From 61fd5bb61d7c7a8e5692df07daf10e454d6e3ef6 Mon Sep 17 00:00:00 2001
From: bobarna <barnabas.borcsok@gmail.com>
Date: Sun, 30 Jan 2022 17:11:06 +0100
Subject: [PATCH] Almost finish the presentation + add images

---
 img/ahsoka-smoke.png     | Bin 0 -> 1165849 bytes
 img/ray-marching.pdf     | Bin 0 -> 4040 bytes
 img/ray-marching.pdf_tex |  65 ++++
 img/ray-marching.svg     | 573 ++++++++++++++++++++++++++++++
 img/tracking.pdf         | Bin 0 -> 9580 bytes
 img/tracking.pdf_tex     |  78 ++++
 img/tracking.svg         | 748 +++++++++++++++++++++++++++++++++++++++
 main.tex                 |  39 +-
 8 files changed, 1491 insertions(+), 12 deletions(-)
 create mode 100644 img/ahsoka-smoke.png
 create mode 100644 img/ray-marching.pdf
 create mode 100644 img/ray-marching.pdf_tex
 create mode 100644 img/ray-marching.svg
 create mode 100644 img/tracking.pdf
 create mode 100644 img/tracking.pdf_tex
 create mode 100644 img/tracking.svg

diff --git a/img/ahsoka-smoke.png b/img/ahsoka-smoke.png
new file mode 100644
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diff --git a/img/ray-marching.pdf_tex b/img/ray-marching.pdf_tex
new file mode 100644
index 0000000..a7f5f1c
--- /dev/null
+++ b/img/ray-marching.pdf_tex
@@ -0,0 +1,65 @@
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+%% Accompanies image file 'ray-marching.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
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+%%   \input{<filename>.pdf_tex}
+%%  instead of
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+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
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+%% in the preamble, and then including the image with
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+%% Alternatively, one can specify
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diff --git a/img/tracking.pdf_tex b/img/tracking.pdf_tex
new file mode 100644
index 0000000..8133276
--- /dev/null
+++ b/img/tracking.pdf_tex
@@ -0,0 +1,78 @@
+%% Creator: Inkscape inkscape 0.92.5, www.inkscape.org
+%% PDF/EPS/PS + LaTeX output extension by Johan Engelen, 2010
+%% Accompanies image file 'tracking.pdf' (pdf, eps, ps)
+%%
+%% To include the image in your LaTeX document, write
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics{<filename>.pdf}
+%% To scale the image, write
+%%   \def\svgwidth{<desired width>}
+%%   \input{<filename>.pdf_tex}
+%%  instead of
+%%   \includegraphics[width=<desired width>]{<filename>.pdf}
+%%
+%% Images with a different path to the parent latex file can
+%% be accessed with the `import' package (which may need to be
+%% installed) using
+%%   \usepackage{import}
+%% in the preamble, and then including the image with
+%%   \import{<path to file>}{<filename>.pdf_tex}
+%% Alternatively, one can specify
+%%   \graphicspath{{<path to file>/}}
+%% 
+%% For more information, please see info/svg-inkscape on CTAN:
+%%   http://tug.ctan.org/tex-archive/info/svg-inkscape
+%%
+\begingroup%
+  \makeatletter%
+  \providecommand\color[2][]{%
+    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
+    \renewcommand\color[2][]{}%
+  }%
+  \providecommand\transparent[1]{%
+    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
+    \renewcommand\transparent[1]{}%
+  }%
+  \providecommand\rotatebox[2]{#2}%
+  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
+  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
+  \ifx\svgwidth\undefined%
+    \setlength{\unitlength}{361.89146507bp}%
+    \ifx\svgscale\undefined%
+      \relax%
+    \else%
+      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
+    \fi%
+  \else%
+    \setlength{\unitlength}{\svgwidth}%
+  \fi%
+  \global\let\svgwidth\undefined%
+  \global\let\svgscale\undefined%
+  \makeatother%
+  \begin{picture}(1,0.38130608)%
+    \lineheight{1}%
+    \setlength\tabcolsep{0pt}%
+    \put(0,0){\includegraphics[width=\unitlength,page=1]{tracking.pdf}}%
+    \put(0.22939413,0.11234945){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_0}$\end{tabular}}}}%
+    \put(0,0){\includegraphics[width=\unitlength,page=2]{tracking.pdf}}%
+    \put(0.20344574,0.06568419){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{\omega_0}$\end{tabular}}}}%
+    \put(0.09908508,0.28773184){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{\omega_1}$\end{tabular}}}}%
+    \put(0.22861112,0.26330659){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_1}$\end{tabular}}}}%
+    \put(0.33834962,0.16625601){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_2}$\end{tabular}}}}%
+    \put(0,0){\includegraphics[width=\unitlength,page=3]{tracking.pdf}}%
+    \put(0.29744591,0.23221995){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$t_1$\end{tabular}}}}%
+    \put(0.23474059,0.18484979){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$t_0$\end{tabular}}}}%
+    \put(0,0){\includegraphics[width=\unitlength,page=4]{tracking.pdf}}%
+    \put(0.69271413,0.1175451){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_0}$\end{tabular}}}}%
+    \put(0,0){\includegraphics[width=\unitlength,page=5]{tracking.pdf}}%
+    \put(0.66676587,0.07087984){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{\omega_0}$\end{tabular}}}}%
+    \put(0.56240515,0.29292747){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{\omega_1}$\end{tabular}}}}%
+    \put(0.69193116,0.26850221){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_1}$\end{tabular}}}}%
+    \put(0.82923069,0.17006108){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_2}$\end{tabular}}}}%
+    \put(0.75419181,0.24408339){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$t_1$\end{tabular}}}}%
+    \put(0.68811668,0.17329753){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$t_0$\end{tabular}}}}%
+    \put(0,0){\includegraphics[width=\unitlength,page=6]{tracking.pdf}}%
+    \put(0.74320045,0.19443365){\color[rgb]{0,0,0}\transparent{0.94}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$\bm{x_d}$\end{tabular}}}}%
+  \end{picture}%
+\endgroup%
diff --git a/img/tracking.svg b/img/tracking.svg
new file mode 100644
index 0000000..7b4b70d
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+++ b/img/tracking.svg
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+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   xmlns:dc="http://purl.org/dc/elements/1.1/"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   width="210mm"
+   height="297mm"
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diff --git a/main.tex b/main.tex
index d08567f..580a1cd 100644
--- a/main.tex
+++ b/main.tex
@@ -59,6 +59,8 @@
     \import{./img/}{#1.pdf_tex}
 }
 
