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1 | 1 | \documentclass[compress]{beamer}
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2 | 2 | \usepackage[latin1]{inputenc}
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3 | 3 | \usepackage{alltt}
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| 4 | +\newdimen\topcrop |
| 5 | +\topcrop=8cm %alternatively 10cm |
| 6 | +\newdimen\topcropBezier |
| 7 | +\topcropBezier=16cm %alternatively 19cm |
4 | 8 |
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5 | 9 | \setbeamertemplate{footline}[frame number]
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6 | 10 | \title{Smooth trajectories in straight line mazes}
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9 | 13 | \date{April 2023}
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10 | 14 | \mode<presentation>
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11 | 15 | \begin{document}
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| 16 | + |
12 | 17 | \maketitle
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13 | 18 | \begin{frame}
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14 | 19 | \frametitle{The game}
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31 | 36 | \end{frame}
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32 | 37 | \begin{frame}
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33 | 38 | \frametitle{Example}
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34 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{empty_spiral.pdf} |
| 39 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{empty_spiral.pdf} |
35 | 40 | \end{frame}
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36 | 41 | \begin{frame}
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37 | 42 | \frametitle{Cell decomposition}
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61 | 66 | \end{frame}
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62 | 67 | \begin{frame}
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63 | 68 | \frametitle{Intermediate position for vertical cell decomposition (1)}
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64 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{partial_spiral.pdf} |
| 69 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{partial_spiral.pdf} |
65 | 70 |
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66 | 71 | \end{frame}
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67 | 72 | \begin{frame}
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68 | 73 | \frametitle{Intermediate position for vertical cell decomposition (2)}
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69 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{partial_spiral2.pdf} |
| 74 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{partial_spiral2.pdf} |
70 | 75 |
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71 | 76 | \end{frame}
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72 | 77 | \begin{frame}
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85 | 90 | \end{frame}
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86 | 91 | \begin{frame}
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87 | 92 | \frametitle{Vertical cell decomposition example}
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88 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{cells_spiral.pdf} |
| 93 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{cells_spiral.pdf} |
89 | 94 | \end{frame}
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90 | 95 | \begin{frame}
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91 | 96 | \frametitle{Cell assumptions}
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113 | 118 | \end{frame}
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114 | 119 | \begin{frame}
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115 | 120 | \frametitle{Two examples of elementary safe paths}
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116 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{spiral_safe2.pdf} |
| 121 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{spiral_safe2.pdf} |
117 | 122 | \end{frame}
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118 | 123 | \begin{frame}
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119 | 124 | \frametitle{Making a broken line path between points}
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131 | 136 | \begin{frame}
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132 | 137 | \frametitle{broken line safe path between points}
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133 | 138 | \label{broken-line}
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134 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{spiral_bline.pdf} |
| 139 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{spiral_bline.pdf} |
135 | 140 | \end{frame}
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136 | 141 | \begin{frame}
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137 | 142 | \frametitle{Making corners smooth}
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164 | 169 | \item Straight edge tips of this drawing are control points
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165 | 170 | \item The curve is inside the triangle
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166 | 171 | \end{itemize}
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167 |
| -\includegraphics[trim={0 6cm 0 19cm}, clip, width=\textwidth]{bezier_example.pdf} |
| 172 | +\includegraphics[trim={0 6cm 0 \topcropBezier}, clip, width=\textwidth]{bezier_example.pdf} |
168 | 173 | \end{frame}
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169 | 174 | \begin{frame}
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170 | 175 | \frametitle{Plotting the Bezier curve}
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173 | 178 | \item Control points for the two subcurves are given by the new point,
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174 | 179 | the initial starting and end points, and the solid green straight edge tip
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175 | 180 | \end{itemize}
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176 |
| -\includegraphics[trim={0 6cm 0 19cm}, clip, width=\textwidth]{bezier_example2.pdf} |
| 181 | +\includegraphics[trim={0 6cm 0 \topcropBezier}, clip, width=\textwidth]{bezier_example2.pdf} |
177 | 182 | \end{frame}
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178 | 183 | \begin{frame}
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179 | 184 | \frametitle{Using Bezier curves for smoothing}
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231 | 236 | \begin{frame}
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232 | 237 | \frametitle{Final trajectories}
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233 | 238 | \label{final-spiral-with-br}
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234 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{smooth_spiral.pdf} |
| 239 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{smooth_spiral.pdf} |
235 | 240 | \end{frame}
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236 | 241 | \begin{frame}
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237 | 242 | \frametitle{Final trajectories}
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238 | 243 | \label{final-spiral}
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239 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{smooth_spiral2.pdf} |
| 244 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{smooth_spiral2.pdf} |
240 | 245 | \end{frame}
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241 | 246 | \begin{frame}
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242 | 247 | \frametitle{Final trajectories: repaired curve example}
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243 | 248 | \label{final-polygon}
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244 |
| -\includegraphics[trim={0 0 0 10cm}, clip, width=\textwidth]{polygon.pdf} |
| 249 | +\includegraphics[trim={0 0 0 \topcrop}, clip, width=\textwidth]{polygon.pdf} |
245 | 250 | \end{frame}
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246 | 251 | \begin{frame}
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247 | 252 | \frametitle{Proof tools}
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