Acoustic simulation using hierarchical time-varying radiant exchanges

Sound is essential to enhance any visual experience and is becoming an important issue in virtual reality systems, computer animation and interactive computer graphics applications such as video games. Real-time rendering of sound from a source positioned arbitrarily in space around the listener, often referred to as “3Dsound”, has seen dynamic development in the recent years. Many approaches have been proposed leading to quite impressive results [4, 2, 6, 23, 3]. However, these methods are usually not sufficient to model the complex, environment-dependent phenomena resulting from sound propagation, diffusion or diffraction that are key components of virtual sound fields, addressed in this paper. One of the principal elements of virtual sound rendering is the process of auralization or rendering a virtual sound field audible [20, 13]. Auralization involves digital filtering of a “rough”, anechoic sound signal by a filter or pressure impulse response proper to a given environment (Figure 1). The pressure impulse response associated with a source/receiver couple may be seen as the sound pressure signal received by the receiver when the source emits a single sound pressure “impulse” (Dirac signal). To compute this digital filter, different phenomena must be taken into account: sound emission, free sound propagation in the medium, occluders that cause reflection, diffusion and diffraction of waves and sound reception. If we assume all these phenomena to be linear, the transformations undergone by the original signal in the environment before it reaches the receiver can be expressed as a convolution product (in temporal domain): y(t) = h(t) x(t) = Z +1 0 h( )x(t )d ; where y(t) is the received signal, x(t) is the original signal and h(t) is the pressure impulse response of the environment. Formerly developed in acoustics to study sound reverberation in concert halls, various computer models are now used in auralization systems. They usually imply significant computational costs which restricts their use in interactive applications to very simple environments and/or ones for which basic sound propagation models are sufficient. We present a new geometric approach to acoustic simulation. High quality sound fields, including effects of sound global specular and diffuse reflections are using a time-varying and hierarchical radiant exchange technique, similar to hierarchical radiosity used in lighting simulations [29].