Modeling nonuniform energy decay through the modal decomposition of acoustic radiance transfer (MoD-ART)

TL;DR

MoD-ART introduces a modal decomposition of acoustic radiance transfer to model late reverberation in real-time for complex environments with multiple moving sources and listeners. By expressing the TD-ART transfer as a sum of energy-decay modes with poles and residues, the method isolates environment-dependent propagation from interactive elements, enabling a compact, efficient representation. The approach can capture multiple decay slopes and flutter echoes by selecting salient poles and separating input-output coupling, offering significant reductions in runtime cost and memory relative to RTM and full TD-ART. This yields practical benefits for VR/AR audio in coupled volumes and other geometrically intricate spaces, while preserving physical interpretability and accuracy of late reverberation.

Abstract

Modeling late reverberation in real-time interactive applications is a challenging task when multiple sound sources and listeners are present in the same environment. This is especially problematic when the environment is geometrically complex and/or features uneven energy absorption (e.g. coupled volumes), because in such cases the late reverberation is dependent on the sound sources' and listeners' positions, and therefore must be adapted to their movements in real time. We present a novel approach to the task, named modal decomposition of acoustic radiance transfer (MoD-ART), which can handle highly complex scenarios with efficiency. The approach is based on the geometrical acoustics method of acoustic radiance transfer, from which we extract a set of energy decay modes and their positional relationships with sources and listeners. In this paper, we describe the physical and mathematical significance of MoD-ART, highlighting its advantages and applicability to different scenarios. Through an analysis of the method's computational complexity, we show that it compares very favorably with ray-tracing. We also present simulation results showing that MoD-ART can capture multiple decay slopes and flutter echoes.

Figures (8)

• Figure 1: Illustration of three volumetric paths. In total, there are two volumetric paths connecting each pair of patches with an unobstructed view of each other (one path in each direction). The paths in this figure go from patch 1 to patch 2 ($P_{1,2}$) , from 1 to 3 ($P_{1,3}$) , and from 2 to 3 ($P_{2,3}$) . The figure also shows a sound source and a listener, respectively supplementing and detecting the energy contained by the volumetric paths.
• Figure 2: Block diagram of a TD-ART model, as expressed in \ref{['eq:ZD-ART']}. The filters in $\bm{B}(z)$ describe how the input energy $\bm{x}(z)$ is distributed among the volumetric paths, and the filters $\bm{C}(z)$ describe how the volumetric paths' energy $\bm{s}(z)$ is gathered into the energy outputs $\bm{y}(z)$. The delays $\bm{T}_\textrm{a} (z)$ model the propagation of energy along each volumetric path, and the matrix $\bm{A}$ describes how energy is reflected/scattered from each path to the others. The filters $\bm{D}(z)$ model the direct energy propagation between sources and listeners.
• Figure 3: Positional dependence of residues in a scene featuring three coupled rooms. The position of the sound source is fixed, and residues' values are plotted as a function of the listener's position. The three shown residues are those related to the poles with \ref{['fig:Residue_map_1']} largest, \ref{['fig:Residue_map_2']} second-largest, and \ref{['fig:Residue_map_3']} third-largest magnitudes, all of which are real and positive. Note that the three plots' color bars cover different ranges.
• Figure 4: Computational complexity comparison of RTM, TD-ART, and MoD-ART, as discussed in Section \ref{['sec:complexity-conclusions']}. All methods consider interactively updated source and listener positions, except for "TD-ART, static sources" where only listeners are updated. Complexity is plotted in \ref{['fig:Complexity_triple']} as a function of sources and listeners, considering the three-room case shown in \ref{['fig:environment']} in terms of numbers of polygons and visibility (${N_\text{Polys} = 140}$, ${V \approx 0.4}$). In \ref{['fig:Complexity_visibility']}, complexity is plotted as a function of the number of polygons, with ${S = L = 10}$ sources and listeners, in three hypothetical environments with different visibility factors: ${V = 0.25}$ (solid lines, low visibility), ${V = 0.5}$ (dashed lines, moderate visibility), and ${V = 1}$ (dotted lines, strictly convex enclosure).
• Figure 5: The environment used in the presented tests. Source and listener positions are also reported in Table \ref{['tab:positions']}.