This paper addresses the problem of geometry-based sound reverberation for applications of virtual acoustics. In particular, we propose a novel method that allows us to significantly speed-up the construction of the beam tree in beam tracing applications, by avoiding space subdivision. This allows us to dynamically recompute the beam tree as the sound source moves. In order to speedup the construction of the beam tree, we determine what portion of which reflectors the beam “illuminates” by performing visibility checks in the “dual” of the geometric space.