Computational approaches to model the response of particular rooms (defined by complete geometrical specifications) are generally grouped into two categories:
The wave-based approaches generally require significantly more computational resources, though ray-tracing techniques can be quite demanding as well.
In GA, wave properties are neglected and sound is assumed to propagate as rays, which is more valid when wavelengths are short compared to surface dimensions and overall dimensions of the space (at high frequencies) but less accurate at lower frequencies.
GA approaches can be energy- or pressure-based, the former resulting in energy-time (or echogram) responses and the latter resulting in impulse responses.
Figure 2:
Image-source representation of a shoebox-shaped room (left) and a more complex geometry (right), from (Savioja and Svensson, 2015). Original sources are designated by , first-order ISs with , second-order ISs with , and third-order ISs with . For the right figure, the receiver is designated with , ISs with reflection points outside the polygon by and an IS with a valid reflection point but obstructed path with
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The image-source (IS) method is a ray-based model for room reflections that assumes specular reflections from large, smooth surfaces (as illustrated in Fig. 2). “Virtual sources” are determined at mirror image locations with respect to reflecting surfaces. Once the virtual sources are determined, propagation distances can be easily calculated from two- or three-dimensional Euclidean geometry. Note that path validity checks are necessary.
The IS method can be used to efficiently compute early reflections but the technique becomes challenging to manage at higher orders.
Various approaches to model reflections from curved or non-smooth surfaces, as well as diffraction at finite surface edges have been proposed in GA.
In ray-tracing techniques, the main prinicple is to randomly cast rays from a sound source and to register valid paths to a listener. Source directivity patterns can easily be accommodated by weighting the ray distribution. Diffuse reflection properties can be modeled by casting numerous reflected rays at a boundary, as illustrated on the right side of Fig. 3.
Figure 3:
Specular (left) and diffuse reflection (right) ray tracing examples, from (Savioja and Svensson, 2015).
Another approach in GA is beam tracing, in which a volumetric region is tracked rather than a single ray. There are two different branches of beam tracing, one being similar to ray tracing (Fig. 4) and the other being more related to the image-source method (Fig. 5).
