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Fix ICD formula for solved PDF in Importance Sampling (#1622) #1705

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@spayne spayne commented May 11, 2025

  1. This pull request fixes the ICD math. What was published was $8 d^\frac{1}{3}$. What we want is: $2 d^\frac{1}{3}$.
  2. Note that when generating the estimate, the ICD gets cancelled out anyway. The code sum += x*x/pdf(x) is $\sum \frac{icd^2}{pdf(icd)} = \sum \frac{icd^2}{\frac{3}{8}icd^2} = \frac{8}{3}$. The text doesn't mention this cancellation but does bring up the ICD again when talking about the PDF. I think it's wiser to stick to the PDF so I updated this reference as well.
  3. I also updated CHANGELOG.md and the integrate_x_sq.cc

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spayne commented May 11, 2025

Requesting review from @RayTracing/reviewers

@spayne spayne marked this pull request as draft May 11, 2025 18:49
@spayne spayne marked this pull request as ready for review May 11, 2025 18:49
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