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dimensions for cropping are not good with new versions of LaTeX
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documents/intro_slides.tex

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\documentclass[compress]{beamer}
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\usepackage[latin1]{inputenc}
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\usepackage{alltt}
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\newdimen\topcrop
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\topcrop=8cm %alternatively 10cm
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\newdimen\topcropBezier
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\topcropBezier=16cm %alternatively 19cm
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\setbeamertemplate{footline}[frame number]
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\title{Smooth trajectories in straight line mazes}
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\date{April 2023}
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\mode<presentation>
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\begin{document}
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\maketitle
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\begin{frame}
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\frametitle{The game}
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\end{frame}
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\begin{frame}
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\frametitle{Example}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{empty_spiral.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{empty_spiral.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Cell decomposition}
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\end{frame}
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\begin{frame}
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\frametitle{Intermediate position for vertical cell decomposition (1)}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{partial_spiral.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{partial_spiral.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Intermediate position for vertical cell decomposition (2)}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{partial_spiral2.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{partial_spiral2.pdf}
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\end{frame}
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\begin{frame}
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\end{frame}
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\begin{frame}
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\frametitle{Vertical cell decomposition example}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{cells_spiral.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{cells_spiral.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Cell assumptions}
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\end{frame}
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\begin{frame}
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\frametitle{Two examples of elementary safe paths}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{spiral_safe2.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{spiral_safe2.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Making a broken line path between points}
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\begin{frame}
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\frametitle{broken line safe path between points}
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\label{broken-line}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{spiral_bline.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{spiral_bline.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Making corners smooth}
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\item Straight edge tips of this drawing are control points
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\item The curve is inside the triangle
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\end{itemize}
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\includegraphics[trim={0 6cm 0 19cm}, clip, width=\textwidth]{bezier_example.pdf}
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\includegraphics[trim={0 6cm 0 \topcropBezier}, clip, width=\textwidth]{bezier_example.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Plotting the Bezier curve}
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\item Control points for the two subcurves are given by the new point,
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the initial starting and end points, and the solid green straight edge tip
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\end{itemize}
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\includegraphics[trim={0 6cm 0 19cm}, clip, width=\textwidth]{bezier_example2.pdf}
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\includegraphics[trim={0 6cm 0 \topcropBezier}, clip, width=\textwidth]{bezier_example2.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Using Bezier curves for smoothing}
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\begin{frame}
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\frametitle{Final trajectories}
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\label{final-spiral-with-br}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{smooth_spiral.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{smooth_spiral.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Final trajectories}
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\label{final-spiral}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{smooth_spiral2.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{smooth_spiral2.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Final trajectories: repaired curve example}
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\label{final-polygon}
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\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{polygon.pdf}
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\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{polygon.pdf}
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\end{frame}
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\begin{frame}
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\frametitle{Proof tools}

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