A study about the form factors kernel functions

Abstract

This paper presents a study of the form factors (FF) function kernel. The accuracy of FF estimate is known as a difficult problem when simulating radiative energy exchanges between objects inside an enclosure. By carefully studying the FF function between two polygons we are able to propose a very interesting characterization of its behaviour according to the relative distance between those polygons (general form of the function, location and height of its unique maximum, effect of polygons orientation and distance, ...). According to the results of this study we estimate the FFs between any two polygons by distinguishing the areas where the kernel has smooth variations from the those where it changes quickly. A fine integration is thus performed for the more varying parts of the kernel whereas the other parts are computed more easily. We show that even a very simple implementation of our approach provides accurate estimates of the FF close to the results provided by the Schroeder formula in a time 8 up to 10 times faster. Moreover our approach does not suffer from lack of accuracy when surfaces are very closed from each other thus outperforming classical methods.