The design of diffusing surfaces started as an art form, with statuary and various forms of surface ornamentation, and evolved into a science, with Manfred Schroeder’s seminal papers on the use of mathematical number theory sequences. In the past 13 years, since we commercialized the QRD® diffusor, we have been fortunate to be a part of thousands of facilities containing tens of thousands of our diffusor systems. However, RPG has never been content to rest on its past accomplishments. In fact, our company vision is to maintain our leadership position by providing continuous acoustical innovation. Thus, to further expand the acoustical palette and address issues such as aesthetics, surface shape optimization, coverage, diffusion and absorption, RPG has developed a new design tool called Intelligent Shape Optimization™.

ANY SHAPE, ANY SIZE, ANY PERFORMANCE, any use, ANY MATERIAL AND ANY FINISH
RPG is now collaborating with Dr. Trevor Cox, who introduced the concept of optimizing scattering surfaces using boundary element methods in 1995, to make this new innovative technology a reality. To do so we have developed an in-house predictive software technology, which allows us to optimize any surface for a specific use. Therefore, in addition to our “real” products, which we inventory, we will also offer “virtual” shapes, which will be designed and manufactured in a just-in-time process. It is now possible to automatically derive an appropriate curved, stepped, or fractal 1D or 2D surface shape, subject to various architectural constraints, which produces a desired diffusivity or coverage. Since these are “virtual” products, their design involves collaboration between the consultant and RPG. To facilitate this collaboration, we have developed an Arcousthetics™ team at RPG, to create optimized surfaces on demand, that satisfy all of the architectural, acoustic, and aesthetic needs of the project. This “A-team” of acousticians, CAD engineers, manufacturing and finishing specialists will be at the disposal of the acoustical consultant to collaborate in the creation of the best surface for the job. This integrated design and manufacturing capability is now available after many years of software and manufacturing development. We can offer these optimized shapes in Fiber Reinforced Gypsum, Class A Polyester plastic or wood, finished as desired.

ACOUSTICAL SHELLS, OVERHEAD CANOPIES, WALLS, CEILINGS, OVERHEAD REFLECTORS, ETC
Thus a stage canopy can be engineered which provides a desired coverage on stage to specified observation locations, from specified sources. Now much of the guess work of canopy and acoustical shell design can be minimized with accurate coverage plots, using full Boundary Element techniques. Rear and side walls of a venue can be optimized as well as overhead reflectors. Significant improvements in performance are now possible over traditional periodic arcs and other geometrical shapes. This is all possible because we have developed a diffusion coefficient metric to evaluate the diffusivity of a surface. Using an optimization algorithm, we can automatically adjust the Fourier coefficients defining a surface shape until a match between the desired coverage and predicted coverage is reached. A simplified flow diagram of the optimization process is shown in the Figure. The optimization process uses wave acoustics instead of geometrical acoustics. As computational power increases this approach will become even more powerful allowing larger surfaces and wider frequency ranges to be considered. To be continued . . .

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