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Update on Overleaf.

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uxwmp 2023-06-15 14:59:48 +00:00 • committed by node
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presentation/modules/problems.tex
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@ -10,69 +10,11 @@
\item Rendering integral contains the geometry term that is not differentiable
\item The gradiant of the visibility can lead to dirac delta terms which have 0 probability of being sampled correctly [\cite{ACM:diracdelta},\cite{ACM:diffable_raytracing}]
\item Differentiation with respect to certain scene parameters possible but we need to differentiate with respect to any scene parameter
\end{itemize}
\pause
\begin{center}
\begin{minipage}{0.4\linewidth}
\begin{figure}
\centering
\begin{minipage}{0.5\linewidth}
\begin{tikzpicture}[domain=-0.5:2]
\draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);
\draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
\draw[->] (0,-0.7) -- (0,2.2) node[above] {$V(x,\omega)$};
\draw (0,0) -- (1,0) plot coordinates {(0,0) (1,0)}[color=red];
\draw (1,1) -- (2,1) plot coordinates {(1,1) (2,1)}[color=red];
\draw (0,0) node[left] {$0$};
\draw (0,1) node[left] {$1$};
\draw (1,-0.7) node[below] {$\omega_0$};
\end{tikzpicture}
\end{minipage}
\hspace{3mm}
\begin{minipage}{0.4\linewidth}
\caption{Visibility of a point $x$ with respect to $\omega$. Observe the discontinuity at $\omega_0$.}
\label{fig:visibility}
\end{minipage}
\end{figure}
\end{minipage}
% second diagram
\begin{minipage}{0.5\linewidth}
\begin{figure}
\centering
\begin{minipage}{0.5\linewidth}
\begin{tikzpicture}[domain=-0.5:2]
\draw[very thin,color=gray] (-0.1,-0.6) grid (2.1,2.1);
\draw[->] (-0.2,-0.5) -- (2.2,-0.5) node[right] {$\omega$};
\draw[->] (0,-0.7) -- (0,2.2) node[above] {$\frac{\partial}{\partial\omega}V(x,\omega)$};
\draw (0,0) -- (2,0) plot coordinates {(0,0) (2,0)}[color=red];
\draw (0,0) node[left] {$0$};
\draw (0,1) node[left] {$1$};
\draw (0,2) node[left] {$\infty$};
\draw (1,2) node[color=red] {$\bullet$};
\draw (1,-0.7) node[below] {$\omega_0$};
\end{tikzpicture}
\end{minipage}
\begin{minipage}{0.4\linewidth}
\caption{Differentiation of the left graph with respect to $\omega$. Observe the discontinuity at $\omega_0$ in the left graph leading to a dirac delta spike at $\omega_0$ in the differentiation.}
\label{fig:dirac-delta-spike}
\end{minipage}
\end{figure}
\end{minipage}
\end{center}
\end{itemize}
\end{frame}
\begin{frame}{Geometry term}
\centering
\begin{minipage}{0.4\linewidth}
\includegraphics[width=\linewidth]{presentation/img/blockers.png}
\end{minipage}
\hspace{15mm}
\begin{minipage}{0.4\linewidth}
\includegraphics[width=\linewidth]{presentation/img/blockers_diff.png}
\end{minipage}
\input{presentation/diagrams/diagramm_occlusion.tex}
\end{frame}
\subsection{Former methods}
\begin{frame}{Former methods}