Acoustic Simulation

Computer simulations can be used to generate the spatial and temporal data describing the acoustical behavior of performance halls, but typically the analytical results are difficult to assimilate and compare. By using c o m p u t e r graphics to display the multi-dimensional data, substantially greater amounts of information than that conveyed by standard techniques can he communicated to the designer. This allows designs of different acoustical spaces to be tested, evaluated, and compared. An example comparing the acoustical behavior of three different concert halls demonstrates these techniques and allows for the simultaneous assimilation of much of the information necessary to evaluate the acoustical nature of a space. The use of three-dimensional images, color, animation and abstract representation allows for the comprehension of the complex results of a scientific simulation. Specifically, the simultaneous display of particular icons familiar to the discipline enabled the simultaneous presentation of up to twelve parameters. From a more general point of view, the procedures demonstrate how computer graphics can be utilized for the portrayal of multi-dimensional time dependent data. The visualization techniques are potentially useful for the display of three-dimensional vector fields in many scientific and design applications. C R C a t e g o r i e s a n d S u b j e c t D e s c r i p t o r s : 1.3.0 [Computer Graphics]: General; J.2 [Computer Applications]: Physical Sciences and Engineering A d d i t i o n a l K e y w o r d s a n d P h r a s e s : a c o u s t i c s , simulation, scientific visualization, ray tracing, Monte Carlo. I n t r o d u c t i o n When architecture firms design major auditoriums and concert halls, they frequently build scale models and test them visually and acoustically. By coating the interiors of the models with reflective material and shining lasers from the stage positions, the sight and sound lines of the audience in a hall can be assessed. Acoustical qualities of the proposed space can be measured by conducting acoustical tests on the model using sources and receivers scaled in both frequency and size. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. While these processes do give some insight into the acoustical behavior of the real hail, they are laborious, costly, and t ime consuming endeavors. It is more effective to use computer simulations combined with computer graphics visuatization to test and evaluate the acoustical behavior in performance halls. There are numerous advantages inherent in using computer simulation and visualization over the traditional approach of using scale modeling for acoustical analysis. With the increasing use of computers in the modeling and design of buildings, the geometric models needed to conduct the acoustical analysis will already exist, making additional simulations using the same database very c o n v e n i e n t . Furthermore, the same computing environment used to design geometric spaces can be used to run acoustical analyses. Computer simulation of acoustical behavior would also be more flexible than physical scale modeling, since it would allow for changes to be easily made and then analyzed in a design. Lastly, computer simulation and visualization would make the acoustical nature of a space more easily and more thoroughly understood since the visualizat ion allows for a global evaluation of many unique locations simultaneously through time. The primary objective of this paper is to i n v e s t i g a t e techniques of displaying multi-dimensional data which are both comprehendible and useful to the user. The techniques will be specifically used to visualize acoustical measurements derived from the simulation data. Three model halls will be evaluated and compared. G e o m e t r i c A p p r o x i m a t i o n o f S o u n d P r o p a g a t i o n The relationship between Computer Graphics and acoustical design is more than the use of computers to model the physical environments and to display the results of the acoustic simulation. Sound propagation can be simulated with many techniques that are similar to those used to model illumination. These methods, in particular geometric ray tracing and reflection modeling, have been highly refined. By modifying these methods to take into account a few basic differences between light and sound, they can be well suited to acoustic simulation. Sound can be described as wave motion within matter, but solving the three-dimensional wave equation for arbitrary geometrical environments is a difficult task. Formal analyses have been presented for some idealized shapes, such as a simple cube [12][5], but the application of wave theory to complexly shaped rooms is virtually impossible at this time because the boundary conditions to the wave equation cannot be formulated in a satisfactory way. The use of acoustical ray theory can ©1989 ACM-0-89791-312-4/89/007/0195 $00.75