Volumetric Modeling of Acoustic Fields in CNMAT's Sound Spatialization Theatre
CNMAT, UC Berkeley
1750 Arch Street
Berkeley, CA 94709
(510) 643 9990 x 308
A new tool for real-time visualization of acoustic sound fields has been developed for a new sound spatialization theatre. Unique features of the theatre and the acoustic and volumetric modeling software are described.
Sound Spatialization Theatre
The Center for New Music and Audio Technologies, CNMAT, is an interdisciplinary research center at the University of California at Berkeley. Our sound spatialization theatre is built into the main performance and lecture space at CNMAT's facility. A unique feature of the theatre is a flexible suspension system built primarily for loudspeakers. Each speaker hangs from a rotating beam. The pivot point for each speaker runs in a track that slides along rails bolted to the ceiling. With height adjustment of each suspension cable, this system safely allows speakers to be moved anywhere in the room and oriented along two of the three possible axes (Figure 1). Rotational symmetry of the concentric drivers in Meyer HM-1 speakers obviates the need for adjustments around the third or "roll" axis. Real-time, low-latency audio signal processing for the speaker array is performed on a multiprocessor Silicon Graphics Octane workstation. This machine was chosen because of its built-in multi-channel audio, reliable real-time performance, and the availability of sound synthesis and processing software .
Most current applications of spatial audio are based on a model where source material is spatially encoded for an ideal room with a predetermined speaker geometry . The result is often unsatisfactory because of the difficulty in adapting real rooms to the ideal. Our research is based on a more general model where the source material may be from instruments and performers in the room, and therefore real-time spatial processing is required for all sources.
Optimizing the speaker array positioning and sound processing for each performance in the theatre is challenging. The traditional empirical approach is far too time-consuming to support situations in which there are weekly (and sometimes daily) performances with varied configurations. The problem with the trial and error approach is the difficulty of evaluating the effects of new speaker positions and software parameter changes for all listening positions. It is easy to optimize the listening experience for the lucky person in the "sweet spot" at the expense of the rest of the audience. The challenge is to find a compromise where as many listeners as possible experience the intent of the sound designer and as few listeners as possible endure disastrous seats.
To aid sound designers and composers in achieving a good compromise for the diverse applications of the theatre, we have developed software for visualizing speaker signals, a model of the acoustic sound field in the room, and interpretations of the field according to perceptual models. Important examples of prior work in this area include and . Unique features of the work described here include the emphasis on interactive, real-time visualization, the use of a highly configurable performance space, and the focus on adapting the processing and space to achieve diverse artistic goals.
The visualization software is part of a complete system managing audio, gestural flow and visual display (Figure 2). The heart of the system is a database describing the room. It contains information on geometric features such as the shape of the room, positioning and orientation of the speakers, microphones and audience seating, live performer location and their musical instruments location. Acoustic properties of each object in the room include: frequency dependent radiation patterns and the location of their acoustic "centers".
This database is used by the spatial sound processing software to process source signals to create an audience percept of virtual sources from arbitrary regions in space. The desired percept may also involve creating the illusion that listeners are in a room of a different size than the actual theatre . The location of these sources is controlled in real-time through gestures or arbitrary control messages arriving from the network .
The visualization software has access to the room database and real-time parameter estimates from the spatialization software. Since it has no access to the real sound pressure levels in the room it must estimate these based on an acoustic model of the room. The image source method was used because of its amenability to real-time computation.
Volumetric visualization of the time varying sound pressure level in CNMAT's sound spatialization theatre is illustrated in Figure 3. The reader is advised to explore the color images available athttp://www.cnmat.berkeley.edu/~khoury for a better indication of the programs potential than can be communicated with the monochrome reproduction of this preprint. Pressure is shown using a color map on a horizontal cut plane through the space. This movable plane is typically set to the average positions of audience's ears in the room. This surface may be changed to show, for example, effects of tiered seating or to evaluate the experience of a performer who may be standing on a raised stage. Several simultaneous cut surfaces may be necessary, for example, for balcony seating in large theatres.
It is interesting to contrast this volumetric visualization with traditional audio metering where scalar signal levels are displayed for various nodes in the signal processing chain. Such metering is useful for managing signal levels in the electrical elements of the audio system to avoid distortion and speaker overload. However it is hard even for experienced sound engineers to use scalar metering to predict actual sound pressure levels in many locations in a venue.
Figure 4 is a vector field display of the perceived direction of a virtual sound source according to a commonly adopted strategy for sound localization with speaker arrays, the summing localization model , known in its general form as vector panning . The idea of the technique is that a virtual source can be placed between a pair (or triple in the 3-D case) of speakers by dosing the level of the source signal appropriately to each pair or triple .
Our initial experience with this method was good. Speakers were placed at equal distances from the center of the room and panning worked smoothly around the room. When the speakers were moved to more practicable locations, above the audience and closer to the walls and corners of the room, vector panning failed to provide good virtual source imaging. This may be explained by the precedence effect which may work against summation localization. As the difference in the time of arrival of wavefronts from the two speakers approaches one millisecond, the source of the earliest wavefront is perceived as the actual source, regardless of the amplitude dosing performed by vector-panning. Visualization of an isosurface along which wavefront time difference is a constant illustrates the geometric implications of this perceptual phenomenon (Figure 5). This isosurface representation is also used to view other important time delay effects in spatial hearing such as the varied values of the echo threshold, backward masking, and multiple event thresholds . The impact of the precedence effect can be controlled by introducing an appropriate delay into the feeds of the speakers in the room so that they all have the same effective distance from a chosen "center" of the listening space. The desired center about which audio spatialization is performed is often different from the geometric center of the listening space. This discrepancy arises because the performance area generally occupies the front third of a theater, with the audience seated in the rearward two-thirds.
