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RPG Waveform Bicubic


Overhead canopies are used in auditoriums to blend the direct and early reflected sound, increasing speech intelligibility and enhancing musical clarity and intimacy. Traditionally, non-optimized, periodic flat panels and arcs have been used. These arrays can give rise to non-uniform coverage, due to array gaps, non-optimal shaping and periodicity effects. RPG has developed an optimization algorithm called the Shape Optimizer, to provide optimal shaping and tilting offering omnidirectional scattering. RPG’s patent pending aperiodic modulation of a single asymmetric base shape minimizes periodicity arraying effects and provides uniform coverage. Aperiodic modulation of a single asymmetric base shape allows infinite, seamless tiling and unlimited shapes are possible with different tiling patterns. Waveform Bicubic represents the next generation in acoustical canopy design. No other system provides the aesthetic and performance possibilities. Several depths are available in Class A GRG and GRG/Honeycomb/GRG (referred to as GHG) novel materials.

When multiple spaced canopy panels are used in an array, the scattering response or coverage is the combination of the response of a singel panel and the periodic arrangement. Periodicity results in scattering in prefered directions, which depend on the array configuration. The sound level in these preferred diffraction directions depends on the uniform scattering capability of each individual panel. As a result, coverage is often compromised unless optimization is utilized.

To solve this problem, RPG developed the first Shape Optimization program , which automatically determines the best shape, tilt and arraying to insure uniform coverage. The Shape Optimizer combines the power of the boundary element and multi-dimensional optimization techniques, incorporating the diffusion coefficient as the metric of optimal performance. Therefore, optimal shape provides uniform coverage. Periodicity effects are minimized by modulating the asymmetric base shape, thus allowing the canopy array to perform as one of the individual optimized canopy elements. Thus Waveform Bicubic offers a level of performance and aesthetics formerly not available in commercial canopies.

bicubic orientationDiffusion
Aperiodic Modulation of a Single Asymmetric Base Shape
RPG’s patent pending Aperiodic Modulation of a Single Asymmetric Base Shape allows the creation of wide area coverage seamlessly with a single asymmetric base shape (top), thus minimizing periodicity effect. This is possible, because the asymmetric central shape, determined by the architect or acoustician, morphs to identical sides, which have a zero gradient allowing adjacent tiles to seamless transition without discontinuity in any orientation (middle) forming a larger aperiodic array (bottom 4x4 array). Thus with an optimized aperiodic array, canopy performance can finally be mathematically determined and evaluated. The performance of the aperiodic array is similar to that of one of the acoustically optimized canopy elements.

The Waveform Bicubic can be used as an overhead canopy and also in a wall mounting. Overhead mounting is accomplished by bolting adjacent modules together and suspending from integral hairpin hanging loops with aircraft cables. Wall mounting is accomplished by attaching through the sides into cleats mounted to the substrate.

Worship Spaces, Band Rooms, Choral Rooms, Stage Shells, Recording and Broadcast Studios, Auditoriums, Performing Arts Centers, Theaters and Cinemas.Worship Spaces, Band Rooms, Choral Rooms, Stage Shells, Recording and Broadcast Studios, Auditoriums, Performing Arts Centers, Theaters and Cinemas.

ceiling arraySpecifications
Product Option Sheet
Waveform® Bicubic panels are available in 4’x4’x2”, 4’x4’x4” and 4’x4’x8” sizes. The Bicubic is fabricated from Glass Reinforced Gypsum and the surface weight ranges from 3 to 5 lbs/sf.
Panels can be factory or field painted. When joined into aperiodic two dimensional arrays, seams can be filled, sanded and field painted.


  • Optimized shape
  • Optimized arraying and positioning
  • Single asymmetric base shape
  • Asymmetric shape capable of unlimited wide area aperiodic modulation patterns
  • Seamless tiling for wide area coverage
  • Integrated mounting hardware
  • Glass Reinforced Gypsum (GRG) fabrication
  • Field finished


  • Optimized shape insures uniform coverage
  • RPG provides optimal arraying and tilting to insure uniform coverage and eliminate guesswork in the field
  • RPG’s patent pending aperiodic modulation of a single asymmetric base shape allows modulation to minimize periodicity effects
  • Adjacent panels seamlessly tile in either direction for wide area coverage simulating a single canopy element
  • GRG is non-combustible and hence can be used in all applications requiring a Class A rated material
  • Field finishing allows joints to be taped forming a continuous surface, which can also be field painted
  • Installation is quick and easy using integral metal hairpin hanging loops and aircraft cables

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