Monte Carlo approximation of form factors with error bounded a priori

Abstract

The exchange of radiant energy (e.g., visible light, infrared radiation) in simple macroscopic physical models is sometimes approximated by the solution of a system of linear equations (energy transport equations). A variable in such a system represents the total energy emitted by a discrete surface element. The coefficients of these equations depend on the form factors between pairs of surface elements. A form factor is the fraction of energy leaving a surface element which directly reaches another surface element. Form factors depend only on the geometry of the physical model. Determining good approximations of form factors is the most time-consuming step in these methods, when the geometry of the model is complex due to occlusions.