de Greve B., Willems T., De Muer T., Botteldooren D.

Constructing noise maps for large urban areas is a tedious and CPU intensive task. Engineering approximations to outdoor sound propagation are commonly introduced to reduce the computational complexity. In particular, diffuse reflections are often neglected because of their great computational expense. This paper reports on an effort to approximate the diffusely reflected field by using a technique called phonon mapping. In noise mapping, many techniques can and are adapted from the field of computer graphics where various techniques to approximate indirect lighting exist. A popular technique in computer graphics is photon mapping. It was introduced in 1995 by Jensen and is known as one of the fastest algorithms for simulating indirect lighting. In this paper, it will be shown how this photon mapping algorithm can be adapted to the field of noise mapping to simulate diffuse reflections. The phonon mapping algorithm exists of two passes. In the first pass, a phonon map is build by bouncing phonons, abstract sound particles, through the environment. On each interaction with a (partially) diffuse surface, it is stored in the phonon map. The Russian Roulette technique is then used to determine if the phonon is absorbed, specular or diffusely reflected. Upon reflection, the phonon is traced through the environment again. This process is continued until the phonon map is sufficiently populated. The second pass is a more traditional backward ray tracer. Rays are emitted from the receivers. Specular reflections are handled as usual but for diffuse reflections, no secondary, reflected rays are cast. Instead, the phonon map is queried for nearby phonons. Their presence is used to estimate the energy that is available from this diffuse reflector.