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One point: the Lambert BRDF is not $N\cdot L$, it's just the albedo divided by pi. The $N \cdot L$ factor comes from the $\cos \theta$ in the rendering equation. So, when sampling with a cosine-weighted distribution the $N \cdot L$s and pis will cancel out and you should just be accumulating $\frac{1}{N} \sum L_i * \text{albedo}$. It looks like in your code ...


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Q1: how to represent path tracing as the first one... Your materials have brought enough information, the first formula, quoted from your material, presents as The path integral formulation of light transport formalizes the idea by writing the camera response as an integral over all light transport paths of all lengths in the scene, which given path ...


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Disclaimer: I am assuming that you are implementing a classical Monte Carlo estimator. The Problem Discarding samples will change PDF of your sampling technique. You are cutting off part of the sampled domain where PDF is non-zero, which effectively leads to a trimmed version of the original PDF but implicitly re-normalized so the remaining part integrates ...


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