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According to Peter Shirely paper, one pdf(probability density function) can be defined for the union of the light sources and pick only one using a random number from this density:

p(x)=α1P1(x)+(1α1)P2(x)

This has been referred to as mixture densities. where α1[0,1] and P1 is a pdf for selecting a point on the L1 geometry (usually 1/A). If the random number is less than α1 then the total estimate is (estimated L1)/α1.

This has been extended for N: p(x)=α1P1(x)+α2P2(x)++αnPn(x)

My question is how one pick two or multiple light sources, instead of just one, from the above density and what the estimate would be in that case.

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    Not sure I'm understanding your question. Are you asking how do you sample from the mixture of n lights? If you want to sample two or more lights, you would just repeat the procedure to sample a single light (with fresh random numbers), right? Or is there something else you're asking? Commented Feb 14, 2017 at 23:18
  • Thanks Nathan, you are correct you as to do the procedure again for multiple lights. But I wonder if the above mixture density allows one to pick two or more samples from the distribution.
    – ali
    Commented Feb 16, 2017 at 12:08
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    Are you worried about anything in particular with just repeating the process multiple times? Were you concerned about sometimes choosing the same light more than once? Commented Feb 19, 2017 at 20:54
  • @trichoplax. No. I just want to understand mathematically how one choose multiple samples from a merge density.
    – ali
    Commented Feb 20, 2017 at 12:53

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