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TheRestOfYourLife: Light Scattering, Where did you get that equation? #415
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Problems with clarity in Light Scattering are well known, see #277 My understanding of your issue is The integration is over the half-sphere above the plane. So theta from 0 to pi/2 It's not entirely clear what's happening in that paragraph, but the point is to normalize the PDF to 1. We know that for a lambertian, the PDF should scale with cos(theta). So, we integrate over the half-sphere (scaled with cos(theta)), to determine the are over the surface. Once we find this (pi). We then scale the PDF by this factor (pi). The cos(theta) * sin(theta) is because integrating over spherical polar coordinates means dA = sin(theta) dtheta dpi So Integral integral cos(theta) dA Or Integral integral cos(theta) sin(theta) dtheta dphi |
I checked the previous If cos(theta) is PDF, then the integral of it is the area of PDF. I was thinking about the area of hemisphere, that's why it's misleading for me. Now, it make sense. if |
The third book has been largely rewritten, and changes reside in branch |
Hi, Why does the sin using the same theta as cos? What's the physical meaning? I never seen any sphere area integral like. After alot google search, I didn't find this equation from anywhere.
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