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This paper presents the beam tracing with refraction method, developed to examine the possibility of creating the beam tracing simulation of sound propagation in environments with piecewise nonhomogenous media. The beam tracing with refraction method (BTR) is developed as an adaptive beam tracing method that simulates not only the reflection but also the refraction of sound. The scattering and the diffraction of sound are not simulated. The BTR employs 2D and 3D topology in order to efficiently simulate scenes containing non-convex media. After the beam tracing is done all beams are stored in a beam tree and kept in the computer memory. The level of sound intensity at the beginning of each beam is also memorized. This beam data structure enables fast recalculation of results for stationary source and geometry. The BTR was compared with two commercial ray tracing simulations, to check the speed of BTR algorithms. This comparison demonstrated that the BTR has a performance similar to state-ofthe-art room-acoustics simulations. To check the ability to simulate refraction, the BTR was compared with a commercial Finite Elements Method (FEM) simulation. In this comparison the BTR simulated the focusing of the ultrasound with an acoustic lens, with good accuracy and excellent performance.

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Original scientific paperIn order to expand the area of use of the beam tracing method, the beam tracing with the refraction method (BTR) was developed. The BTR is best suited for acoustic and hydro-acoustic simulation of non-homogenous environments. The BTR can trace the refraction as well as the reflection of the sound wave, using triangular beams. The geometry of the scene in the BTR is based on triangle meshes rather than polygons. This enables the BTR to simulate complex, irregular shaped objects, including non-convex volumes. Furthermore, the BTR traces beams through several entities filled with different media. This paper presents algorithms and data structures used to divide beams during the interaction of a beam with the complex, non-convex environment. This paper also brings measurements of the implemented beam division code and the comparison of measured results with results of other methods. Key words: Acoustics, Beam tracing, Hidden surface removal, Hydro-acoustics, SimulationDijeljenje snopova kod akustičke simulacije nehomogenih sredina. Proširena metoda praćenja snopova (PMPS) razvijena je kako bi se proširilo područje primjene metode praćenja snopova. PMPS je prilagoîena akustičkim i hidroakustičkim simulacijama nehomogenih sredina. Geometrija scene se u PMPS-u temelji na nepravilnim trokutastim mrežama, a ne na poligonima, tako da je moguće simulirati složene, nepravilne objekte. Osim toga, PMPS prati širenje snopova kroz više nekonveksnih entiteta, ispunjenih sa različitim medijima. U ovom radu predstavljeni su algoritmi i strukture podataka pomoću kojih se vrši dijeljenje snopova u PMPS-u. Dijeljenje snopova se dogaîa prilikom interakcije snopa sa složenom, nekonveksnom sredinom. U radu su takoîer prikazana mjerenja vremenske složenosti koda PMPS-a, te usporedba sa drugim metodama.