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248 III Lighting

(a) (b) (c)

Figure 4.2. (a) When the function is regular, the Monte Carlo integration works well

with a small number of samples. (b) When the function is irregular, it gets harder to

estimate. (c) Importance sampling focuses on the difficult areas and gives us a better

approximation.

by removing the F and G terms. At runtime, we compensate for this error by

multiplying by a Fresnel term.

This derivation results in a prefiltering that is very similar to the split-sum

method introduced by Brian Karis [Karis 13]. The difference is that by splitting

the sum, they take into account the F and G terms, which produces more accurate

results in the ...