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Update web docs
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bejado committed Apr 17, 2023
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8 changes: 4 additions & 4 deletions docs/Filament.html
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</p><p>

However, in practice we're using <em class="underscore">importance sampling</em> which needs to take the \(pdf\) of the distribution
into account and adds a term \(\frac{\left&lt;\VoH\right&gt;}{D(h_i, \alpha)\left&lt;\NoH\right&gt;}\).
into account and adds a term \(\frac{4\left&lt;\VoH\right&gt;}{D(h_i, \alpha)\left&lt;\NoH\right&gt;}\).
See <a href="#importancesamplingfortheibl">Importance Sampling For The IBL</a> section:

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</p><p>

$$\begin{equation}
p(T_r(x)) = p(x) |J(T_r)|
p(T_r(x)) = p(x) |J(T_r)|^{-1}
\end{equation}$$

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</p><p>

$$\begin{equation}\label{iblPDF}
p(l,v,\Theta) = D(h,\alpha) \left&lt; \NoH \right&gt; |J_{h \rightarrow l}| \\
|J_{h \rightarrow l}| = \frac{1}{4 \left&lt; \VoH \right&gt;}
p(l,v,\Theta) = D(h,\alpha) \left&lt; \NoH \right&gt; |J_{h \rightarrow l}|^{-1} \\
|J_{h \rightarrow l}| = 4 \left&lt; \VoH \right&gt;
\end{equation}$$

</p>
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