# Questions tagged [monte-carlo]

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### Transforming between solid angle and spherical angle distribution in PBRT

In the Monte Carlo chapter of PBRT, in the section Transforming Between Distributions, they say "The density with respect to $\theta$ and $\phi$ can therefore be derived", but they start ...
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### MSE & Variance of Monte Carlo Estimator

I am trying to prove the equality of $$\rm MSE(\langle I\rangle)=Var(\langle I \rangle)+Bias(\langle I \rangle)^2$$ but obviously I got something wrong as they don't equal in my calculation: So here ...
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1 vote
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### Applying Monte-Carlo methods in path tracing

I've noticed that I consistently get worse results in path-tracing when I try to do monte-carlo correctly compared to when I don't, and I think this might be because of a fundamental misunderstanding. ...
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### importance sampling rectangular light

I have been struggling very much to wrap my head around this part of Peter Shirley's book. There is no explanation what the angle Alpha represents and to make things worse in the code the cos(Alpha) ...
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### Generation of stratified cosine weighted samples on hemisphere

I have had luck with cosine weighted hemisphere samples, and I know how to generate stratified uniform samples, but I wanted to experiment with combining the two. However, how do I correctly stratify ...
• 315
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### Does cosine weighted hemisphere sampling still require NdotL when calculating contribution for indirect light?

When converting from uniform hemisphere sampling to cosine weighted hemisphere sampling I am confused by a statement in an article. My current indirect contribution is calculated as: ...
• 315
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### Is this Russian roulette code correct?

I'm using www.scratchapixel.com among other resources to help me learn how to implement a renderer. I am looking at the following code from this page where a packet of photons moving through a ...
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### Why random monte carlo sampling instead of uniform sampling?

Why is it that it's so common to use monte carlo randomized sample locations, instead of uniform sampling? I'm assuming that taking randomized samples gives some benefit but I don't know what they ...
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### Full Monte-Carlo Volumetric Scattering

I would like to add full monte-carlo volumetric scattering to my path tracer, but I'm having a hard time researching how to do it. Let me explain what I would like to do: A ray enters a material, and ...
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