message: Update incorrect equations of importance sampling
diff: @@ -3621,13 +3621,13 @@ $$\begin{equation}
  The PDF of the BRDF can therefore be expressed as in equation $\ref{importantPDF}$:
  $$\begin{equation}\label{importantPDF}
  -p(\theta,\phi) = \frac{\alpha^2}{\pi(cos^2\theta (\alpha^2-1) + 1) cos\theta sin\theta}
  +p(\theta,\phi) = \frac{\alpha^2}{\pi(cos^2\theta (\alpha^2-1) + 1)^2} cos\theta sin\theta
  \end{equation}$$
  The term $sin\theta$ comes from the differential solid angle $sin\theta d\phi d\theta$ since we integrate over a sphere. We sample $\theta$ and $\phi$ independently:
  $$\begin{align*}
  -p(\theta) &= \int_0^{2\pi} p(\theta,\phi) d\phi = \frac{2\alpha^2}{cos^2\theta (\alpha^2-1) + 1} cos\theta sin\theta \\
  +p(\theta) &= \int_0^{2\pi} p(\theta,\phi) d\phi = \frac{2\alpha^2}{(cos^2\theta (\alpha^2-1) + 1)^2} cos\theta sin\theta \\
  p(\phi) &= \frac{p(\theta,\phi)}{p(\phi)} = \frac{1}{2\pi}
  \end{align*}$$
  