GPU Pro 6

258 III Lighting

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Figure 4.13. PDF and its corresponding CDF.

1. Generate a random number α in the range [0 : 1].

2. Find an i where CDF(i) ≤ α.

3. Then, i is the resulting sample with PDF(i).

Because we have the PDF, CDF, and inverse CDF, we can now generate the

environment map samples. It is worth noting that since the samples’ locations

depend on neither the BRDF nor the shading point location and orientation, the

samples can be pregenerated on the CPU.AttheGPUstage,wesimplyintegrate

using those samples.

The final sample generation process can thus be described as follows:

1. ...