@lisyarus Thanks for the writeup! One thing I always struggle with (MIS, ReSTIR, etc.) is how do you compute the probability p(i)? Is it just a matter of looking it up for a given function? Or can it be derived given your function? For instance, for a uniform distribution, I assume p(i) is 1 because each sample has the same probability of being picked? Or is it 1/interval? Maybe I just need to brush up on probability theory :)
@theWarhelm Usually you explicitly compute it, yep! For a uniform distribution on a set with "size" A, the probability is 1/A (e.g. 1/(b-a) for an interval [a,b], or 1/(2*pi) for a hemisphere). For more complicated distributions like VNDF there's just a formula for the actual probability.
@theWarhelm I'll add that sometimes the probability isn't actually known, and in this case you can't use the method for Monte-Carlo. E.g. in smth called "sampling importance resampling" they generate N samples with distribution P and select one of them with some weights to approximate some other distribution Q. When N=1, you get the original distribution P. When N -> infinity, you get Q. In the middle, you get some distribution with pretty much unknown probability.
@j_bertolotti@lisyarus It is very common in graphics literature though. It is indeed cursed as some people using it as directions while other people use it for angles
@j_bertolotti@lesley Tbh I don't like this practice - it clutters formulas way too much. From my experience, this is rarely done in in math literature.
You still have to remember which variable means what, so remembering what is a vector and what isn't doesn't seem like it changes that much.
@lisyarus Hard disagree. Together with using standard symbols for standard quantities (in Physics&co the same quantities keep turning up over and over), it helps parsing an otherwise complex equation at a glance. @lesley
@lisyarus@j_bertolotti I always find working memory overload to be one of the major obstacles when reading math-heavy literature, so I definitely appreciate whatever notations that alleviate this cognitive burden
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