Topological Sound Propagation with Reverberation Graphs


Efstathios Stavrakis

Nicolas Tsingos

Paul Calamia



Rensselaer Polytechnic Institute


(a) (b) (c) (d)

Figure 1: (a) Our approach uses a 3D scene, decomposed into cells and portals, to compute reverberation effects interactively. (b) We estimate global pressure decays along possible sound propagation routes in the cell adjacency graph describing the 3D geometry. (c) The pressure decay for a route (highlighted in red in (b)) is obtained by convolving room-to-room transport operators computed off-line. (d) Our graph-based reverberation engine has been integrated into a 3D game with scalable reverberation processing and supports up to 30 sources interactively. Inset shows the spectrogram of a reconstructed binaural reverberation filter.





Reverberation graphs is a novel approach to estimate global sound pressure decay and auralize corresponding reverberation effects in interactive virtual environments. We use a 3D model to represent the geometry of the environment explicitly, and we subdivide it into a series of coupled spaces connected by portals. Off-line geometrical-acoustics techniques are used to precompute transport operators, which encode pressure decay characteristics within each space and between coupling interfaces.


At run-time, during an interactive simulation, we traverse the adjacency graph corresponding to the spatial subdivision of the environment. We combine transport operators along different sound propagation routes to estimate the pressure decay envelopes from sources to the listener. Our approach compares well with off-line geometrical techniques, but computes reverberation decay envelopes at interactive rates, ranging from 12 to 100 Hz.


We propose a scalable artificial reverberator that uses these decay envelopes to auralize reverberation effects, including room coupling. Our complete system can render as many as 30 simultaneous sources in large dynamic virtual environments.








 author = "Stavrakis, Efstathios and Tsingos, Nicolas and Calamia, Paul",
 title = "Topological Sound Propagation with Reverberation Graphs ",
 journal = "Acta Acustica/Acustica - the Journal of the European Acoustics Association (EAA)",
 year = "2008",
 url = ""



Demo Videos




Simple two-room environment


Multi-room environment





Pyramid Large two-room environment




This demo was created using the Penta-G game.

Thanks to Chris Chiu and Michael Wimmer for providing the source code of the game engine.

The Pyramid level was created by Fanouris Moraitis.



3-Room environment


Demonstration of reverberation graphs with multiple dynamic sources and the effects of room coupling.




This demo was created using the Penta-G game.

Thanks to Chris Chiu and Michael Wimmer for providing the source code of the game engine.



You need the DivX codec to play back the videos.