We present a method for accelerating the computation of specular reflections in complex 3D enclosures, based on acoustic beam tracing. Our method constructs the beam tree on the fly through an iterative lookup process of a precomputed data structure that collects the information on the exact mutual visibility among all reflectors in the environment (region-to-region visibility). This information is encoded in the form of visibility regions that are conveniently represented in the space of acoustic rays using the Plücker coordinates. During the beam tracing phase, the visibility of the environment from the source position (the beam tree) is evaluated by traversing the precomputed visibility data structure and testing the presence of beams inside the visibility regions. The Plücker parameterization simplifies this procedure and reduces its computational burden, as it turns out to be an iterative intersection of linear subspaces. Similarly, during the path determination phase, acoustic paths are found by testing their presence within the nodes of the beam tree data structure. The simulations show that, with an average computation time per beam in the order of a dozen of microseconds, the proposed method can compute a large number of beams at rates suitable for interactive applications with moving sources and receivers.