculations must be done over all surfaces, and the unique
``valid'' point of intersection identified.
(Note that the straight line of the particle trajectory, in general,
intersects every straight line defining every surface in the enclosure.)
Specifically,
Figure 4
shows emitting and intersecting surfaces as
numbers 13 and 12, respectively (recall that we disallow intersections from
the back of a surface---i.e., surface 3; in a well-specified geometry, there is
always an intersection prior to one from behind---here, the prior intersection
is that of surface 12).

Figure 4: Particle Intersection.

The ``valid'' intersection is identified as the one of minimum distance from the point of emission to the point of intersection (for example, surface 12 instead of surface 2), but this comprises a daunting problem numerically, of order . Specifically, we seek ways to limit this search to render the problem tractable. Emissions are done from all surfaces and each emission requires testing all surfaces for the unique, ``valid'' intersection.

Strategies to limit the search are depicted in Figure 5 for a general surface L. Among them are:

Figure 5: Conditions to Invalidate a Potential Intersection.

- 2.4.1 Figure 5(a)---Dot Product Test
- 2.4.2 Figure 5(b)---Intersection Lies Outside of Surface
- 2.4.3 Figure 5(c)---Surface of Intersection Lies Behind Emitting Point