View factors-when is ray tracing a good idea?

Abstract

In this paper a number of variants of the Monte-Carlo method and quasi-Monte-Carlo method are used to evaluate three view factor configurations. The key question asked is “Is the ever-popular Monte-Carlo method combined with ray tracing the best approach for evaluating view factors?”. For two of the view factor configurations a Monte-Carlo method and quasi-Monte-Carlo method based on the numerical integration of the view factor integral are much more accurate than a Monte-Carlo method and quasi-Monte-Carlo method based on ray tracing. An interesting conclusion is that when ray tracing is inefficient, i.e., the view factor is small, numerical integration works very well, exactly when ray tracing has poor accuracy.For the third view factor where the two surfaces have a common edge the view factor integral has a singularity at the common edge and ray tracing works well relative to numerical integration. A new hybrid Monte-Carlo method and quasi-Monte-Carlo method that combines the advantages of ray tracing and numerical integration for the view factor configuration with a common edge is presented. The hybrid quasi-Monte-Carlo method is shown to be the most efficient method of evaluating the view factor integral.