Physical Modelling for Sound Synthesis - Game Sound Technology and Player Interaction: Concepts and Developments - page 346

to dissuade its widespread use in musical appli-
cations. However, the primary sound sources in
a typical virtual environment are rarely plucked
strings and woodwind instruments and so digital
waveguide synthesis has not been so commonly
adopted in these situations. The effect of stiffness
can be realised by using more sophisticated, and
hence more computationally expensive, digital
filters. Some research has been carried out in an
attempt to do this in an inexpensive way (Essl,
Serafin, Cook, & Smith, 2004) but, to accurately
realise the full effect of stiffness, the total com-
putation required would equal that of the next
physical modelling technique to be discussed.
The method which has become the most popu-
lar for real-time sound synthesis in interactive
virtual environments is modal synthesis. It is a
physically based method that has many advantages
for real-time interactive sound synthesis. As it is
used by many of the projects discussed in this
chapter, it is beneficial to understand some theory
behind it. There follows a brief description of the
technique and, for a more detailed examination,
one may wish to read Jean-Marie Adrien's seminal
work on the subject, The Missing Link: Modal
Synthesis (1991).
To understand modal synthesis, one should
consider the sound of a vibrating object as a sum
of decaying sinusoids. The frequencies of these
sinusoids correspond to an object's modes of
vibration and, in modal synthesis, they are recre-
ated by a bank of oscillators working in parallel.
Each mode of vibration also has an associated
decay rate and a shape function or shape matrix
and, together with its frequency, they represent
an object's modal data, that is, all the information
needed to carry out modal synthesis for that object.
A shape function, or shape matrix, provides the
gain of a given mode for a specific contact location
meaning that modal synthesis can create contact
location-specific sounds, an obvious advantage
in virtual interactive environments where real-
ism is desired and perpetual cues are important.
A common way of implementing oscillators for

modal synthesis is to create a digital filter tuned
to resonate at the desired frequency and with the
desired decay rate. To simulate object excitation,
an impulse signal is input into each filter inde-
pendently. The location-dependent gain can either
be incorporated into the design of each filter, or,
if the contact location is to be varied during run
time, applied to the impulse signal before input
to each of the filters.
It is with good reason that modal synthesis
has become the most popular physical modelling
technique to be applied in interactive virtual envi-
ronments. Its many advantages will be presented
here in detail as they are relevant to the projects
discussed later in this chapter. Firstly, modal
synthesis generates sound as a sum of sinusoids
which correlates naturally with the way in which
humans perceive sound. The computational ex-
pense of the technique is directly proportional to
the number of modes being used and, as in theory
this is unlimited, one cannot simply assert that it
is a cheap technique. However, many studies have
indicated that realistic object contact sounds can be
created with little computational expense and that
its memory usage is much lower than that of the
digital waveguide technique. Furthermore, studies
have implemented modal synthesis in such a way
that the processing power afforded it can be varied
at run time with a graceful, if at all noticeable,
degradation in sound quality. The ability to set a
sonic level of detail is particularly appealing in a
large environment where some sounding objects
may be far away from the observer or occluded,
or in a busy game environment where the player's
attention is to be focused on a particular aspect. It
is also attractive to have an audio engine that can
utilise more processing power when it is available
and make do with less when it is not.
Although, like digital waveguide synthesis,
modal synthesis cannot easily model distributed
nonlinear effects, it can model the effect of bending
stiffness at no extra cost and hence synthesise the
sound of inharmonic objects. This is important in
a typical virtual environment where the majority