The effect of refraction as a non-linear transformation on beam tracing simulation of sound propagation

Comprehensive beam tracing method is a simulation method that calculates refraction as well as reflection of sound. Due to the non-linear nature of Snell’s law, refraction (in contrast to reflection) is not a linear transformation. Because of this triangular beams used in comprehensive beam tracing simulation lose focus after refraction. In this paper the problem of non-linearity of refraction of beams is discussed. The solution used in comprehensive beam tracing method is an approximation used during calculation of geometry of refracted beams. This approximation is presented, and the error induced by this approximation is analyzed. Using the comprehensive beam tracing method, the propagation of ultrasound in a simple scene is simulated. Results obtained with this simulation are compared with theoretical prediction in order to check the influence of the approximation. Results show that error induced by approximation can be tolerated, especially for narrow beams, and for environments where speed of sound between different entities doesn't differ much.