Advances in Edge-Diffraction Modeling for Virtual-Acoustic Simulations

In recent years there has been growing interest in modeling sound propagation in complex, three-dimensional (3D) virtual environments. With diverse applications for the military, the gaming industry, psychoacoustics researchers, architectural acousticians, and others, advances in computing power and 3D audio-rendering techniques have driven research and development aimed at closing the gap between the auralization and visualization of virtual spaces. To this end, this thesis focuses on improving the physical and perceptual realism of sound-field simulations in virtual environments through advances in edge-diffraction modeling. To model sound propagation in virtual environments, acoustical simulation tools commonly rely on geometrical-acoustics (GA) techniques that assume asymptotically high frequencies, large flat surfaces, and infinitely thin ray-like propagation paths. Such techniques can be augmented with diffraction modeling to compensate for the effect of surface size on the strength and directivity of a reflection, to allow for propagation around obstacles and into shadow zones, and to maintain soundfield continuity across reflection and shadow boundaries. Using a time-domain, line-integral formulation of the Biot-Tolstoy-Medwin (BTM) diffraction expression, this thesis explores various aspects of diffraction calculations for virtual-acoustic simulations. Specifically, we first analyze the periodic singularity of the BTM integrand and describe the relationship between the singularities and higher-order reflections within wedges with open angle less than 180◦. Coupled with analytical approximations for the BTM expression, this analysis allows for accurate numerical computations and a continuous sound field in the vicinity of an arbitrary wedge geometry insonified by a point source. Second, we describe an edge-subdivision strategy that allows for fast diffraction calculations with low error relative to a numerically more accurate solution. Third, to address the considerable increase in propagation paths due to diffraction, we describe a simple procedure for identifying and culling insignificant diffraction components during a virtual-acoustic simulation. Finally, we present a novel method to find GA components using diffraction parameters that ensures continuity at reflection and shadow boundaries.