Chapter 20. GPU-Based Importance Sampling

Because BRDFs are a part of the integration, they serve as a good measure to guide the simpling to produce directions that best approximate the integral. Here, we use a normalized BRDF as the PDF for sampling. To sample this PDF, we convert a random number pair into an important direction for the BRDF.

• 通过在 CDF 中进行 Uniform Sampling 反推样本值 $P(s) = \int_0^s p(\theta)\mathrm{d}\theta$
• 需要先将 BRDF 归一化，才能用作 PDF

注意此时求出来的 specular direction 朝向 z 轴

• 两个样本量的分离，可以通过求边缘概率 marginal probability 来获得

• 根据 CDF 公式 $P(s) = \int_0^s p(\theta)d\theta$，然后对 $p(\theta_s)$ 求积分，最后再通过：

$$ \theta_s = P^{-1}(Uniform Sampling) $$

• 求出 $\theta_s$
• 怎么求出 $\phi_s$？文章里提到的条件概率我没太看懂