Truncated Cone - A Universal Primitive Shape for Axisymmetric View Factor Systems

It is demonstrated that axisymmetric view factor systems can be modelled as a composite of truncated cones. For the hemisphere primitive shape, it is represented as a composite of truncated cones. One conclusion of the investigation is eight truncated cones are required to give a reasonable approximation to a hemisphere. The sensitivity of the run-time for the Monte-Carlo methods to the number of surfaces is investigated and the run-time of the Monte-Carlo method combined with ray tracing scales as the square of the number of surfaces, whereas the run-time of the hybrid Monte-Carlo method scales in a weakly linear way with the number of surfaces. Representing a hemisphere with 8 surfaces, for the view factor system considered and an RMS threshold of 0.001 the hybrid Monte-Carlo method and quasi-Monte-Carlo method have a speed-up of 8.3 and 55 compared to the Monte-Carlo method with ray tracing.