Abstract: A new form factor analogy, that has been derived from results of integral geometry, is introduced. The new analogy is shown to be useful for stochastic evaluation of the local form of the rendering equation used in various Monte Carlo methods for calculating global illumination. It makes it possible to improve importance sampling in these methods, thereby speeding up convergence. A new class of bidirectional reflection distribution functions that directly benefits from the analogy and permits exact evaluation and calculation of correctly distributed vectors for Monte Carlo integration is presented.