Physical Modelling for Sound Synthesis - Game Sound Technology and Player Interaction: Concepts and Developments - page 347

tHE PAPEr trAIL OF
PHYsIcAL MODELLING IN
VIrtUAL ENVIrONMENts

of sounding objects will have a level of stiffness
that is significant from an acoustic point of view.
Like digital waveguide synthesis, it is possible
with modal synthesis to give the effect of sound-
ing different materials by changing how quickly
the composite frequencies are damped with time.
This is straightforward to implement with modal
synthesis-damping can be simply applied to each
mode of vibration-as opposed to digital waveguide
synthesis which requires filters to be designed
with this in mind.
Another advantage of modal synthesis is its
versatility with regard to how an object's modal
data is obtained. Projects have determined infor-
mation on an object's modes of vibration from
calculations, from recordings of real sounding
objects, and by using finite element analysis with
each of these methods having its own advantages
and disadvantages.
A final physical modelling technique to be
aware of is called the functional transformation
method (FTM) (Trautmann & Rabenstein, 2003).
Originally developed in the 1990s, this more
formalised form of modal synthesis derives the
modal data directly from the underlying PDEs
that describe the object's vibrations, using Laplace
and Sturm-Liouville transformations. The FTM
can be applied in 1D, 2D, and 3D linear systems
with regular shapes and provides a more structural
approach to interconnecting vibrating structures.
Multi-rate techniques, which involve simulating
lower frequencies with a lower sample rate without
affecting the sound quality (a technique which
can also be applied to modal synthesis), enable
FTM to be used in real-time on a typical desktop
PC. However, to date, this technique has not been
utilised in an interactive virtual environment.

The idea of sound rendering for computer anima-
tion was introduced by Tapio Takala and James
Hahn in their paper Sound Rendering (1992) and
they pioneered many of the ideas used in more
recent projects. They presented a methodology for
combining procedural sounds into a synchronised
soundtrack based on an animation. Each object in
a scene is associated with a characteristic sound
and a sound script is created for an animation
detailing “how a prototype sound signal will be
instantiated, and how it is transformed by the
acoustic environment” (Takala & Hahn, 1992, p.
218). Although they acknowledge the potential
for physical modelling, saying “sound can be
synthesized from physical principles” (Takala &
Hahn, 1992, p. 214), and they describe how an
object's complex vibration can be computed as a
sum of its vibration modes (modal synthesis), the
main focus of the paper is on the modulation of
sounds due to propagation in a three-dimensional
environment.
The authors touch upon the idea of driving
sound synthesis from a physics engine when
they propose “key events of a script can be […]
automatically computed by a behavioural or
physically-based motion control” (Takala & Hahn,
1992, p. 215). This idea has been built upon by
some of the projects presented later in this chapter
which successfully extract and use not only event
triggers, but also information from a physics
engine. Takala and Hahn also give their insight
into how sound is produced when two surfaces
slide over each other:

the surface features cause both of the objects to
vibrate in the same way as a phonograph needle
vibrates when dragged in the groove of a record
disk. The waveform of the sound generated is
similar to the shape of surface imperfections of
the objects. The so called 1 / f noise could be used