Evaluating View Factors Using a Hybrid Monte-Carlo Method

This paper demonstrates that the well-known method for calculating view factors, the Monte Carlo method, combined with ray tracing is not necessarily the most efficient strategy. The Monte Carlo method and quasi-Monte Carlo method combined with numerical integration, provided the surfaces in a configuration are not too close together, are more accurate for the same run-time than a ray tracing-based Monte Carlo method. The Monte Carlo method based on numerical integration is complementary to the Monte Carlo method based on ray tracing. When many rays are required to calculate an accurate view factor, few function evaluations in a numerical integration approach are necessary to achieve the same accuracy. Where the surfaces in a configuration are touching, the Monte Carlo method with numerical integration converges to the exact view factor very slowly due to a singularity in the view factor multi-integral. For these configurations, a hybrid Monte Carlo method and quasi-Monte Carlo method are demonstrated to be the stochastic methods of choice.