TABLE OF CONTENTS The robust and efficient computation of the form factors F ij between each pair of input patches is a major problem with the classic radiosity method. In this section, we will show that the form factors can be viewed as probabilities, and we will present an overview of algorithms for sampling according to form factor probabilities. The fact that form factors are probabilities that can be sampled efficiently leads to algorithms that allow us to solve the radiosity system of equations without the need to ever compute the value of a form factor. These algorithms will be described in Sections 6.3 and 6.4.
Recall that the form factor F ij is given by the following four-dimensional integral (Equation 6.7):
with
We will need the following properties of the form factors:
The form factors are all positive or zero in a scene consisting of closed, opaque objects: they cannot be negative because the integrand is positive or zero. They will be equal to zero for a pair of patches i and j that are mutually invisible.
The form factors F ij between a patch i and all other patches j in a scene sum to at most one. If the scene is closed, then
If the scene is not closed, the sum of the form factors is less than 1.
The form factors satisfy the following reciprocity relation:
