It's interesting that the Monte Carlo Algorithm can be applied to so many different realms. Here, the randomness actually allows for both higher efficiency and accuracy. This contrasts with some of the other Monte Carlo algorithms that reduce the accuracy of the calculation.
Js2604
This shadow problem seems similar to the processing involved in ray tracing. Is Monte Carlo integration something that gets applied to ray tracing given its potential to be high cost when pursuing high quality renders?
ashvindhawan
This reminds me a lot of the images we looked at when studying antialiasing. The randomness of Monte Carlo actually helps us reduce unrealistic artifacts, which is surprising because as @StephenYangjz describes Monte Carlo algorithms in other applications do not attempt to improve/find an objectively better solution
shreyaskompalli
Could we perhaps get even closer to the true answer by introducing partial color values for the ray-traced pixels in the Monte-Carlo example? For instance, we perform random sampling to get a "blocked" or "unblocked" result, and then weight the eventual pixel value by the inverse of the distance to the nearest boundary of the blocker. This would probably be more computationally expensive, but I think it would bring the image closer to the True Answer.
ksaralle
point light sources does not exist, and there are many many rays of light emitting from the source. the reasoning that monte carlo brings our rendering result closer to true answer is that it takes into account the fact that in reality a point on the ground is not rendered by an absolute boolean value that indicates whether it is shadowed or not. the point may receive some of the light rays, and is blocked from some other light rays. by sampling random point on light, the edge of the shadow will be smoothed in some sense
atsu-kotani
Is applying a simple box/Gaussian filter (convolution) for points on the floor a reasonable alternative? Considering a point A and its immediate neighbor B on the floor, I imagine B can be interpreted as an approximation of A when the sampled light point is shifted by a little (and therefore approximation of another sample for point A).
crystal-zq-wang
even though the result of randomly sampling a point on the light does pretty decently in getting to the true answer, is there a "cutoff" point after which we've taken N samples such that the approximation is close enough to the real thing? And how would such a cutoff be determined?
It's interesting that the Monte Carlo Algorithm can be applied to so many different realms. Here, the randomness actually allows for both higher efficiency and accuracy. This contrasts with some of the other Monte Carlo algorithms that reduce the accuracy of the calculation.
This shadow problem seems similar to the processing involved in ray tracing. Is Monte Carlo integration something that gets applied to ray tracing given its potential to be high cost when pursuing high quality renders?
This reminds me a lot of the images we looked at when studying antialiasing. The randomness of Monte Carlo actually helps us reduce unrealistic artifacts, which is surprising because as @StephenYangjz describes Monte Carlo algorithms in other applications do not attempt to improve/find an objectively better solution
Could we perhaps get even closer to the true answer by introducing partial color values for the ray-traced pixels in the Monte-Carlo example? For instance, we perform random sampling to get a "blocked" or "unblocked" result, and then weight the eventual pixel value by the inverse of the distance to the nearest boundary of the blocker. This would probably be more computationally expensive, but I think it would bring the image closer to the True Answer.
point light sources does not exist, and there are many many rays of light emitting from the source. the reasoning that monte carlo brings our rendering result closer to true answer is that it takes into account the fact that in reality a point on the ground is not rendered by an absolute boolean value that indicates whether it is shadowed or not. the point may receive some of the light rays, and is blocked from some other light rays. by sampling random point on light, the edge of the shadow will be smoothed in some sense
Is applying a simple box/Gaussian filter (convolution) for points on the floor a reasonable alternative? Considering a point A and its immediate neighbor B on the floor, I imagine B can be interpreted as an approximation of A when the sampled light point is shifted by a little (and therefore approximation of another sample for point A).
even though the result of randomly sampling a point on the light does pretty decently in getting to the true answer, is there a "cutoff" point after which we've taken N samples such that the approximation is close enough to the real thing? And how would such a cutoff be determined?