Suppose we’re trying to use Monte Carlo techniques toĮvaluate some integral integral f left-parenthesis x right-parenthesis normal d x. We will not provideĪ rigorous proof of this fact but will instead present an informal and Is similar in shape to the integrand, variance is reduced. Integrand (the BSDF, the incoming illumination distribution, etc.),Īs long as the random variables are sampled from a probability distribution that More generally, ifĭirections are sampled from distributions that match other factors of the The likelihood of choosing directions near the horizon. General, we would be better served if we sampled directions in a way that reduced Wasted, as the contribution to the final result will be minuscule. All the expense of evaluating the BSDF and tracing a ray toįind the incoming radiance at that sample location will be essentially That is nearly perpendicular to the surface normal, the cosine term will beĬlose to 0. Integral is estimated if a direction is randomly sampled Than (2) applying importance sampling and choosing stratified rays fromįor example, suppose we are evaluating the scattering equation,Įquation ( 5.9). Of rays over the hemisphere gives an image with much more variance Figure 13.19: (1) Using a stratified uniform distribution
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