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Is it possible that an "iterative" equation exists? Or is it just in the nature of this problem that we can really only reason about ray tracing recursively?


Is this 'angle between incoming direction and normal' the same meaning as Lambert's angle?


Is it ever possible to use data to train a model for reflection?


Say our point lies on the top of a cone, can't the energy contribution come from below the hemisphere too? Why do we only integrate over the hemisphere?


Is seems like a very mathematically intense computation to make. Is there a way that it is broken up into smaller iterative pieces to make faster or it is just some sort of hardware arithmetic in the GPU that can do something like this very quickly?


Why do we only consider all directions in a hemisphere here?


I am confused about the integrals here... Why do I need to sum them up instead of taking only 1 direction?


Just to clarify: is the cosine here based on Lambert's law or on spherical integrals?


For the unknown reason, I really like this slide. The equation shows the great high level overview of how outgoing radiance looks like in terms of incoming and emitted radiance.


Does this equation apply to non-hemispheric situations?


In order to speed up calculations, are memo tables used to store intermediate radiance values, or are there simply too many radiance values involved in a single scene for this to make sense?


This equation being recursive is the reason raytracing is so costly, right?


Is there any optimization on continuous recursion? i.e. save stack space used by recursion?


How is it that all of these variables can have their effects summarized by a single radiance value? Wouldn't the equation be more like "x + y = z + w", kind of thing?