Acoustic models have to take into account phase from coherent sources of sound. Figure 3 shows the sound pressure level of a sine tone at a particular frequency in the room. At low frequencies destructive and constructive interference create markedly different sound levels at varying room locations.
When a loudspeaker is placed close to a hard wall, reflected waves interfere with the direct source, distorting the frequency and phase response of the loudspeaker. These effects are modeled by introducing the reflections as further sources, as illustrated by the smaller speakers outside the room in Figure 6.
Visualization and User Interaction
The high level programming tool that binds the spatial visualization system together is Tcl/Tk , a scripting language and graphical user interface toolkit (Figure 7).
The Visualization Toolkit (VTK) , a C++ class library for visualizing data, provides a set of bindings to the Tcl language that allow access to all the classes in the system. Through this scriptable interface, it is possible to create visualizations which change interactively and dynamically in response to user input data. A VTK data object is maintained internally for each sample region in the listening space. This data object is synchronized with the sample points in the region.
Interactive tasks such as moving and orientating sound sources take advantage of user-interface event bindings in Tk. Real-time operation based on monitoring signals being supplied to the sound sources is achieved by a Tcl thread that repeatedly requests current energy estimates, computes the acoustic model and visualization of that model, and renders the scene.
Geometric Acoustic Modeling
Three kinds of objects are modeled: active sound sources for loudspeakers and musical instruments, passive reflective objects for walls and diffusers, and finally listening points.
Listening space geometry is represented using a set of polygonal faces corresponding to walls, ceilings, floor etc. Each face is decorated with information describing its sound properties, such as frequency dependent reflection coefficients. Small room models can be easily described numerically. More complicated models may be imported from a specialized 3D modeling package. Maya is interesting in this respect because it supports storage of arbitrary data (i.e. acoustic) in nodes of its scene graph.
Listening points are represented as two-dimensionally sampled bounded surfaces in three dimensional space. This representation allows for fine sampling at important locations without the computational load that would be required for complete volumetric models. Common surfaces used include cut planes corresponding to ear level of seated listeners and performers; and meshes of planes for tiered seating.
Sources are represented using as polygonal models. Each model is decorated with information describing its acoustic properties such as its acoustic center location and frequency-dependent directivity.
Image Source Modeling
In this acoustic modeling technique, information is computed for each listening point in turn. Conceptually, lines are projected from the listening point to the acoustic center of each source and to the acoustic center of reflections of each source from the passive reflecting objects in the space. The lengths of these lines are used to estimate energy reaching the listening point. The solid angles of each line are used to compute the effect of source directivity, and energy loss as a function of frequency and angle of incidence.
This method leads to the following expression for the space-complexity of modeling up to the n'th order reflections of a listening space with f faces of defining geometry and s direct sound sources.
Note that when calculating the next successive order of reflections, a source r which was created by reflecting across a face g culls away face g for the next iteration. This must be true for the following reason: g's surface normal must have been facing s in order for the reflection to have been performed. So for this new virtual source r, it must be the case that g's surface normal now points away from s and is discarded from consideration for reflections. This explains the (f-1) term above. However, in more complex models, particularly those that possess non-convex geometry, more than just the previous face will be culled for a given reflected source. Thus, the expression above is an upper bound on the maximum number of sources that could possibly be generated when calculating reflections.
Separate computation and display of direct and reverberant energy is simple to achieve with image source models by introducing upper and lower "reflection limits". The upper reflection limit terminates the reflection-generation process -- essentially halting the recursive process by which source reflections are generated. The display software maintains an active source list. consisting of all the sources, both direct and virtual, which exist between the upper and lower reflection limits, inclusively (Figure 8). A lower reflection limit of zero indicates that the direct sources should be included in the active source list. Setting the upper and lower reflection limits equal to one another allows the acoustic power from a single order of reflections to be modeled.
Once the geometric implications of the relative positions of sources, listening points, and reflecting objects are calculated, the actual acoustic modeling calculation can be performed. The simplest computation uses sine wave probe tones directly calculating and vector summing the phase and amplitude of wave fronts arriving at each listening point. For real-time modeling an optimization is required. The idea is to avoid the expense of the sequence of convolutions that would be required at the full audio sample rate by using energy estimates of frequency bands averaged at the visual display rate. This method allows for plausible approximations of energy, although pathological locations where cancellations may occur would not be accurately displayed.
Conclusion and Future Work
The visualization system described here is a valuable tool for spatial sound researchers. sound engineers and composers using CNMATs sound spatialization theatre. Further work is in progress on the adaptation of better acoustic simulation methods for more accurate display of the quality of the reverberant field. The room database will be automatically extracted from a model built with 3D modeling software . Volume visualization strategies are being explored to display sounds in spectral and impulse response form.
We gratefully acknowledge support from :
Richard Andrews, Tom Johnson, Tibor Knowles and Matt Wright developed the speaker mounting and audio patching system for the theatre. René Caussé, Jean-Marc Jot and John Meyer provided essential insights and data on room and loudspeaker acoustics.