In developing virtual acoustic environments, it is important to understand the relationship between the computation cost and the perceptual significance of the resultant numerical error. In this article, we propose a quality criterion that evaluates the error significance of path-tracing-based sound propagation simulators. We present an analytical formula that estimates the error signal power spectrum. With this spectrum estimation, we can use a modified Zwicker's loudness model to calculate the relative loudness of the error signal masked by the ideal output. Our experimental results show that the proposed criterion can explain the human perception of simulation error in a variety of cases.

We introduce Bidirectional Sound Transport (BST) , a new algorithm that simulates sound propagation by bidirectional path tracing using multiple importance sampling. Our approach can handle multiple sources in large virtual environments with complex occlusion, and can produce plausible acoustic effects at an interactive rate on a desktop PC. We introduce a new metric based on the signal-to-noise ratio (SNR) of the energy response and use this metric to evaluate the performance of ray-tracing-based acoustic simulation methods. Our formulation exploits temporal coherence in terms of using the resulting sample distribution of the previous frame to guide the sample distribution of the current one. We show that our sample redistribution algorithm converges and better balances between early and late reflections. We evaluate our approach on different benchmarks and demonstrate significant speedup over prior geometric acoustic algorithms.