+\usepackage{bm}
+
 % presentation metadata
 \title{Rendering Participating Media}
 \subtitle{Data Visualization Seminar}
@@ -116,6 +118,15 @@
   \end{figure}
 \end{frame}
 
+
+\begin{frame}{Motivation}
+  \begin{figure}
+      \centering
+      \includegraphics[width=\textwidth]{img/ahsoka-smoke.png}
+      \label{fig:teaser}
+  \end{figure}
+\end{frame}
+
 \begin{frame}{Propagation of light in a medium}
     \begin{figure}[ht]
         \centering
@@ -218,7 +229,7 @@ $$\sigma_a(\boldsymbol{x})L_e(\bx, \bomega)$$
         \item Loses $\sigma_a L(x, \omega)$ due to absorption
         \item Loses $\sigma_s L(x, \omega)$ due to out-scattering
         \item Gains $\sigma_s L_i(x, \omega)$ due to in-scattering
-        \item Gains $\sigma_a L(x, \omega)$ due to emission
+        \item Gains $\sigma_a L_e(x, \omega)$ due to emission
     \end{itemize}
 \end{frame}
 
@@ -389,22 +400,26 @@ $$ T(t) = e^{-\tau(t)} = e^{-\int_0^t \sigma_t(\bx-s\bomega)ds} $$
 \end{itemize}
 \end{frame}
 
-\begin{frame}{Ray Marching}
-\begin{columns}
-    \column{.49\textwidth}
-    $\int_0^t \sigma_t(\bx-s\bomega)ds = \tau(t)$\\
-        \textit{"optical thickness" $\tau$}
-    \column{.49\textwidth}
-    $T(\bx, \by) = e^{-\tau(t)}$
-\end{columns}
+\begin{frame}{In homogeneous volumes}
+    $$T(t) = e^{-\int_0^t \sigma_t(\bx-s\bomega)ds} = e^{-\int_0^t \sigma_t ds} 
+    = e^{-\sigma_t t}$$
 \end{frame}
 
 
-\begin{frame}{Delta Tracking}
+\begin{frame}{Regular Tracking}{In homogeneous volumes}
+\begin{figure}[ht]
+    \centering
+    \def\svgwidth{\columnwidth}
+    \import{./img/}{tracking.pdf_tex}
+\end{figure}
 \end{frame}
 
-
-\begin{frame}{Transmittance Estimation}
+\begin{frame}{Transmittance Estimation}{Ray Marching}
+\begin{figure}[ht]
+    \centering
+    \def\svgwidth{0.6\columnwidth}
+    \import{./img/}{ray-marching.pdf_tex}
+\end{figure}
 \end{frame}
 
 \begin{frame}{Acceleration Data Structures}
-- 
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