8:25 Why is E[X] being represented on the graph as a value on the "t" axis? If it's an integral, doesn't that make it a measure of "area under the curve", and not a unidimentional value?
We are integrating x p(x), and not p(x), so the interpretation of area under the curve is not valid here. Note that p(x) is a DENSITY function, and x p(x) integrated over a domain, gives a value from that domain.
why does the ring around the midle for the spectrum of blue noise correspond to the small features? I thought small frequencies (near origin) would correspond to large features? Maybe the finite domain you are using?
If you want to reduce rendering times, you want to be able to decrease variance as fast as possible with the least amount of samples. The earlier you have a good estimate of the image, the earlier you can stop calculating. Taking infinitely many samples is not possible on a computer (well possibly, but not fast), it's approximated discretely.
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books on poisson disk sampling, or other sampling methods?
8:25 Why is E[X] being represented on the graph as a value on the "t" axis? If it's an integral, doesn't that make it a measure of "area under the curve", and not a unidimentional value?
We are integrating x p(x), and not p(x), so the interpretation of area under the curve is not valid here.
Note that p(x) is a DENSITY function, and x p(x) integrated over a domain, gives a value from that domain.
why does the ring around the midle for the spectrum of blue noise correspond to the small features? I thought small frequencies (near origin) would correspond to large features? Maybe the finite domain you are using?
in fourier transform, near origin frequencies are low frequency components of the signal, which are thought to carry no information
I dont understand why path tracing isnt consistent. Why doesnt it cover all possible paths in the limit of infinitely many samples?
I guess it's referring to specular surfaces and point lights
If you want to reduce rendering times, you want to be able to decrease variance as fast as possible with the least amount of samples. The earlier you have a good estimate of the image, the earlier you can stop calculating. Taking infinitely many samples is not possible on a computer (well possibly, but not fast), it's approximated discretely.