Handbook for Sound Engineers

1372 Chapter 35

So one gets usable results for models with N<50
and i< +6. For larger models and more complicated
investigations the next method is more advantageous.

35.3.2.3 Ray Tracing

In contrast to image modeling, here the path of a single
sound particle radiated under a random angle into the
room along a ray is followed. All surfaces are checked
to find the reflection points (with or without absorption
or diffusion). The tracing of the single ray is terminated
when the remaining sound energy has decreased to a
certain level or when the particle hits an appropriately
arranged counting balloon with a finite diameter, typi-
cally at the location of a listener in the room, Fig. 35-38.

Phase considerations are not possible directly, but
can be derived if an image model routine is run that
retraces the last ray after intercepting the counting
balloon or if the ray retains the information about its
sequence of reflection points throughout the process.

This method runs significantly faster and the calcula-
tion time is only proportional to the number N of the
model walls. Ray-tracing methods can be even faster, if
they are based on logarithmic search for the intersection
points (~ logN).

35.3.2.4 Cone Tracing

This method is used in various CAD programs. Its
advantage is the directed ray radiation over the differ-
ent room angles, Fig. 35-39.

Because of these cones, fast ray calculations can

proceed. The fact that the cones do not cover the source

“sphere” surface completely turns out to be a disadvan-

tage. It is necessary to overlap adjacent cones and an

algorithm is required to avoid multiple detections or to

“weight” the energy so that the multiple contributions

produce (on average) the correct sound level. Some

famous conical beam tracers are known,^ implementing

different techniques to correct this point.44,45,46

35.3.2.5 Pyramid Tracing

This method was introduced by Farina in the program

“Ramsete” in 1995.^47

Farina demonstrated that the pyramid beams do not

suffer from the cone-trace overlap, as adjacent pyramids

cover perfectly the source sphere, Fig. 35-40.

Originally a subdivision of the surface in triangles

was made by subsequent subdivisions of the 8 octants

of the sphere: according to Farina “this way the number

Figure 35-38. Ray calculation with ray-tracing algorithm.

Listener L

Wall 2

Wall 1

Source S

Direct path

Not counted

Path S-1-2-L

Path S-1-L

Counting

balloon

Figure 35-39. Ray radiation in cones.

Figure 35-40. Ray radiation in pyramids.