From a2de55ad6bc2c3151b7440d25060f1e356cb62f1 Mon Sep 17 00:00:00 2001
From: Jason Foat <jasonfoat@gmail.com>
Date: Mon, 22 Jan 2024 11:20:24 -0800
Subject: [PATCH] Fix typo in HW1

---
 handouts/homework1.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/handouts/homework1.tex b/handouts/homework1.tex
index 066816e..d3004bb 100644
--- a/handouts/homework1.tex
+++ b/handouts/homework1.tex
@@ -215,7 +215,7 @@ \section{Metal}
 \begin{aligned}
 G_m &= G(\omega_{\text{in}}) G(\omega_{\text{out}}) \\
 G(\omega) &= \frac{1}{1 + \Lambda(\omega)} \\
-\Lambda(\omega) &= \frac{\sqrt{1 + \frac{\left(\omega_l.x \cdot \alpha_x\right)^2 + \left(\omega_l.y \cdot \alpha_y\right)^2}{\omega_l.z^2}} - 1}{2}
+\Lambda(\omega) &= \frac{\sqrt{1 + \frac{\left(\omega.x \cdot \alpha_x\right)^2 + \left(\omega.y \cdot \alpha_y\right)^2}{\omega.z^2}} - 1}{2}
 \end{aligned}.
 \end{equation}
 
@@ -275,7 +275,7 @@ \section{Clearcoat}
 D_c &= \frac{\alpha_g^2 - 1}{\pi \log(\alpha_g^2) \left( 1 + (\alpha_g^2 - 1) \left(h^l_z\right)^2 \right)} \\
 G_c &= G_{c}(\omega_{\text{in}}) G_{c}(\omega_{\text{out}}) \\
 G_{c}(\omega) &= \frac{1}{1 + \Lambda_c(\omega)} \\
-\Lambda_c(\omega) &= \frac{\sqrt{1 + \frac{\left(\omega_l.x \cdot 0.25\right)^2 + \left(\omega_l.y \cdot 0.25\right)^2}{\omega_l.z^2}} - 1}{2}
+\Lambda_c(\omega) &= \frac{\sqrt{1 + \frac{\left(\omega.x \cdot 0.25\right)^2 + \left(\omega.y \cdot 0.25\right)^2}{\omega.z^2}} - 1}{2}
 \end{aligned}.
 \end{equation}
 The Schlick Fresnel $F_c$ has a hard-coded index of refraction $\eta = 1.5$. The normal distribution function $D_c$ uses an isotropic roughness $\alpha = \alpha_g$. The masking-shadowing term $G_c$ uses a fixed roughness $0.25$. Note that this is an ad-hoc fit, and there is no clear geometric meaning of this microfacet BRDF.