@article{Lu_Song_2018, title={Development Of A Method To Realize A Uniform Sound Field In Three- Dimensional Spaces Based On The Ray-Tracing Algorithm}, volume={46}, url={https://jcaa.caa-aca.ca/index.php/jcaa/article/view/3213}, abstractNote={<div class="page" title="Page 5"><div class="section"><div class="layoutArea"><div class="column"><p><span>In this study, a method of mapping ray motions in three-dimensional geometrical spaces was theoretically established using the ray-tracing algorithm. The paths along which the acoustic ray propagates in enclosed rectangular and concave spaces are described according to the ray-tracing algorithm. The location and the direction of the acoustic ray at arbitrary points on the paths were explored. The largest Lyapunov exponents (LLEs) of the ray systems in the rectangular and concave spaces were determined using the Wolf algorithm based on the points on the propagation paths with equal length in the time series. A new chaotic concave geometry is produced with a positive LLE. The LLEs of ray dynamics between the two geometrical spaces were compared and the results showed that the ray moves in a regular fashion in the rectangular space with an LLE of 0 whereas the ray exhibits chaotic behavior in the concave space with a positive LLE. The acoustic fields in both of these spaces in were described by applying ray chaos to the building acoustics. The acoustic diffusion was evaluated based on the uniformity of the sound pressure levels at different positions in the sound field using Odeon room acoustics software. The results showed that the proposed model has the potential to simulate chaotic dynamics of acoustic rays in enclosed spaces. </span></p></div></div></div></div>}, number={3}, journal={Canadian Acoustics}, author={Lu, Yigang and Song, Hengling}, year={2018}, month={Nov.}, pages={5–14} }