(L) [2006/09/12] [greenhybrid] [pdf] Wayback!Hi,
I have a question about pdf's.
I have a pdf_c(x)=1 and a pdf_x(x)=x (=acceptance probability, x is the cos(angle) of the new direction to the surf-normal)
Now I sample the hemisphere, once according to pdf_c, once to pdf_x. For sure pdf_x gives better noise reduction, but:
The image is to bright compared to the pdf_c.
Thinking about it and drawing the graph of the functions on a paper-sheet, it made kinda clik:
pdf_c gives a x-axis parallel line, or one could say for pdf_c[0..1] a rectangle. pdf_x[0..1] gives a triangle (half the area of the rectangle). So I multiplied the lighting given due the path-tracing with 0.5, et voila, results are correct (?) again.
Now, I think that's not correct, it's just a hack that accidentally gives the correct result. I've seen no paper which normalizes the result of the lighting by 0.5 or so.
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(L) [2006/09/12] [goodbyte] [pdf] Wayback!Hi, I'm not really sure what you are doing, how do you sample with pdf_c=1? For uniform hemisphere sampling you need to normalize with 1/(2pi), and with cosine sampling you need to normalize with cos(x)/pi...
(have a look in Global Illumination Compentium, paragraph 34-35, [LINK http://www.cs.kuleuven.ac.be/~phil/GI/TotalCompendium.pdf]).
(L) [2006/09/13] [greenhybrid] [pdf] Wayback!brainvoid this week, forget about my question.
If you uniformly generate numbers [0..1] using the acceptance probalitity 1, then the avg. value is simply 0.5
And when importance sampling numbers like this: