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

It is demonstrated that axisymmetric view factor systems can be modeled 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 eight surfaces, for the view factor system considered and an root mean squared error (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.