Abstract

Acoustics is important for planning of rooms for musical or speech presentations, such as theaters, concert halls, and lecture rooms. Today a computer aided simulation of acoustical behavior inside closed rooms is possible. There exists a variety of simulation algorithms which can be classified into two groups: wave-based and geometric approaches. The former numerically solve the wave equation. Geometrical acoustics deals with the examination of the propagation of single sound rays from a source to a particular listener position. The visualization of the sound wave behavior inside the room is important, not only for teaching purposes, but also for engineers designing and modifying rooms. Visual representation of sound propagation as well as representation of sound received at a listener position can help understanding these complex processes.

Visualization using phonon tracing

The phonon tracing algorithm is a geometric approach, which computes the sound energy or pressure decomposition for each particle (phonon) sent out from a sound source (phonon emission) and uses this in a second pass (phonon collection) to construct the impulse response (which characterizes the acoustics of the room) for multiple listeners. From our visualization, the effect of different materials on the spectral energy distribution can be observed. The first few reflections already show whether certain frequency bands are rapidly absorbed. The absorbing materials can be identified and replaced in the virtual model, improving the overall acoustic quality of the simulated room. For the representation of the acoustics at a certain listener position, we use colored spheres deformed according to the received sound. To analyze the acoustic quality in a room by use of well known acoustic metrics, we map the impulse response contribution of the geometry to the reflecting surfaces.

Visualization using reduced state-space model

To simulate the low frequency part of the sound field we have to fall back on wave acoustics. For closed rooms the wave equation is preferably solved by the finite element method (FEM), which approximates the wave equation by a large system of ordinary differential equations (ODEs) the unknowns of which are the pressures at grid points covering the room. Since there are by far too many unknowns to solve these systems of ODEs in real time, reduction is needed. System dynamics can be represented quite well by a superposition of a few eigenfrequencies of the room, whose coefficients are the unknowns of the new reduced system. Using this reduced state-space model we are able to visualize the solution for arbitrary frequencies. We can interactively ''slide'' through the frequencies and observe the change in the pressure field. We render single surface for one isovalue or multiple isosurfaces throughout the whole range of values. Furthermore we explore the pressure field by determining the local extrema of its scalar values. We then visualize the topology of the scalar field by drawing arrows at the position of the mesh points corresponding to the direction of the gradient or by integrating random number of streamlines starting at the surface of a sphere around the saddle points of the gradient field.

Several wave-fronts (1) and first reflection (2) from the floor as triangulated surfaces. (3) Sound reflection from the floor visualized by use of scattered data methods (4). Visualization of the received sound at different listener positions by use of deformed spheres for 1280 Hz. (5) Contribution of the room surfaces to the impulse response for early (<50ms) received sound.

Visualization of the pressure field using isosurfaces for 69.37 Hz (1) and 138.25 Hz (2), and pressure gradient field using arrows (3) and streamlines (4) for 276 Hz.

Acknowledgements

This work was supported by the German Science Foundation as part of the International Research Training Group on Visualization of Large and Unstructured Data Sets (DFG IRTG 1131).

Publications

• Martin Bertram, Eduard Deines, Jan Mohring, Jevgenij Jegorovs, Hans Hagen, Phonon Tracing for Auralization and Visualization of Sound, in: Proceedings of IEEE Visualization '05, pp. 151--158, 2005.
• Eduard Deines, Frank Michel, Martin Bertram, Hans Hagen, Gregory M. Nielson, Visualizing the Phonon Map, in: Proceedings of Eurographics/ IEEE-VGTC Symposium on Visualization (2006), pp. 291--298, 2006.
• Eduard Deines, Martin Bertram, Jan Mohring, Jevgenij Jegorovs, Frank Michel, Hans Hagen, Gregory M. Nielson, Comparative Visualization for Wave-based and Geometric Acoustics, in: Proceedings of IEEE Visualization '06, pp. 1173--1180, 2006.
• Frank Michel, Eduard Deines, Martin Bertram, Christoph Garth, Hans Hagen, Listener-based Analysis of Surface Importance for Acoustic Metrics, in: Proceedings of IEEE Visualization '07, pp. 1680--1687, 2007.

Contact

Eduard Deines edeines@ucdavis.edu